Advanced Engineering Mathematics I
Chapter 8 | Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4
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 (Matrices).
Textbook:
Advanced Engineering Mathematics By Dennis G. Zill and Michael R. Cullen, 7th Edition (2022), Published by Jones and Bartlett Publishers, ISBN: 978-1-284-20624-1
Chapter 8 Matrices
8.1 Matrix Algebra (Lecture Video)
8.2 Systems of Linear Equations (Lecture Video-Part 1), and (Lecture Video-Part 2)
8.4 Determinants (Lecture Video)
8.6 Inverse of a Matrix (Lecture Video)
8.1~8.6 Lecture Video
8.7 Cramer’s Rule (Lecture Video)
8.8 Eigenvalue Problem (Lecture Video-Part 1), and (Lecture Video-Part 2)
Chapter 1 Introduction to Differential Equations
1.1 Definitions and Terminology
1.2 Initial-Value Problems
1.3 Differential Equations as Mathematical Models
Chapter 2 First-Order Differential Equations
2.1 Solution Curves Without a Solution
2.2 Separable Equations (Lecture Video)
2.3 Linear Equations (Lecture Video)
2.4 Exact Equations (Lecture Video)
2.5 Solutions by Substitutions (Lecture Video)
2.7 Linear Models (Lecture Video)
Chapter 3 Higher-Order Differential Equations
3.1 Theory of Linear Equations
3.2 Reduction of Order (Lecture Video)
3.3 Linear Equations with Constant Coefficients (Lecture Video), and (Lecture Video)
3.4 Undetermined Coefficients (Lecture Video)
3.5 Variation of Parameters (Lecture Video), (Lecture Video-Part 1), (Lecture Video-Part 2),
3.6 Cauchy-Euler equation
3.12 Solving Systems of Linear DEs (Lecture Video)
Chapter 4 The Laplace Transform
4.1 Definition of the Laplace Transform (Lecture Video)
4.2 Inverse Transform and Transforms of Derivatives (Lecture Video)
4.3 Translation Theorems (Lecture Video)