Applications of Engineering Mathematics
ECE 310 -- Applications of Engineering Mathematics (4 units)
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.
Grading: Regular grades are awarded for this course: A B C D E.
Usually offered: Fall.
MATH 254 and ECE 207 or 220 and ECE 275.
Advanced Engineering Mathematics, Erwin Kreyszig, Wiley, John & Sons, Incorporated, ISBN: 978-0-470-45836-5, 2011.
Course Learning Outcomes:
Upon completion of this course, students will have:
- 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, probability, and statistics problems
- Linear Algebra: 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, Cramer’s Rule, Inverse of a Matrix, Gauss-Jordan Elimination, Vector Spaces, Inner Product Spaces, Linear Transformations, Eigenvalues, Eigenvectors, Symmetric, Skew-Symmetric, and Orthogonal Matrices, Complex Matrices [24 lectures]
- Probability: 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 [21 lectures].
- 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 [13 lectures].
Four 50-minute lecture sessions per week. One 50-minute session per week was reserved for Matlab instruction in a computer lab.
Approximately thirteen homework sets during semester.
Two in-class examinations plus a final examination.
Computer Usage: MATLAB exercises.
Relationship to Student Outcomes:
(a) an ability to apply knowledge of mathematics, science, and engineering,
(e) an ability to identify, formulate, and solve engineering problems,
(k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.