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ENG272: Advanced Engineering Math I
Course Units: 1.0
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.
Advanced Engineering Mathematics
Authored by Dennis G. Zill and Michael R. Cullen
Published by Jones and Bartlett Publishers
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].
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
Evaluation / Grading
1. Quizzes (30%)
2. Midterm (25%) and Final Exams (35%)
3. Homework and Participation (10%)
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].
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.