**ME 5400 - Numerical Methods for Mechanical Engineering**

Michael A. Latcha, PhD

416 EC, (248) 370-2203

latcha@oakland.edu

Office Hours: 6:30 pm - 7:30 pm Tu Th, or by appointment

**ME 5400: Numerical Methods for Mechanical Engineering (4)**

The course introduces graduate mechanical engineering students to a variety of basic numerical analysis methods that can be used to solve mechanical engineering problems. The emphasis is on applications of these techniques using a mathematical software package such as Matlab. Examples will be drawn from a variety of mechanical engineering problems, including heat transfer, vibrations, dynamics, fluid mechanics, etc. Programming projects will be assigned.

*Numerical Methods for Engineers, 7th Edition*by Steven C. Chapra and Raymond P. Canale, McGraw-Hill, 2014, ISBN: 007339792X*A Guide to Microsoft Excel 2013 for Scientists and Engineers, 1st Edition*by Bernard Liengme, Academic Press, 2015, ISBN: 9780128028179

- VBA for Excel (Macros)
- VBA for Microsoft Excel
- Excel VBA Basic Tutorial Series
- Excel/VBA Color Index reference

- First class - course procedures (9-7-2017)
- Introduction - Error analysis and the Taylor Expansion
- Error Analysis (9-12-2017)
- Roots of Equations
- Bracketing Methods - Bisection and False-Position (9-14-2017)
- Open Methods - Fixed-Point Iteration, Newton-Rapheson, Secant, Modified Secant (9-19-2017)
- Polynominals - Müller and Bairstow methods (9-21-2017)
- Homework #1 - due 10-3-2017
- Linear Algebraic Equations
- Gauss Elimination - Gauss elimination (9-26-2017)
- Decomposition and Matrix Inversion - Gauss and Crout LU decomposition (9-28-2017)
- Special Matrices - Thomas and Cholesky decomposition, Gauss-Seidel (10-3-2017)
- Homework #2 - due 10-12-2017
- Optimization
- One-Dimensional Unconstrained Optimization - Golden Section, Quadratic Interpolation, Newton's Method (10-5-2017)
- Multi-Dimensional Unconstrained Optimization - Random Search (10-10-2017)
- Constrained Optimization - Linear Programming (10-12-2017)
- Homework #3 - due 10-26-2017
- More on linear programming and the Simplex method:
- Curve Fitting
- Polynomial Regression (10-17-2017)
- Interpolation - Newton and Lagrange methods (10-19-2017)
- Interpolation - Spline methods (10-24-2017)
- Fourier Approximation - (10-26-2017)
- Homework #4
- Numerical Integration and Differentiation
- Newton-Cotes Integration Formulas (10-31-2017)
- Integration of Equations, Gauss Quadrature (11-2-2017)
- Numerical Differentation (11-7-2017)
- Homework #5
- Ordinary Differential Equations
- ODE - Runge-Kutta Methods (11-9-2017)
- ODE - Stiffness and MultiStep Methods (11-14-2017)
- ODE - Boundary Value and Eigenvalue Problems (11-16-2017)
- Homework #6
- Partial Differential Equations
- PDE - Finite Difference: Elliptic Equations (11-21-2017)
- PDE - Finite Difference: Parabolic Equations (11-28-2017)
- PDE - Finite Difference: Finite-Element Method (11-30-2017)

The course grade will be based on six homework assignments (66%) and a final project (34%). Homework and projects will be submitted electronically via email on or before the due date and will consist of two files, an Excel file in which the numerical work is performed and a Word or PDF file containing a report that briefly describes the numerical techniques used, the numerical results (tables of values and/or graphs) for each problem in the assignment or project, and a discussion of the numerical technique and its performance observed in the solution of the assignment or project (more details and example). Both the accuracy of the solutions and the quality of the report will be evaluated; the grade for the assignment or project will be the average of the two evaluations. All homework assignments are due at the beginning of class on the due date; no homework assignments will be accepted late.

All email submissions must use this format for the subject line: *ME5400 HW1 LastName*

Final projects are due on or before December 12, 2017 by 7 pm.

No final projects will be accepted late.

Each student in the course is expected to fill out an online course evaluation; directions will be emailed to you towards the end of the semester.

Students are expected to read, understand and comply with the Academic Conduct Policy of Oakland University, found in the schedule of Classes and in the Undergraduate Catalog. Suspected violations will be taken before the Academic Conduct Committee. Students found guilty of academic misconduct in the course will receive a grade of 0.0 in addition to any penalties imposed by the Academic Conduct Committee.

The University add/drop policy will be explicitly followed. It is the student's responsibility to be aware of the University deadline dates for dropping the course.

Students with disabilities who may require special considerations should make an appointment with campus Disability Support Services. Students should also bring their needs to the attention of the instructor as soon as possible.