# ENGRMAE 185 Numerical Analysis in Mechanical Engineering (2015-2016)

#### ENGRMAE 185 Numerical Analysis in Mechanical Engineering

**ENGRMAE 185 Numerical Analysis in Mechanical Engineering (Credit Units: 4)** Soultion of mechanical-engineering equations by means of numerical methods. Errors in numerical analysis. Nonlinear equation and sets of equations. Numerical differentiation and integration. Ordinary differential equations. Boundary-value problems. Partial differential equations.
Prerequisite: MAE10, Mathematics 3D; Mathematics 2E. Civil Engineering and Mechanical Engineering majors have first consideration for enrollment. Only one course from ENGRMAE 185, MATH 105A may be taken for credit. (Design units: 2)

1. Solve numerically a variety of problems that arise from mechanical-engineering systems (EAC a)

2. Develop and apply standard numerical schemes to solve fundamental and practical engineering problems

- Understanding of Computer Algorithms
- Mathematics

- Solving nonlinear equations
- Direct methods for solving linear systems
- Theory of linear systems
- Iterative methods for linear systems
- Curve-fitting and interpolation
- Numerical differentiation
- Numerical integration
- Single step methods for ordinary differential equations
- Multistep methods for ordinary differential equations
- Systems of ordinary differential equations; convergence
- Parabolic partial differential equations
- Hyperbolic partial differential equations

Meets for 3 hours of lecture each week for 10 weeks.

Heavy computer usage. Students are required to develop computer programs for the solution of a design project using FORTRAN under the MS-Windows or (preferably) the Unix platform.

Students are required to work on a comprehensive open-ended project. The term laboratory in this course refers to computer laboratory. The problems are from the field of engineering. Usually, no analytical solutions can be computed. Furthermore, often there is no unique solution. Students are required present a written report with their findings.

Contributes toward the Engineering Topics and/or Design experience for both Mechanical and Aerospace Engineering majors.

There are two projects, each requiring design of an algorithm and extensive programming on the part of the student. Students may work in whatever computer language they choose, and on whatever system to which they have access. As part of the project write-ups, students are required to submit a listing of their program, as well as a sample execution. A major portion of the projects includes use by the student of the software they develop to solve a design problem. Design of software is covered in class for about 20% of the lecture time.

- Midterm Exam: 35%
- Final Exam 40%
- Design Project: 25%
- TOTAL 100%

Mathematics and Basic Science: 0.0 credit units

Computing: 0.0 credit units

Engineering Topics: 4.0 credit units

Engineering Science: 2.0 credit units

Engineering Design: 2.0 credit units