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#### 初级

Knowledge of single variable calculus.

### 您将学到的内容有

• First-order differential equations

• Second-order differential equations

• The Laplace transform and series solution methods

• Systems of differential equations and partial differential equations

### 您将获得的技能

Differential EquationsOrdinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics

#### 初级

Knowledge of single variable calculus.

1

## First-Order Differential Equations

12 个视频 （总计 98 分钟）, 12 个阅读材料, 6 个测验
12 个视频
Course Overview3分钟
Introduction to Differential Equations9分钟
Week One Introduction59
Euler Method9分钟
Separable First-order Equations8分钟
Separable First-order Equation: Example6分钟
Linear First-order Equations13分钟
Linear First-order Equation: Example5分钟
Application: Compound Interest13分钟
Application: Terminal Velocity11分钟
Application: RC Circuit11分钟
12 个阅读材料
Welcome and Course Information1分钟
How to Write Math in the Discussions Using MathJax1分钟
Practice: Runge-Kutta Methods5分钟
Practice: Separable First-order Equations5分钟
Practice: Separable First-order Equation Examples10分钟
Practice: Linear First-order Equations5分钟
Change of Variables Transforms a Nonlinear to a Linear Equation5分钟
Practice: Linear First-order Equation: Examples10分钟
Practice: Compound Interest5分钟
Practice: Terminal Velocity5分钟
Practice: RC Circuit5分钟
6 个练习
Diagnostic Quiz10分钟
Classify Differential Equations5分钟
Separable First-order ODEs10分钟
Linear First-order ODEs10分钟
Applications10分钟
Week One30分钟
2

## Linear Homogeneous Differential Equations

11 个视频 （总计 93 分钟）, 11 个阅读材料, 3 个测验
11 个视频
Euler Method for Higher-order ODEs9分钟
The Principle of Superposition6分钟
The Wronskian8分钟
Homogeneous Second-order ODE with Constant Coefficients9分钟
Case 1: Distinct Real Roots7分钟
Case 2: Complex-Conjugate Roots (Part A)7分钟
Case 2: Complex-Conjugate Roots (Part B)8分钟
Case 3: Repeated Roots (Part A)12分钟
Case 3: Repeated Roots (Part B)4分钟
Complex Numbers17分钟
11 个阅读材料
Practice: Second-order Equation as System of First-order Equations5分钟
Practice: Second-order Runge-Kutta Method5分钟
Practice: Linear Superposition for Inhomogeneous ODEs5分钟
Practice: Wronskian of Exponential Function5分钟
Practice: Roots of the Characteristic Equation5分钟
Practice: Distinct Real Roots5分钟
Practice: Hyperbolic Sine and Cosine Functions5分钟
Do You Know Complex Numbers?
Practice: Complex-Conjugate Roots5分钟
Practice: Sine and Cosine Functions5分钟
Practice: Repeated Roots5分钟
3 个练习
Superposition, the Wronskian, and the Characteristic Equation10分钟
Homogeneous Equations15分钟
Week Two30分钟
3

## Linear Inhomogeneous Differential Equations

12 个视频 （总计 127 分钟）, 9 个阅读材料, 4 个测验
12 个视频
Inhomogeneous Second-order ODE9分钟
Inhomogeneous Term: Exponential Function11分钟
Inhomogeneous Term: Sine or Cosine (Part A)9分钟
Inhomogeneous Term: Sine or Cosine (Part B)8分钟
Inhomogeneous Term: Polynomials7分钟
Resonance13分钟
RLC Circuit11分钟
Mass on a Spring9分钟
Pendulum12分钟
Damped Resonance14分钟
Nondimensionalization17分钟
9 个阅读材料
Practice: Multiple Inhomogeneous Terms5分钟
Practice: Exponential Inhomogeneous Term5分钟
Practice: Sine or Cosine Inhomogeneous Term5分钟
Practice: Polynomial Inhomogeneous Term5分钟
When the Inhomogeneous Term is a Solution of the Homogeneous Equation5分钟
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation5分钟
Another Nondimensionalization of the Mass on a Spring Equation10分钟
Find the Amplitude of Oscillation5分钟
4 个练习
Solving Inhomogeneous Equations15分钟
Particular Solutions15分钟
Applications and Resonance15分钟
Week Three30分钟
4

## The Laplace Transform and Series Solution Methods

11 个视频 （总计 123 分钟）, 10 个阅读材料, 4 个测验
11 个视频
Definition of the Laplace Transform13分钟
Laplace Transform of a Constant Coefficient ODE11分钟
Solution of an Initial Value Problem13分钟
The Heaviside Step Function10分钟
The Dirac Delta Function12分钟
Solution of a Discontinuous Inhomogeneous Term13分钟
Solution of an Impulsive Inhomogeneous Term7分钟
The Series Solution Method17分钟
Series Solution of the Airy's Equation (Part A)14分钟
Series Solution of the Airy's Equation (Part B)7分钟
10 个阅读材料
Practice: The Laplace Transform of Sine5分钟
Practice: Laplace Transform of an ODE5分钟
Practice: Solution of an Initial Value Problem5分钟
Practice: Heaviside Step Function5分钟
Practice: The Dirac Delta Function5分钟
Practice: Discontinuous Inhomogeneous Term5分钟
Practice: Impulsive Inhomogeneous Term5分钟
Practice: Series Solution Method5分钟
Practice: Series Solution of a Nonconstant Coefficient ODE5分钟
Practice: Solution of the Airy's Equation5分钟
4 个练习
The Laplace Transform Method15分钟
Discontinuous and Impulsive Inhomogeneous Terms15分钟
Series Solutions15分钟
Week Four30分钟
4.8
52 条评论

### 来自Differential Equations for Engineers的热门评论

It was a great journey to go through this course. Prof. Jeffery explains the concepts very well. I hope this course will help me greatly in my other courses.

Thank you Prof. Chasnov. The lectures are really impressive and explain derivations throughly. I cannot enjoy more on a math course than this one.

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