# ECE 310

## Applications of Engineering Mathematics

### Course Level

### Units

### Instructor(s)

### Prerequisite(s)

### Course Texts

- Advanced Engineering Mathematics, Erwin Kreyszig, Wiley, John & Sons, Incorporated, 2011.ISBN: 978-0-470-45836-5.
- MATLAB Zybooks: Programming in MATLAB

### Schedule

### Course Description

**Specific Course Information:
2021-2022 Catalog Data:** 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

**Specific Goals for the Course:
Outcomes of Instruction:** By the end of this course the student will be able to:

- An ability to perform matrix algebra.
- An understanding of rank, basis, linear transformations, vector spaces, eigenvalues.
- An ability to solve systems of linear equations.
- An ability to describe basic principles of probability theory.
- An understanding of random variables, probability distributions, means and variances.
- An understanding of statistical principles for point estimation, confidence intervals, and hypothesis testing.
- Practical experience of using MATLAB to solve linear algebra and probability problems.

### Course Topics

**Brief list of topics to be covered:**

- Linear Algebra: Matrices, Vectors: Addition and Scalar Multiplication Matrix Multiplication Linear Systems of Equations, Gauss Elimination Linear Independence, Rank of a Matrix, Vector Space Solutions of Linear Systems: Existence, Uniqueness Determinants, Cramer’s Rule Inverse of a Matrix, Gauss-Jordan Elimination Vector Spaces, Inner Product Spaces, Linear Transformations Eigenvalues, Eigenvectors Some Applications of Eigenvalue Problems Symmetric, Skew-Symmetric, and Orthogonal Matrices Eigenbases, Diagonalization, Quadratic Forms Complex Matrices and Forms.
- Probability, Statistics: Data Representation, Average, Spread Experiments, Outcomes, Events Probability Permutations and Combinations Random Variables, Probability Distributions Mean and Variance of a Distribution Binomial, Poisson, and Hypergeometric Distributions Normal Distribution Distributions of Several Random Variables Introduction to Statistics Random Sampling Point Estimation of Parameters Confidence Intervals Testing Hypotheses.
- MATLAB: Command window, Basic MATLAB syntax, Executing Expressions, MATLAB Editor, Debugging in MATLAB, MATLAB Help, Creating 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, 2D 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:

1. An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.

6. An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.

7. An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.