Type of Course / Elective (Group 2) for ME program
Replaced by CS 384
Catalog Description / Introduction to numerical methods for engineers. Topics include solution methods for nonlinear algebraic equations, sets of linear and nonlinear algebraic equations, eigenvalue problems, interpolation and curve fitting, numerical differentiation and integration, and techniques to solve ordinary and partial differential equations.
Credits / 3
Prerequisite Courses / MA 36300
Corequisite Courses / None
Prerequisites by Topics / Differential Equations and Computer Programming
Textbook / S. S. Rao, Applied Numerical Methods for Engineers and Scientists, Wiley,current edition.
Course Objectives / To expose students to standard numerical methods that are commonly applied to problems in engineering and to help students to become more familiar with the computer as an engineering tool.
Course Outcomes / Students who successfully complete this course will have demonstrated an ability to:
- Understand the concepts of linear equations and nonlinear equations, as well as linearly independent equations. (a, e, 1, 2)
- Solve nonlinear equations by using some typical approximation methods. (a, e, k, 1, 2, 6)
- Solve simultaneous linear algebraic equations, analyze errors from different approximation methods, and choose the proper method for a particular problem. (a, e, k, 1, 2, 6)
- Use standard interpolation methods to estimate intermediate values from a set of discrete values, and determine an interpolating function for a set of data points. (a, e, k, 1, 2, 6)
- Understandthe concepts of eigen-value and eigen-vector, and determine the eigen-values for a matrix.(a, e, k, 1, 2, 6)
- Computethe derivatives of a function when the function is given either as an analytical expression or as a series of numbers at discrete points. (a, e, k, 1, 2, 6)
- Computeintegrals of functions and analyze the errors from different methods. (a, e, k, 1, 2, 6)
- Solve ordinary differential equations with initial and boundary values. (a, e, k, 1, 2, 6)
- Solve partial differential equations with initial and boundary conditions. (a, e, k, 1, 2, 6)
- Understandthe concepts of local optimum, global optimum as well as the necessary and sufficient conditions for optimum. Use linear programming to solve linear optimization problem. (a, e, k, 1, 2, 6)
Lecture Topics /
- Introduction to numerical methods
- Roots of nonlinear equations
- Solution of systems of equations
- Interpolation, curve fitting, and approximation
- Numerical differentiation and integration
- Fourier series and transforms
- Solution of ordinary and partial differential equations
- Linear and non-linear programming
Computer Usage / High
Laboratory Experience / None
Design Experience / None
Coordinator / Donald Mueller, Ph.D., P.E.
Date / 30 September 2015
Department SyllabusME –37300Page | 1