# ME 566 Advanced Engineering Mathematics II

### Catalog Description

ME 566 Advanced Engineering Mathematical Analysis II (3). Prerequisite: ME 565 or equivalent. Engineering systems and phenomena yielding complex domain models/solutions. Power series, Taylor series, and Laurent series. Potential theory. Numerical analysis for complex domain systems. Introduction to optimization and linear programming.

### Prerequisites by Topic

- Multivariate calculus
- Series and transform solutions of ordinary differential equations
- Partial differential equations
- Linear algebra

### Textbook

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

### Coordinator

A.K. Kelecy, Assistant Professor of Mechanical Engineering.

### Course Learning Outcomes

This course provides senior undergraduate and graduate mechanical engineering students with the applied mathematics background necessary to analyze systems where the solutions lie within the complex domain. It also provides an introduction to linear programming and numerical analysis of complex systems.

### Topics Covered

- Vector differential and integral calculus (5 classes)
- Complex numbers and functions, mapping in the complex plane (6 classes)
- Exponential, trigonometric, hyperbolic, and logarithm functions of a complex variable (5 classes)
- Integration in the complex plane/line integrals (4 classes)
- Real and complex series: power, Taylor, and Maclaurin Series (4 classes)
- Laurent Series, residue integration (4 classes)
- Evaluation of real integrals. (3 classes)
- Applications of complex analysis: Laplace’s equation applied to conduction heat transfer and potential fluid flow (5 classes)
- Numerical methods for partial differential equations (4 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.