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Mathematics |
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MATH 6250 - Differential Topology
Topics may include: Differentiable manifolds and smooth maps, tangent bundles, immersions, embeddings, submanifolds, transversality, Sard’s Theorem, intersection theory, and additional topics.
Prerequisites/Corequisites: Prerequisite: MATH 5220
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6300 - Abstract Algebra I
A general study of groups, rings, and modules. A specific study of finite groups, polynomial rings, and Euclidean domains.
Prerequisites/Corequisites: Prerequisite: MATH 5300
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6310 - Abstract Algebra II
A continuation of MATH 6300. Modules, structure theory of modules over principal ideal domains, applications to finitely generated abelian groups, rational and Jordan canonical forms of a linear transformation, bilinear and quadratic forms.
Prerequisites/Corequisites: Prerequisite: MATH 6300
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6370 - Numerical Linear Algebra
The analysis and use of numerical algorithms for solving problems from linear algebra, including matrix norms, singular value decompositions, Gaussian elimination, least squares methods, eigenvalues and iterative methods.
Prerequisites/Corequisites: Prerequisites: MATH 5070 and either (MATH 5100 or MATH 5300).
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6390 - Studies in Algebra
Advanced work organized around topics related to the field of study indicated in the above title.
Credits: 3 hours
Notes: May be repeated for credit. Open to graduate students only.
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MATH 6400 - Graph Theory I
This course and MATH 6410 cover the following topics: Fundamental concepts; eulerian graphs; adjacency and incidence matrices; trees; planar graphs; graph embeddings; connectivity; hamiltonian graphs; matchings; factorization; graphs and groups; Cayley color graphs; line graphs; the Reconstruction Problem; spectra of graphs; graph and map colorings; extremal graph theory; Ramsey theory.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 4 hours
Notes: Open to graduate students only.
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MATH 6410 - Graph Theory II
Continuation of MATH 6400.
Prerequisites/Corequisites: Prerequisite: MATH 6400
Credits: 4 hours
Notes: Open to graduate students only.
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MATH 6440 - Graphs, Groups, and Surfaces
Study of the interaction of graphs, groups, and surfaces. Topics covered include map-coloring problems, symmetrical maps, automorphism groups of graphs, Cayley graphs of groups, genus of graphs, genus of groups, generation of block designs, and applications to church bell ringing.
Prerequisites/Corequisites: Prerequisite: Instructor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6450 - Studies in Combinatorics
Advanced work organized around topics related to the field of study indicated in the above title.
Prerequisites/Corequisites: Prerequisite: Instructor approval.
Credits: 3 hours
Notes: May be repeated for credit. Open to graduate students only.
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MATH 6460 - Combinatorics
This course is divided into two parts. The first part gives a gentle introduction to the subject and covers basic counting techniques (including the inclusion-exclusion principle), recurrence relations and generating functions, and discrete probability with the basic probabilistic method. The second part deals with more challenging topics such as combinatorial designs (including Steiner systems), posets (including the Möbius function), enumeration under group action, and extremal set theory (including Sperner’s and intersecting families, and the Littlewood-Offord problem).
Credits: 3 hours
Restrictions Restricted to master’s and doctoral students in computational mathematics, mathematics education, collegiate math education, or mathematics.
Notes: Open to Graduate students only.
When Offered: Spring every other year.
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MATH 6490 - Studies in Geometry
Advanced work organized around topics related to the field of study indicated in the above title.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: May be repeated for credit. Open to graduate students only.
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MATH 6501 - Teaching of Secondary School Mathematics
This course considers curriculum issues and trends in secondary school mathematics focusing on methods and materials for teaching mathematics effectively to secondary school students. This course will provide students with field experiences in local schools to provide them opportunities to enact the methods and materials that they learn in the classroom.
Prerequisites/Corequisites: Prerequisites: Advisor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6510 - Studies in Teaching Elementary School Mathematics
This is an advanced methods class devoted to analysis of current theoretical and research-based perspectives on mathematics teaching and learning and their implications for instructional practice and evaluation of student performance at the elementary school level. Explicit attention is given to the impact of technology on the teaching/learning process.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: This course is primarily for teachers and ordinarily will not apply towards the Master of Arts in Mathematics. Open to graduate students only.
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MATH 6530 - Studies in Teaching Secondary School Mathematics
This is an advanced methods class devoted to analysis of current theoretical and research-based perspectives on mathematics teaching and learning and their implications for instructional practice and evaluation of student performance at the secondary school level. Explicit attention is given to the impact of technology on the teaching/learning process.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: This course is primarily for teachers and ordinarily will not apply towards the Master of Arts in Mathematics. Open to graduate students only.
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MATH 6540 - Secondary School Mathematics Curriculum Studies
Participants in this course examine curricular issues and trends in secondary school mathematics and analyze recent experimental and commercial curriculum materials in one of four strands of mathematics: algebra, geometry, probability and statistics, or discrete mathematics.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: This course is primarily for teachers and ordinarily will not apply towards the Master of Arts in Mathematics. May be repeated for credit with the approval of the student’s advisor. Open to graduate students only.
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MATH 6550 - Issues and Trends in Secondary School Mathematics
This course examines current policy issues and curricular and instructional trends in secondary school mathematics and related research studies. It is designed to provide a transition to advanced graduate work in mathematics education.
Prerequisites/Corequisites: Prerequisites: Completion of at least 21 graduate credit hours, including either (MATH 6530 or MATH 6520) and MATH 6540, or advisor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6560 - Teaching of College Mathematics
In this course consideration is given to curricular problems and trends in post-high school mathematics; research on specific problems of teaching mathematics effectively to college students will be emphasized.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 2 hours
Notes: Open to graduate students only.
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MATH 6570 - Issues and Trends in Mathematics Education
This course focuses on curricular and instructional issues and trends in K-14 mathematics education, including an examination of major historical themes that have shaped mathematics policy and practice at these levels.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6580 - Psychology of Learning Mathematics
This course focuses on theories of mathematical thinking and knowing and on an examination of major research paradigms and research findings on mathematical learning in children and adults and their implications for instruction.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6590 - Research in Mathematics Education
This course focuses on research issues, methodologies, and trends within mathematics education along with techniques for critical analysis of research. Students are expected to design and present an individual research study.
Prerequisites/Corequisites: Prerequisite: Advisor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6700 - Real Analysis I
The first of a two semester sequence in real analysis. Topics covered in the two semesters will include topology and continuous functions, Lebesgue and general measure and integration, differentiation and the Radon-Nikodym theorem. Hilbert spaces, Banach spaces, and product spaces and Fubini’s theorem.
Prerequisites/Corequisites: Prerequisites: MATH 5220 and MATH 5710.
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6710 - Real Analysis II
The second of a two semester sequence in real analysis. Topics covered in the two semesters will include topology and continuous functions; Lebesgue and general measure and integration, differentiation and the Radon-Nikodym theorem; Hilbert spaces, Banach spaces, and product spaces and Fubini’s theorem.
Prerequisites/Corequisites: Prerequisite: MATH 6700
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6760 - Complex Analysis
Topics include: Cauchy Theory, series expansion, power series, types of singularities, calculus of residues.
Prerequisites/Corequisites: Prerequisite: MATH 5710
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6780 - Introduction to Functional Analysis
Metric spaces; category; compactness; Banach spaces; Hahn-Banach theorem; completely continuous operators; Hilbert spaces; self-adjoint operators; elementary spectral theory.
Prerequisites/Corequisites: Prerequisite: MATH 6710
Credits: 3 hours
Notes: Open to graduate students only.
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MATH 6880 - Research Tools in the Mathematical Sciences
This course consists of various computer applications and computer network activities that are commonly used in mathematics or mathematics education research, including mathematical word processing, computer algebra systems, literature searches, qualitative data analysis tools, and the use of Internet resources. Enrollment is limited to students in a graduate degree program in mathematics or mathematics education. Students must satisfactorily complete an approved number of modules per credit hour selected. If the course is repeated, different modules must be completed. Certain departmental degree programs may require the completion of specific modules.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: May be repeated for credit. Open to graduate students only.
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MATH 6900 - Seminar in Applied Mathematics
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6920 - Seminar in Topology
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6930 - Seminar in Algebra
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6940 - Seminar in Graph Theory
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6950 - Seminar in Mathematics Education
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6970 - Seminar in Analysis
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 3 hours
Notes: Open to graduate students only.
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MATH 6990 - Reading and Research
May be repeated for credit.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 6 hours
Notes: Open to graduate students only.
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MATH 7000 - Master’s Thesis
Please refer to the Graduate College section for the course description of GRAD 7000.
Prerequisites/Corequisites: Prerequisite: Department and Graduate College approval; and approved application.
Credits: 1 to 6 hours
Restrictions Restricted to master’s in Mathematics, and Applied and Computational Mathematics.
Notes: May be repeated for credit. Graded on a Credit/No Credit basis. Open to graduate students only.
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MATH 7120 - Professional Field Experience
Please refer to the Graduate College section for course descriptions.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 2 to 12 hours
Notes: May be repeated for credit. Graded on a Credit/No Credit basis. Open to graduate students only.
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MATH 7300 - Doctoral Dissertation
The Doctoral Dissertation is required in all doctoral programs and is completed under the supervision of a dissertation committee. Prior to the first registration in 7300, Doctoral Dissertation, a Permission to Elect form (available at http://wmich.edu/grad/forms) must be completed and approved by the Dissertation Specialist in the Graduate College so that the student is informed about the regulations pertaining to the preparation and publication of the manuscript and to the requirements for research involving regulated subjects and hazardous materials, and to ensure the student is in good standing. Doctoral dissertations involving research with protected or regulated subjects must include documentation indicating compliance with federal, state, and University requirements for the protection of human/animal subjects or appropriate use of genetic or radioactive materials and chemical hazards. Written approval from the board/committee/official must be included as an appendix to the dissertation. The use of Guidelines for the Preparation of Theses, Projects, and Dissertations is required. This publication is available for downloading at wmich.edu/grad/current-students/. A doctoral dissertation varies in credit from a minimum of 12 credit hours to a maximum of 24 credit hours. The hours required in a program of study are determined by the student’s department; a department may require all students within the program to register for a specific, common total of hours between 12 and 24, or a program may require different students within the program to register for a variety of total hours between 12 and 24. The course 7300, Doctoral Dissertation, may be registered for in increments of one or more hours. Following a student’s first enrollment in 7300, the student must have continuous enrollment in 7300 until all dissertation requirements are completed satisfactorily and approved by the appropriate bodies. A student unable to complete the dissertation within the program-stipulated hours will be required to continue to enroll in 7300; however, only the program-stipulated hours for 7300 will count toward meeting the program requirements for the doctoral degree. For students not enrolled in Summer I and Summer II sessions, pre-enrollment in the subsequent Fall semester is necessary for access to library resources during Summer I and Summer II. Continuous enrollment is defined as enrollment in all Fall and Spring semesters from the initial enrollment to the semester in which the student graduates. If the student will graduate in Summer I or Summer II, the student must be enrolled in that session. The dissertation is graded on a Credit/No Credit basis.
Prerequisites/Corequisites: Prerequisite: Department and Graduate College approval; approved application.
Credits: 1 to 15 hours
Notes: May be repeated for credit. Graded on a Credit/No Credit basis. Open to graduate students only.
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MATH 7350 - Graduate Research
Please refer to the Graduate College section for course descriptions.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 2 to 10 hours
Notes: May be repeated for credit. Graded on a Credit/No Credit basis. Open to graduate students only.
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Mechanical Engineering |
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ME 5200 - Orthopaedic Biomechanics
Current methods for analysis of biomechanical systems that include bone, tendon, ligament, cartilage, and other soft tissue. Mechanics that govern biomechanical systems including beam theory, anisotropic materials, viscoelasticity, and contact. Also prosthetics, orthotics, and other medical devices.
Prerequisites/Corequisites: Prerequisite: ME 3650 or AE 4630, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
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ME 5300 - Theoretical and Computational Fluid Mechanics
The theory and numerical implementation of ideal flow, viscous effects, and exact solutions of Navier-Stokes equations. Special emphasis will be on comparison of analytical and computational methods applicable to one-dimensional and two-dimensional fluid flows. Familiarity with a scientific computer programming language is required.
Prerequisites/Corequisites: Prerequisites: AE 3710 or ME 3560, with a grade of “B” or better; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3-0)
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ME 5350 - Applied Spectroscopy
Fundamentals of spectroscopy including rotational, vibrational and electronic transitions of molecular species, absorption and fluorescence spectra, lineshape profiles and broadening mechanisms. Description of spectroscopic techniques and their application for the measurement of relevant quantities such as concentration, velocity and temperature in practical systems, including internal combustion engines. Experimental hardware used for spectroscopic measurements.
Prerequisites/Corequisites: Prerequisite: ME 3350 with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to seniors or graduate students.
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ME 5360 - Experimental Methods in Fluid Mechanics
This course covers basic characteristics of turbulence, governing equations, and random data, probability and statistics related to turbulence, and experimental methods in fluid flow. Basics of Hot-Wire Anemometry, Laser Doppler Velocimetry, and Particle Image Velocimetry will be covered in detail. Experiments will be conducted to show the basics of these techniques.
Prerequisites/Corequisites: Prerequisites: ME 3350 and (ME 3560 or AE 3610), with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
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ME 5390 - Advanced Thermal Design
Theory and practical thermal system design using advanced computer-aided design tools with emphasis on modeling and optimization of modern thermal elements.
Prerequisites/Corequisites: Prerequisite: ME 4310 with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to seniors or graduate students.
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ME 5410 - Continuous System Modeling and Simulation
Principles and methods associated with simulating dynamic systems in the mechanical and aerospace engineering disciplines. Linear and non-linear systems. Time and frequency domain analyses. Brief introduction to real-time simulation. Extensive use of current simulation software.
Prerequisites/Corequisites: Prerequisite: ME 3600 with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3-0)
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ME 5430 - Mechanical Systems Control
Classical and modern control analysis and design methods for mechanical and aerospace systems; transfer function vs. state-space description, single-input-single-output (SISO) vs. multi-input-multi-output (MIMO) system, linear vs. nonlinear system, linearization, classical control design method, state-space design method, emphasis on ground and space vehicle dynamics and control problems, extensive use of commercial software package.
Prerequisites/Corequisites: Prerequisite: ME 3600 with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
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ME 5450 - Computational Fluid Dynamics I
Basics of Computational Fluid Dynamics (CFD) including classification of partial differential equations, finite difference formulations, parabolic partial differential equation, stability analysis, elliptic equations, hyperbolic equations, scalar representation of the Navier-Stokes equations and grid generation. Familiarity with a scientific computer programming language is required.
Prerequisites/Corequisites: Prerequisites: AE 3710 or ME 3560, with a grade of “B” or better; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5500 - Modern Engineered Materials
Advanced course in both metallic and non-metallic engineering materials, including electronic and magnetic materials and biomaterials. Mechanical, physical and biocompatibility properties will be examined with relationship to materials composition, structure, and processing. Failure mechanisms and prevention will be examined. Open ended projects will be assigned.
Prerequisites/Corequisites: Prerequisites: (ME 2500 or AE 2500) and ECE 2100, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5530 - Advanced Product Design
An engineering design project from concept to adoption. Static and dynamic analysis. Mechanical systems design and layout.
Prerequisites/Corequisites: Prerequisites: ME 3600 and ME 4530, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5550 - Intermediate Dynamics
Three dimensional kinematics and dynamics of rigid bodies; equations of motion; Lagrange’s equations; work and energy; impulse and momentum; virtual work; stability; computer simulation; introduction to vibrations.
Prerequisites/Corequisites: Prerequisites: ME 2580 and MATH 3740, with a grade of “B” or better on all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5580 - Mechanical Vibrations
A study of the oscillatory motion of physical systems with emphasis on the effects of vibrations on the performance and safety of mechanical systems.
Prerequisites/Corequisites: Prerequisites: ME 2580 and MATH 3740, with a grade of “B” or better on all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5600 - Engineering Analysis
Application of vector analysis and differential equations to the solution of complex engineering problems.
Prerequisites/Corequisites: Prerequisite: ME 3600 or equivalent, with a grade of “B” or better; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3-0)
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ME 5610 - Finite Element Method
Development of finite element techniques for solution of one-, two-, and three-dimensional problems in heat transfer, fluid flow, structures and elasticity.
Prerequisites/Corequisites: Prerequisites: ME 2570, ME 3560, ME 4310, and MATH 3740 or equivalents, with a grade of “B” or better on all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3-0)
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ME 5620 - Application of Numerical Methods in Engineering
Finite difference methods for initial value and boundary value problems; 2D finite differencing, boundary element methods applications to differential equations of heat transfer, fluid flow, and solid mechanics.
Prerequisites/Corequisites: Prerequisites: MATH 3740 and ME 3600, with a grade of “B” or better on all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3-0)
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ME 5640 - Engineering Noise Control
Introduction to basic concepts of noise control, nature of sound and its effect on our environment. Indoor and outdoor sound propagation. Noise standards and measurements. Case studies of real-world implementation of noise control engineering. Laboratory experiments.
Prerequisites/Corequisites: Prerequisites: ME 2580 and MATH 3740, with a grade of “B” or better on all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (2 - 3)
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ME 5690 - Principles of Fatigue and Fracture
Basics of experimental techniques and modeling used in industry to study inelastic deformations, fatigue, and fracture of engineering materials and structures.
Prerequisites/Corequisites: Prerequisite: (ME 3650 or AE 4630) with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Cross-Listed: Cross-listed with CCE 5690. A student may not receive credit for both CCE 5690 and ME 5690.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5710 - Gas Dynamics
Basic equations of compressible flow, isentropic relationships, normal and oblique shocks. Prandtl-Meyer expansion, Fanno Line and Rayleigh Line flow. Applications to nozzles, diffusers, supersonic wind tunnels; and linearized flows and method of characteristics.
Prerequisites/Corequisites: Prerequisites: ME 4310 and ME 4320, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5720 - Advanced Thermodynamics
Conditions of equilibrium, process and thermodynamic engines, the extremum principle, Maxwell relations, stability of thermodynamic systems, phase transitions, chemical thermodynamics, irreversible thermodynamics, and introduction to the statistical thermodynamics.
Prerequisites/Corequisites: Prerequisites: ME 4310 and ME 4320, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5730 - Materials Selection in Design
Material selection for resistance to both load and environment. Design parameters for material selection and various metal systems, corrosion, service failures, and mechanical behavior of engineering alloys at high and low temperatures.
Prerequisites/Corequisites: Prerequisite: ME 2500 with a grade of “B” or better, or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5750 - Tribology-Principles and Applications
Surface chemistry, topographical measurement and description, contact mechanics, wear mechanisms, lubrication and film formation, hydrodynamic theory and application in bearings, application to friction and wear in machine elements.
Prerequisites/Corequisites: Prerequisites: ME 3560 or AE 3610, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Restrictions Restricted to students in Aerospace Engineering and Mechanical Engineering.
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5770 - Fuel Cell and Alternative Energy
The course covers fundamentals of fuel cells, working principles and types; function of main components, basic chemistry and thermodynamics, electrochemistry; alternative fuels and emerging energy technologies; and fuel cell and hydrogen era.
Prerequisites/Corequisites: Prerequisites: (ME 3670 or ME 4320) and ME 3560, with a grade of “B” or better in all prerequisites; or instructor approval.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Lecture Hours - Laboratory Hours: (2 - 3)
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ME 5850 - Mechatronics
A course in fundamentals of motion control, primarily as it is applied to robotics. Students will learn the basics of control systems as applied to multiaxis servo systems. Appropriate time will be devoted to develop a sound basis in the electro-mechanical discipline.
Prerequisites/Corequisites: Prerequisites: ECE 2100, ME 2580 and (ECE 3710 or ME 3600), with a grade of “C” or better in all prerequisites.
Credits: 3 hours
Notes: Open to upper level and graduate students.
Cross-Listed: This course is cross-listed with ECE 5850. A student may not receive credit for both ECE 5850 and ME 5850.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 5950 - Topics in Mechanical Engineering
A specialized course dealing with some particular area of mechanical engineering not included in other course offerings.
Prerequisites/Corequisites: Prerequisite: Department approval.
Credits: 1 to 4 hours
Notes: This course may be repeated for credit with a different topic to a total of six credit hours. Open to upper level and graduate students.
When Offered: Fall, Spring, Summer I
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ME 5990 - Practical Training
Designed for Master’s students who wish to pursue practical training in off-campus activities in industrial and/or other settings. To be eligible, students must be registered in the MAE department, must have completed at least 6 credits towards an advanced degree, must have had less than 6 months of prior industrial work experience in the US, and have approval of their faculty advisor and Graduate Programs Director or Department Chair. A maximum of 3 credits may be approved towards a graduate degree. Students enrolled will be classified as having full time status for the purpose of loan deferments and insurance eligibility.
Prerequisites/Corequisites: Prerequisite: Advisor or Departmental approval.
Credits: 1 to 3 hours
Notes: May be repeated for credit. Open to upper level and graduate students.
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ME 6090 - Combustion
Combustion thermodynamics and chemical kinetics. Heat and mass transfer and fluid mechanics in combustion processes. Flame propagation and detonation. Auto-ignition and source of ignition. Quenching and flammability limits. Combustion in practical systems. Students must complete the prerequisite or have the instructor’s approval.
Prerequisites/Corequisites: Prerequisites: ME 5710 or instructor approval.
Credits: 3 hours
Notes: Open to Graduate students only.
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ME 6300 - Advanced Fluid Dynamics
Modern developments in fluid dynamics of compressible and incompressible fluid flow. Includes kinematics of fluid motion, laminar and turbulent flow in pipes, fluid machinery, and supersonic flow.
Prerequisites/Corequisites: Prerequisites: ME 3560, 4320, and MATH 3740.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6320 - Energy Resources and Conversion
Availability and economic utilization of energy resources. Terrestrial and thermodynamic limitations. Energy conversion applications. Fission and fusion. Applications of solar, water, wind, and geothermal energy.
Prerequisites/Corequisites: Prerequisite: ME 2320 or consent of instructor
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6330 - Advanced Control Systems
Digital controls, analog controls, introduction to modern control, state variable analysis, system simulation techniques, optimal design, parameter sensitivity and stability analysis, robotics control applications.
Prerequisites/Corequisites: Prerequisite: ME 3600.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6350 - Turbulence
The physical nature of turbulence. Dimensional analyses. The basic equations for studying the turbulent transport of momentum and heat and their dynamical significance. Characteristics of turbulent wall- and free-shear layers. Probabilities and statistics related to turbulence and experimental methods in fluid flow.
Prerequisites/Corequisites: Prerequisites: ME 5300 and ME 5600.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6360 - Applied Optics and Optical System Design
Classical and conventional optical methods in use by the engineering and research community. Moire, Speckle and Speckle-shearing interferometry. Holographic interferometry. Photo-elasticity and electronic speckle pattern interferometry. Optics and lasers for research and industrial applications. Digital image processing and optical system design.
Prerequisites/Corequisites: Prerequisite: Consent of instructor.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Cross-Listed: This course is cross-listed with ECE 6360.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6370 - Design Optimization
Elements of design optimization. Defining design variables, cost functions, and constraints. Simplex method for linear problems and numerical methods for nonlinear unconstrained and constrained problems.
Prerequisites/Corequisites: Prerequisite: ME 5620
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6450 - Computational Fluid Dynamics II
Advanced topics in Computational Fluid Dynamics (CFD) including transformation of the equations of fluid motion from physical space to computational space, the Euler equations of gasdynamics, the Parabolized Navier-Stokes equations of gasdynamics, the Navier-Stokes equation of gasdynamics, finite volume methods and turbulent flows.
Prerequisites/Corequisites: Prerequisite: ME 5450
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6500 - Smart Materials
Smart materials revolutionized people’s lives in a wide-range of applications including artificial implants, underwater acoustics, pharmaceutical, aerospace, and many more. They include gel, ceramics, metallic alloys, polymers, and composites. This course will cover a variety of smart materials and their applications, explain the physical concepts that result in their “intelligence” and explore possibilities in design. Students must complete the prerequisite or have the instructor’s approval.
Prerequisites/Corequisites: Prerequisite: ME 5500 or instructor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6510 - Advanced Strength of Materials, Elasticity, and Plasticity
Torsion of non-circular cross sections, shear center, curved beams, beams on elastic foundations, flat plates, and an introduction to two-dimensional elasticity and plasticity.
Prerequisites/Corequisites: Prerequisite: ME 3650 or AE 5100.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6520 - Mechanics of Composite Materials
Micromechanics of two-phase solids. The orthotropic layer: on-axis and off-axis moduli and strength. Hygrothermal effects. Laminate stacking, stiffness and strength. Intralaminar failure modes. Failure criteria. First ply and next ply failure. Interlaminar strength. The layered composite tube.
Prerequisites/Corequisites: Prerequisite: ME 3650 or consent of instructor.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6530 - Fatigue of Engineering Materials
Advanced approach to the problem of fatigue damage and life prediction; cyclic stress-strain response under uniaxial and multiaxial loading, fatigue limit, high and low cycle fatigue; surface integrity and fatigue life improvement. Students must complete the prerequisite or have the instructor’s approval.
Prerequisites/Corequisites: Prerequisite: ME 5690 or instructor approval.
Credits: 3 hours
Notes: Open to Graduate students only.
Cross-Listed: Cross-listed with CCE 6500. A student may not receive credit for both CCE 6500 and ME 6530.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6551 - Precision Machining and Micromanufacturing
The course covers precision machining technologies: conventional (machining, drilling, grinding) tolerances, conventional and non-traditional technologies (EDM, Si machining, DRIE), laser micromachining, micromanufacturing, stereolithography, micro-nano embossing, microinjection molding, etc.
Prerequisites/Corequisites: Prerequisites: ME 5500 or ME 5750 or instructor approval.
Credits: 3 hours
Notes: Open to Graduate students only.
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ME 6555 - Nanofabrication Technology
The course topics include Micro/nano lithography, nanostructured layer deposition, electroforming of nanostructures, electron, ion and x-ray beam lithographies, alternative lithography technologies, carbon nanotubes fabrication, nanowires, characterization of nanostructures. Students must complete the prerequisite or have the instructor’s approval.
Prerequisites/Corequisites: Prerequisites: ME 5500 or ME 5730 or instructor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6610 - Advanced Finite Elements
Implementation of the finite element methods: Mixed formulations. Plate bending. Time dependent problems in solid mechanics and heat transfer. Introduction to nonlinear problems.
Prerequisites/Corequisites: Prerequisite: ME 5610
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6630 - Structural Vibrations
Vibration response of coupled and uncoupled structures. Wave propagation, transmission, and reflection. Effects of internal and external damping, impedance discontinuities and curvature. Four-pole parameter technique for vibration isolation system design. Modal analysis. Sound generation.
Prerequisites/Corequisites: Prerequisite: ME 5550 or ME 5580.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6640 - Acoustics
Principles of acoustics, stressing the physical concepts underlying the derivations, associated assumptions and solutions to the wave equations in bounded and unbounded fluids and solids. Topics include: acoustic wave equations; integral equations; attenuation; acoustics of pipes, ducts, cavities, wave guides and resonators; environmental, architectural, underwater acoustic transducers.
Prerequisites/Corequisites: Prerequisite: ME 5640 or consent of instructor.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6650 - Sound and Structure Interaction
Introduction to acoustic radiation from vibrating infinite and finite plates and the effect of fluid-loading on them. Acoustic transmission through and reflection from single-leaf and double-leaf partitions. Acoustic excitation of elastic plates and coupling between panels and open and enclosed acoustic spaces. Students must complete the prerequisite or have the instructor’s approval.
Prerequisites/Corequisites: Prerequisite: ME 5640 or consent of instructor.
Credits: 3 hours
Notes: Open to Graduate students only.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6690 - Engineering Fracture Mechanics
Fundamentals of the theory of linear elastic fracture mechanics (LEFM), crack-tip opening displacement (CTTOD), J-integral, R-curve, mixed-mode fracture and fracture toughness testing.
Prerequisites/Corequisites: Prerequisite: ME 5690 or consent of instructor.
Credits: 3 hours
Notes: Open to Graduate Students Only.
Cross-Listed: Cross-listed with CCE 6690. A student may not receive credit for both CCE 6690 and ME 6690.
Lecture Hours - Laboratory Hours: (3 - 0)
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ME 6710 - Advanced Heat Transfer I-Conduction Heat Transfer
Fundamental aspects of conductive heat transfer applied to steady state and transient conditions. One-, two-, and three-dimensional conduction problems with exact and approximate solution techniques utilizing the computer are studied.
Prerequisites/Corequisites: Prerequisites: ME 4310 and ME 4320.
Credits: 3 hours
Notes: Open to Graduate Students Only.
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ME 6720 - Advanced Heat Transfer II-Convection and Radiation Heat Transfer
Fundamentals of thermal radiation for black, gray, non-gray, diffuse, and specular surfaces. Gaseous radiation and special applications of thermal radiation including derivation and application of equations of mass, energy, and momentum transfer.
Prerequisites/Corequisites: Prerequisites: ME 4310 and ME 4320.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6730 - Power Plant Design
Theory and application of internal combustion engines, gas turbine power plants, steam turbine power plants, and other prime movers. Emphasis is on application of thermodynamic principles combined with open-ended design problems in power plant applications.
Prerequisites/Corequisites: Prerequisites: ME 4310 and ME 4320.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6740 - Thermoelectric Design
Thermoelectric design covers the fundamental theories, optimal design, applications for thermoelectric generators and coolers. The fundamental theories include the Seebeck effect, Peltier effect, and Thomson relation, optimal design, compatibility factor, and thermal and electrical contact resistances. The applications discuss waste heat recovery, automotive thermal comport, solar thermoelectric generator, electronic thermal control, and medical instruments.
Prerequisites/Corequisites: Prerequisite: ME 4310 or instructor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6750 - Thermoelectric Materials
Thermoelectric Materials covers the fundamental theories for thermoelectric bulk and nanostructured materials. The fundamental theories include physics of electrons and phonons, thermoelectric transport properties such as the Seebeck coefficient, electrical conductivity, and electronic and lattice thermal conductivity. The theoretical model discusses nonparabolic two-band Kane model for electrons and phonons. Nanostructure includes nanocomposites, two-dimensional and one-dimensional nanostructures.
Prerequisites/Corequisites: Prerequisite: ME 5500 or instructor approval.
Credits: 3 hours
Notes: Open to graduate students only.
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ME 6950 - Advanced Topics in Mechanical Engineering: Variable Topics
A specialized course dealing with some particular advanced area of Mechanical Engineering not included in other course offerings.
Prerequisites/Corequisites: Prerequisite: Consent of instructor.
Credits: 1 to 4 hours
Notes: Open to Graduate Students Only. May be repeated for credit with a different topic up to six credits.
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ME 6970 - Problems in Mechanical Engineering
Special problems of individual need or interest under the direction of a member of the graduate faculty. May be elected with approval of department chairperson and faculty member. Application must be submitted and approved prior to the election of the course.
Credits: 1 to 6 hours
Notes: Open to Graduate Students Only. May be repeated up to maximum of six hours.
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ME 6990 - Practical Training
Designed for doctoral students who wish to pursue practical training in off-campus activities in industrial and/or other settings. To be eligible, students must be registered in the MAE department, must have completed at least 6 credits towards an advanced degree, must have had less than 6 months of prior industrial work experience in the US, and have approval of their faculty advisor and Graduate Programs Director or Department Chair. A maximum of 3 credits may be approved towards a graduate degree. Students will be classified as having full-time status for the purpose of loan deferments and insurance eligibility. International students must contact the International Services and Student affairs Office before requesting department approval enroll in this course.
Prerequisites/Corequisites: Prerequisite: Advisor or Departmental approval.
Credits: 1 to 3 hours
Restrictions Open to graduate students only.
Notes: May be repeated for credit.
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ME 7000 - Master’s Thesis
Please refer to The Graduate College section for course descriptions.
Prerequisites/Corequisites: Prerequisite: Approved application from department and Graduate College.
Credits: 1 to 6 hours
Notes: Graded on a Credit/No Credit basis. May be repeated for credit. Open to Graduate students only.
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ME 7100 - Independent Research
Please refer to The Graduate College section for course description.
Prerequisites/Corequisites: Prerequisite: Approved application.
Credits: 2 to 6 hours
Notes: Graded on a Credit/No Credit basis. May be repeated for credit. Open to Graduate students only.
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ME 7300 - Doctoral Dissertation
The Doctoral Dissertation is required in all doctoral programs and is completed under the supervision of a dissertation committee. Prior to the first registration in 7300, Doctoral Dissertation, a Permission to Elect form (available at http://wmich.edu/grad/forms) must be completed and approved by the Dissertation Specialist in the Graduate College so that the student is informed about the regulations pertaining to the preparation and publication of the manuscript and to the requirements for research involving regulated subjects and hazardous materials, and to ensure the student is in good standing. Doctoral dissertations involving research with protected or regulated subjects must include documentation indicating compliance with federal, state, and University requirements for the protection of human/animal subjects or appropriate use of genetic or radioactive materials and chemical hazards. Written approval from the board/committee/official must be included as an appendix to the dissertation. The use of Guidelines for the Preparation of Theses, Projects, and Dissertations is required. This publication is available for downloading at wmich.edu/grad/current-students/. A doctoral dissertation varies in credit from a minimum of 12 credit hours to a maximum of 24 credit hours. The hours required in a program of study are determined by the student’s department; a department may require all students within the program to register for a specific, common total of hours between 12 and 24, or a program may require different students within the program to register for a variety of total hours between 12 and 24. The course 7300, Doctoral Dissertation, may be registered for in increments of one or more hours. Following a student’s first enrollment in 7300, the student must have continuous enrollment in 7300 until all dissertation requirements are completed satisfactorily and approved by the appropriate bodies. A student unable to complete the dissertation within the program-stipulated hours will be required to continue to enroll in 7300; however, only the program-stipulated hours for 7300 will count toward meeting the program requirements for the doctoral degree. For students not enrolled in Summer I and Summer II sessions, pre-enrollment in the subsequent Fall semester is necessary for access to library resources during Summer I and Summer II. Continuous enrollment is defined as enrollment in all Fall and Spring semesters from the initial enrollment to the semester in which the student graduates. If the student will graduate in Summer I or Summer II, the student must be enrolled in that session. The dissertation is graded on a Credit/No Credit basis.
Prerequisites/Corequisites: Prerequisite: Approved application.
Credits: 1 to 15 hours
Notes: Graded on a Credit/No Credit basis. May be repeated for credit. Open to Graduate students only.
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ME 7350 - Graduate Research
This course is used for research projects for doctoral students only. Such projects may be taken more than once by the student.
Prerequisites/Corequisites: Prerequisite: Graduate advisor and instructor approval.
Credits: 3 hours
Restrictions Restricted to MAE doctoral students only.
Notes: Graded on a Credit/No Credit basis. May be repeated for credit. Open to Graduate students only.
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MDSC 6100 - Special Topics in Physician Assistant
This course examines selected topics in medicine. Topics considered will vary from semester to semester.
Prerequisites/Corequisites: Prerequisites: Enrollment in the Physician Assistant program and successful completion of previous MDSC courses.
Credits: 1 to 3 hours
Notes: Open to Graduate students only. May be repeated for credit.
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MDSC 6110 - The Diagnostic Process I
This is the first in a series of three courses designed to develop the knowledge, attitudes and skills requisite for medical history taking, physical examination, clinical problem solving, diagnostic assessment, treatment implementation, and for counseling and educating patients. Learning methods include lecture format, skills performance, clinical decision-making, role-playing, individual research, and case problem solving to integrate and synthesize these competencies.
Prerequisites/Corequisites: Prerequisite: Admission to the Physician Assistant program or departmental permission.
Credits: 2 hours
Notes: Open to Graduate students only.
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MDSC 6120 - The Diagnostic Process II
This is the second in a series of three courses presented sequentially through the pre-clinical year of training. This course provides opportunities for the systematic evaluation of patient problems through history and physical examination, problem exploration, critical thinking and creative problem solving, lectures, demonstrations, group problem solving, practicum sessions, student examination of patients, as well as written and performance evaluation of these modalities, are included among the learning methodologies. Emphasis is placed on interviewing and physical examination, but more so on information gathering and synthesis to accomplish problem oriented patient care. Students will refine skills in eliciting and recording a complete patient database, as well as formulating differential diagnoses.
Prerequisites/Corequisites: Prerequisite: Successful completion of prior semester P.A. course work or departmental permission.
Credits: 2 hours
Notes: Open to Graduate students only.
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MDSC 6130 - The Diagnostic Process III
This is the summative offering in this series of three courses designed to develop competence in both the art and the science of patient evaluation. Students will continue to assess patients utilizing history taking and physical examination skills. Students will master special examinations such as for the pediatric patient, as well as the pregnant patient. Further emphasis will be placed on formulating diagnoses, therapeutic and patient education plans. Students will develop competencies in prevention strategies, and recording and communicating information in a medical team model.
Prerequisites/Corequisites: Prerequisite: Admission to the Physician Assistant program.
Credits: 1 hours
Notes: Open to Graduate students only.
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MDSC 6210 - Medical Pathophysiology I
This is the first in a three part sequence designed to provide the physician assistant student with a foundation for understanding human diseases. Students will review clinically relevant physiology and acquire a working knowledge of pathophysiology. Emphasis will be on the cellular mechanisms of disease and the body’s reactions to them. Topics covered will parallel those in concurrent clinical science courses.
Prerequisites/Corequisites: Prerequisite: Successful completion of prior semester P.A. course work or departmental permission.
Credits: 1 hour
Notes: Open to Graduate students only.
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MDSC 6220 - Medical Pathophysiology II
This is the second in a three part sequence designed to provide the physician assistant student with a foundation for understanding human diseases. Students will review clinically relevant physiology and acquire a working knowledge of pathophysiology. Emphasis will be on the cellular mechanisms of disease and the body’s reactions to them. Topics covered will parallel those in concurrent clinical science courses.
Prerequisites/Corequisites: Prerequisite: Successful completion of prior semester P.A. course work or departmental permission.
Credits: 1 hour
Notes: Open to Graduate students only.
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MDSC 6230 - Medical Pathophysiology III
This is the third in a three part sequence designed to provide the physician assistant student with a foundation for understanding human diseases. Students will review clinically relevant physiology and acquire a working knowledge of pathophysiology. Emphasis will be on the cellular mechanisms of disease and the body’s reactions to them. Topics covered will parallel those in concurrent clinical science courses.
Prerequisites/Corequisites: Prerequisite: Successful completion of prior semester P.A. course work or departmental permission.
Credits: 1 hour
Notes: Open to Graduate students only.
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MDSC 6310 - Integrated Medicine 1
This is the first of a series of nine primary care medicine courses, each of which will introduce students to a different area of primary care medicine. The courses will help students develop the knowledge required for the practice of medicine. The courses will cover clinical topics using a systems approach. Within each system, a lifespan approach will be used ranging from the pediatric patient through the geriatric patient. Each topic will be examined using the integration of pathophysiology, clinical diagnostic testing, diagnosis, treatment, including nutritional issues and available alternative medicine options. Students will also learn the knowledge, skills and attitudes required for counseling patients concerning clinical problems and educating patients in wellness and disease management and prevention. The integrated medicine course will form the basis for clinical evaluation, diagnosis, management, and appropriate referral when necessary, of various health and wellness processes throughout a person’s life.
Prerequisites/Corequisites: Prerequisite: Admission to the Physician Assistant program.
Credits: 2 hours
Notes: Open to Graduate students only.
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