# ECE 310

## Applications of Engineering Mathematics

### Course Level

### Units

### Prerequisite(s)

### Course Texts

Kreyszig, Erwin. *Advanced Engineering Mathematics*. 10th ed. John Wiley & Sons, 2011.

### Schedule

### Course Description

This course is approximately one-half linear algebra and one-half probability and statistics. Linear algebra topics include matrix operations, systems of linear equations, determinants, Gauss-Jordan elimination, vector spaces, basis and dimension, projections, determinants, eigenvalues and eigenvectors. Probability and statistics topics include probability, random variables, density and distribution functions, sample mean and variance, estimation and confidence intervals. An introduction to Matlab and Matlab projects.

### Learning Outcomes

By the end of this course, students will be able to:

- Perform matrix algebra
- Understand rank, basis, linear transformations, vector spaces, eigenvalues
- Solve systems of linear equations
- Describe basic principles of probability theory
- Understand random variables, probability distributions, means and variances

### Course Topics

**Linear Algebra (24 lectures)**

Matrix and vector algebra, linear systems of equations, Gauss elimination, linear independence, rank of a matrix, vector space, solutions of linear systems (existence/uniqueness), determinants, Cramerâ€™s rule, inverse of a matrix, Gauss-Jordan elimination, vector spaces, inner product spaces, linear transformations, eigenvalues, eigenvectors, symmetric/skew-symmetric/orthogonal matrices, complex matrices

**Probability (21 lectures)**

Experiments, outcomes, events, probability, permutations and combinations, random variables, probability distributions, mean and variance of a distribution, binomial/poisson/hypergeometric distributions, normal distribution, distributions of several random variables

**Matlab (13 lectures)**

Command window, basic Matlab syntax, executing expressions, Matlab editor, debugging in Matlab, Matlab Help, creatiion of vectors and matrices, dot operations, matrix operations (addition/subtraction/multiplication), determinants, matrix inverse, solution of a system of linear equations, control of program flow (If and Switch statements), For and While loops, 2-D plotting commands, graph annotation and enhancement (labels, mathematical symbols, attributes of axes, curves and legends), descriptive statistics, probability distributions

### Relationship to Student Outcomes

ECE 310 contributes directly to the following specific electrical and computer engineering student outcomes of the ECE department:

- Ability to apply knowledge of mathematics, science and engineering
- Ability to identify, formulate and solve engineering problems
- Ability to use the techniques, skills and modern engineering tools necessary for engineering practice