### Numerical Methods in Mechanical Engineering

#### ME 58100 / 3 Cr. (3 Class)

The solution to problems arising in mechanical engineering using numerical methods. Topics include nonlinear algebraic equations, sets of linear algebraic equations, eigenvalue problems, interpolation, curve fitting, ordinary differential equations, and partial differential equations. Applications include fluid mechanics, gas dynamics, heat and mass transfer, thermodynamics, vibrations, automatic control systems, kinematics, and design.

**Available Online:** No

**Credit by Exam:** No

**Laptop Required:** No

**Prerequisites/Co-requisites:**

P: ME 31400 and 37200.

##### Textbooks

M.T. Heath, Scientific Computing: An Introductory Survey, McGraw-Hill, New York, 2nd Edition, 2002.

##### Goals

This course is designed to introduce the student to both classical and modern numerical methods available for solving problems in science and engineering. At the same time, the course aims to familiarize the student with the computer as an valuable problem solving tool and to improve programming skills utilizing structured programming languages. The emphasis in this course is on fundamental understanding of the methods and the importance of errors that are inevitably associated with scientific computing.

##### Outcomes

**After completion of this course, the students should be able to:**

- Develop, code, and use algorithms for computer solution of algebraic equations. [a,k]
- Develop, code, and use basic algorithms for computer solution of eigenvalue problems. [a,k]
- Develop, code, and use basic algorithms for computer solution of nonlinear equations. [a,k]
- Develop, code, and use algorithms for polynomial approximation and interpolations. [a,k]
- Develop, code, and use algorithms for numerical integration. [a,k]
- Develop, code, and use algorithms for numerical differentiations. [a,k]
- Develop, code, and use basic algorithms for solution of differential equations. [a,k]
- Develop, code, and use basic algorithms for solution of partial differential equations.[a,k]

*NOTE: Extra project and homework problems will be assigned to graduate students on these items on the ME 581 Numerical Methods in Mechanical Engineering.

Note: The letters within the brackets indicate the general program outcomes of mechanical engineering. See: ME Program Outcomes.

##### Topics

Below is a list of the major topics and the number of 75-minute periods devoted per each topic to be covered:

- Introduction to scientific computing (1 period)
- Introduction to MATLAB, FORTRAN, and C/C++ programming languages (3 periods)
- Systems of linear algebraic equations (4 periods)
- Solution to matrix eigen problems (3 periods)
- Solution of nonlinear equations (3 periods)
- Polynomial approximation and interpolation (3 periods)
- Numerical integration (2 periods)
- Ordinary differential equations (5 periods)
- Partial differential equations (4 periods)

##### Assignments, Exams, and Grading

There will be two mid-term exams, one final exam, and several homework assignments given throughout the semester. The homework assignments will include computer programming of various numerical methods taught in the course, using Matlab, Fortran, or C languages. The grading will be based on 20% for each mid-term, term 30% for final, and 30% homework assignments.