# ME 565 Advanced Engineering Mathematics I

### Catalog Description

ME 565 Advanced Engineering Mathematical Analysis I (3). Prerequisites: ENGR 201, ENGR 205, or equivalents. Formulation and solution of mathematical models for engineering problems leading to systems of ordinary and partial differential equations. The course emphasizes transform solution methods and linear algebra concepts, including real and complex-domain eigenvalue problem solutions.

### Prerequisites by Topic

- Multivariate calculus
- Introduction to ordinary differential equations

### Textbook

E. Kreyszig, Advanced Engineering Mathematics, 9th edition, Wiley, 2006.

### Coordinator

R.D. Bradshaw, Associate Professor of Mechanical Engineering.

### Course Learning Outcomes

This course provides senior undergraduate and graduate mechanical engineering students with the applied mathematics background necessary to model a wide range of physical phenomena. It emphasizes the formulation and solution of mathematical models for engineering problems resulting in systems of ordinary differential equations and partial differential equations, as well as transform solution techniques and linear algebra.

### Topics Covered

- Overview of the formulation and solution of mathematical models for engineering applications (1 class)
- Linear and matrix algebra, solutions of linear algebraic equations, eigenvalue problems (6 classes)
- Review of solution methods for 1st, 2nd and higher order ordinary differential equations (7 classes)
- Solution of systems of ordinary differential equations; behavior and stability of solutions including phase plane analysis (4 classes)
- Series solutions of differential equations with variable coefficients – Frobenius method, Bessel functions, Sturm-Liouville problems and orthogonal functions (5 classes)
- Review of Laplace transforms and application to systems of differential equations (4 classes)
- Fourier analysis-Fourier series, Fourier integrals, and Fourier transforms (5 classes)
- Partial differential equations - separation of variables: one-dimensional and two-dimensional wave equations, one-dimensional heat equation, Laplace’s equation (8 classes)
- Examinations (2 classes)

### Computer Use

Appropriate software (primarily MATLAB and Mathcad) is used to benchmark and validate some analytical solutions.

### Class/Laboratory Schedule

Three 50 minute sessions per week devoted to lecture, discussion, and problem solving.

### Evaluation

Homework - 10%, quizzes - 5%, midterm exams - 50%, final exam - 35%.

### Curriculum Criterion Contribution

Engineering science: 3 credits.

### Relationship to Program Outcomes

This course supports Mechanical Engineering Department B.Sc. program objectives by developing:

- An ability to apply knowledge of mathematics, science, and engineering in the field of mechanical engineering.
- An ability to identify, formulate and solve problems in the field of mechanical engineering.
- An ability to use the techniques, skills, and modern tools necessary for the practice of mechanical engineering.