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Lecture Notes on Differential Equations

Supplemental Board Notes on Linear Algebra Concepts

Homework Materials

ENG272: Advanced Engineering Math I

Catalog Information

Course Units: 1.0

Prerequisite: MAT128

Course Description

This course provides students with knowledge of and the ability to solve first and higher-order differential equations via methods such as substitution, undetermined coefficients, variation of parameters, Laplace Transform, and numerical (e.g. Euler’s). It also addresses issues such as ordinary vs. partial differential equations, linearity vs. nonlinearity, modeling of a physical system as one or more differential equations, and eigenvector analysis.

Primary Textbook

Advanced Engineering Mathematics

Authored by Dennis G. Zill and Michael R. Cullen

Published by Jones and Bartlett Publishers

ISBN: 978076374591

Course Objectives*

Objective 1: To teach students the basic principles of linear algebra, differential equations, Laplace transform, and power series [a].

Objective 2: To train students to identify, formulate and solve engineering problems using linear algebra, differential equations [a].

Topics Covered

1. Linear Algebra

a. vector algebra

b. matrix inversion

c. eigenvalue / eigenvector analysis

d. solution of system of equations

2. Introduction to Differential Equations

3. First-Order Differential Equations

a. direction fields

b. autonomous equations

c. separable equations

d. linear equations

e. exact equations

f. solution by substitution

g. solution via numerical methods (e.g. Euler’s Method)

h. linear and nonlinear physical models

4. Higher-Order Differential Equations

a. theory of linear equations

b. solution via reduction of order

c. homogeneous linear ODE’s with constant coefficients

d. solution via method of undetermined coefficients

e. solution via variation of parameters

f. Cauchy-Euler equation

g. solving systems of linear equations

5. The Laplace Transform

a. theory and definition of Laplace

b. transform of differential functions

c. translational theorems

d. operational properties of the Laplace

e. convolution

Evaluation / Grading

1. Quizzes (30%)

2. Midterm (25%) and Final Exams (35%)

3. Homework and Participation (10%)

Performance Criteria

Objective 1: Students will demonstrate an understanding of linear algebra, differential equations, Laplace transform, and power series [1,2].

Objective 2: Students will demonstrate the ability to apply linear algebra, differential equations, Laplace transform, and power series to engineering problems [1,2].

Contributions

Engineering Science (0%)

Engineering Design (0%)

* Lower case letters in brackets refer to Educational Objectives of the department.

** Capital letters in brackets refer to evaluation methods used to assess student performance.