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EECE 4694: Spring 2024
Class time:
Mon & Thu 11:45am - 1:25pm
Location: Ryder Hall 296
Office Hours:Mon, Wed, & Thur 10:30am to 11:30am
Course Syllabus
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Spring 2024
Course Description and Overview: This course presents numerical techniques used in solving scientific and engineering problems with the aid of digital computers. The course offers a clear understanding of the ideas and techniques underlying the numerical algorithms, and pitfalls encountered when performing numerical operations on computational systems.
Topics include numerical solutions of linear as well as nonlinear systems of equations; the theory of numerical integration and differentiation; numerical solution of ordinary differential equations; theory of interpolation; the theory of least squares; and numerical optimization techniques. The course emphasizes algorithm development, implementation with MATLAB and Python, and practical applications in the areas of electrical and computer engineering.
Course Objectives:
- To gain knowledge and skills in numerical methods for computational problems in electrical and computer engineering.
- To gain an understanding of the algorithms and pitfalls encountered when performing numerical operations on computational systems.
- To gain practical programming experience with MATLAB or Python and their applications in numerical algorithms.
Course Textbook (optional):
Numerical and Analytical Methods with MATLAB for Electrical Engineers
by William Bober and Andrew Stevens,
1st edition, 2012, Publisher: McGraw Hill, ISBN-10:0072467509 / ISBN-13:978-0072467505
(Other Reference) Numerical Methods for Engineers, Raymond P. Canale and Steven C. Chapra
any edition from 5rd to 9th, McGraw-Hill, ISBN-13: 978-0073401065
Software:Please see the following link on how to download Matlab
MATLAB Installation Instructions
Students are expected to bring laptops with Matlab installed in it.
Course Topics:
Basics of Matlab and Matrix Operations
- Addition/Subtraction of Matrices
- Multiplication of Matrices
- Element-wise operations
- Determinant
- Triangular Matrices
Review of Linear Algebra
- Systems of linear equations
- Gauss elimination
- Gauss Elimination with Partial Pivoting
- Inverse Matrix and PLU Decomposition
Numerical Integration
- Trapezoidal Rule
- Simpson's rule (1/3 & 3/8 Rules)
- Romberg Integration
- Adaptive Quadrature
- Gaussian Quadrature
Ordinary Differential Equations (ODE)
- Initial value problems
- Euler and Modified Euler formulas
- Runge-Kutta methods: First, Second, and fourth order
- Boundary value problems
- Finite differences and gradients
Interpolation and curve fitting
- Least-Squares Regression
- Linear functions
- Polynomial functions
- Nonlinear functions
- Interpolation
- Newton's Divided Difference Polynomials
- Lagrange Polynomials
- Splines Interpolation
Optimization
- Unconstrained Optimization
- Golden section search
- Gradient descent methods
- Newton's method
- Constrained optimization: Linear Programming
- Graphical solutions
- The simplex method
- Lagrange multipliers
- Interior-point methods
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