## 课程信息

57,663 次近期查看

#### 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

Ordinary 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 97 分钟）, 11 个阅读材料, 6 个测验
12 个视频
Course Overview2分钟
Introduction to Differential Equations | Lecture 19分钟
Week One Introduction59
Euler Method | Lecture 29分钟
Separable First-order Equations | Lecture 38分钟
Separable First-order Equation: Example | Lecture 46分钟
Linear First-order Equations | Lecture 513分钟
Linear First-order Equation: Example | Lecture 65分钟
Application: Compound Interest | Lecture 713分钟
Application: Terminal Velocity | Lecture 811分钟
Application: RC Circuit | Lecture 911分钟
11 个阅读材料
Welcome and Course Information1分钟
How to Write Math in the Discussions Using MathJax1分钟
Runge-Kutta Methods10分钟
Separable First-order Equations10分钟
Separable First-order Equation Examples10分钟
Linear First-order Equations5分钟
Change of Variables Transforms a Nonlinear to a Linear Equation10分钟
Linear First-order Equation: Examples10分钟
Compound Interest10分钟
Terminal Velocity10分钟
RC Circuit10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 One Assessment30分钟
2

## Homogeneous Linear 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 ODEs | Lecture 109分钟
The Principle of Superposition | Lecture 116分钟
The Wronskian | Lecture 128分钟
Homogeneous Second-order ODE with Constant Coefficients| Lecture 139分钟
Case 1: Distinct Real Roots | Lecture 147分钟
Case 2: Complex-Conjugate Roots (Part A) | Lecture 157分钟
Case 2: Complex-Conjugate Roots (Part B) | Lecture 168分钟
Case 3: Repeated Roots (Part A) | Lecture 1712分钟
Case 3: Repeated Roots (Part B) | Lecture 184分钟
Complex Numbers17分钟
11 个阅读材料
Second-order Equation as System of First-order Equations5分钟
Second-order Runge-Kutta Method10分钟
Linear Superposition for Inhomogeneous ODEs10分钟
Wronskian of Exponential Function5分钟
Roots of the Characteristic Equation10分钟
Distinct Real Roots10分钟
Hyperbolic Sine and Cosine Functions10分钟
Do You Know Complex Numbers?
Complex-Conjugate Roots10分钟
Sine and Cosine Functions10分钟
Repeated Roots10分钟
3 个练习
Superposition, the Wronskian, and the Characteristic Equation10分钟
Homogeneous Equations15分钟
Week Two Assessment30分钟
3

## Inhomogeneous Linear 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 ODE | Lecture 199分钟
Inhomogeneous Term: Exponential Function | Lecture 2011分钟
Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 219分钟
Inhomogeneous Term: Sine or Cosine (Part B) | Lecture 228分钟
Inhomogeneous Term: Polynomials | Lecture 237分钟
Resonance | Lecture 2413分钟
RLC Circuit | Lecture 2511分钟
Mass on a Spring | Lecture 269分钟
Pendulum | Lecture 2712分钟
Damped Resonance | Lecture 2814分钟
Nondimensionalization17分钟
9 个阅读材料
Multiple Inhomogeneous Terms5分钟
Exponential Inhomogeneous Term10分钟
Sine or Cosine Inhomogeneous Term10分钟
Polynomial Inhomogeneous Term5分钟
When the Inhomogeneous Term is a Solution of the Homogeneous Equation10分钟
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation10分钟
Another Nondimensionalization of the Mass on a Spring Equation5分钟
Find the Amplitude of Oscillation10分钟
4 个练习
Solving Inhomogeneous Equations15分钟
Particular Solutions15分钟
Applications and Resonance15分钟
Week Three Assessment30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 Transform | Lecture 2913分钟
Laplace Transform of a Constant Coefficient ODE | Lecture 3011分钟
Solution of an Initial Value Problem | Lecture 3113分钟
The Heaviside Step Function | Lecture 3210分钟
The Dirac Delta Function | Lecture 3312分钟
Solution of a Discontinuous Inhomogeneous Term | Lecture 3413分钟
Solution of an Impulsive Inhomogeneous Term | Lecture 357分钟
The Series Solution Method | Lecture 3617分钟
Series Solution of the Airy's Equation (Part A) | Lecture 3714分钟
Series Solution of the Airy's Equation (Part B) | Lecture 387分钟
10 个阅读材料
The Laplace Transform of Sine10分钟
Laplace Transform of an ODE10分钟
Solution of an Initial Value Problem10分钟
Heaviside Step Function10分钟
The Dirac Delta Function5分钟
Discontinuous Inhomogeneous Term5分钟
Impulsive Inhomogeneous Term5分钟
Series Solution Method5分钟
Series Solution of a Nonconstant Coefficient ODE5分钟
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 Four Assessment30分钟
4.9
69 条评论

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

Very good course if you want to start using differential equations without any rigorous details. Thanks to professor`s explanation everything is very clear. Good basis to continue to dive deeper.

The instructor and materials were excellent. The quizzes at the end of each section were non-trivial and it's a great course to jumpstart your ability to work with ODEs and PDEs.

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