课程信息
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100% 在线

立即开始,按照自己的计划学习。

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初级

Knowledge of single variable calculus.

完成时间大约为14 小时

建议:5 hours per week...

英语(English)

字幕:英语(English)

您将学到的内容有

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    First-order differential equations

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    Second-order differential equations

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    The Laplace transform and series solution methods

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    Systems of differential equations and partial differential equations

您将获得的技能

Differential EquationsOrdinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics

100% 在线

立即开始,按照自己的计划学习。

可灵活调整截止日期

根据您的日程表重置截止日期。

初级

Knowledge of single variable calculus.

完成时间大约为14 小时

建议:5 hours per week...

英语(English)

字幕:英语(English)

学习Course的学生是

  • Risk Managers
  • Scientists
  • Biologists
  • Machine Learning Engineers
  • Technical Solutions Engineers

教学大纲 - 您将从这门课程中学到什么

1
完成时间为 6 小时

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 Equations9分钟
Week 1 Introduction47
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
11 个阅读材料
Welcome and Course Information2分钟
Get to Know Your Classmates10分钟
Practice: Runge-Kutta Methods10分钟
Practice: Separable First-order Equations10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 Equation10分钟
Practice: Linear First-order Equation: Examples10分钟
Practice: Compound Interest10分钟
Practice: Terminal Velocity10分钟
Practice: RC Circuit10分钟
6 个练习
Diagnostic Quiz15分钟
Classify Differential Equations10分钟
Separable First-order ODEs15分钟
Linear First-order ODEs15分钟
Applications20分钟
Week One1小时
2
完成时间为 8 小时

Second-Order Differential Equations

22 个视频 (总计 218 分钟), 20 个阅读材料, 3 个测验
22 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
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
Complex Numbers17分钟
Nondimensionalization17分钟
20 个阅读材料
Practice: Second-order Equation as System of First-order Equations10分钟
Practice: Second-order Runge-Kutta Method10分钟
Practice: Linear Superposition for Inhomogeneous ODEs10分钟
Practice: Wronskian of Exponential Function10分钟
Do You Know Complex Numbers?
Practice: Roots of the Characteristic Equation10分钟
Practice: Distinct Real Roots10分钟
Practice: Hyperbolic Sine and Cosine Functions10分钟
Practice: Complex-Conjugate Roots10分钟
Practice: Sine and Cosine Functions10分钟
Practice: Repeated Roots10分钟
Practice: Multiple Inhomogeneous Terms10分钟
Practice: Exponential Inhomogeneous Term10分钟
Practice: Sine or Cosine Inhomogeneous Term10分钟
Practice: Polynomial Inhomogeneous Term10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 Equation10分钟
Find the Amplitude of Oscillation10分钟
3 个练习
Homogeneous Equations20分钟
Inhomogeneous Equations20分钟
Week Two1小时
3
完成时间为 6 小时

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 Sine10分钟
Practice: Laplace Transform of an ODE10分钟
Practice: Solution of an Initial Value Problem10分钟
Practice: Heaviside Step Function10分钟
Practice: The Dirac Delta Function15分钟
Practice: Discontinuous Inhomogeneous Term20分钟
Practice: Impulsive Inhomogeneous Term10分钟
Practice: Series Solution Method10分钟
Practice: Series Solution of a Nonconstant Coefficient ODE1分钟
Practice: Solution of the Airy's Equation10分钟
4 个练习
The Laplace Transform Method30分钟
Discontinuous and Impulsive Inhomogeneous Terms20分钟
Series Solutions20分钟
Week Three1小时
4
完成时间为 8 小时

Systems of Differential Equations and Partial Differential Equations

19 个视频 (总计 177 分钟), 17 个阅读材料, 6 个测验
19 个视频
Systems of Homogeneous Linear First-order ODEs8分钟
Distinct Real Eigenvalues9分钟
Complex-Conjugate Eigenvalues12分钟
Coupled Oscillators9分钟
Normal Modes (Eigenvalues)10分钟
Normal Modes (Eigenvectors)9分钟
Fourier Series12分钟
Fourier Sine and Cosine Series5分钟
Fourier Series: Example11分钟
The Diffusion Equation9分钟
Solution of the Diffusion Equation: Separation of Variables11分钟
Solution of the Diffusion Equation: Eigenvalues10分钟
Solution of the Diffusion Equation: Fourier Series9分钟
Diffusion Equation: Example10分钟
Matrices and Determinants13分钟
Eigenvalues and Eigenvectors10分钟
Partial Derivatives9分钟
Concluding Remarks2分钟
17 个阅读材料
Do You Know Matrix Algebra?
Practice: Eigenvalues of a Symmetric Matrix10分钟
Practice: Distinct Real Eigenvalues10分钟
Practice: Complex-Conjugate Eigenvalues10分钟
Practice: Coupled Oscillators10分钟
Practice: Normal Modes of Coupled Oscillators10分钟
Practice: Fourier Series10分钟
Practice: Fourier series at x=010分钟
Practice: Fourier Series of a Square Wave10分钟
Do You Know Partial Derivatives?10分钟
Practice: Nondimensionalization of the Diffusion Equation10分钟
Practice: Boundary Conditions with Closed Pipe Ends10分钟
Practice: ODE Eigenvalue Problems10分钟
Practice: Solution of the Diffusion Equation with Closed Pipe Ends10分钟
Practice: Concentration of a Dye in a Pipe with Closed Ends10分钟
Please Rate this Course5分钟
Acknowledgements
6 个练习
Systems of Differential Equations20分钟
Normal Modes30分钟
Fourier Series30分钟
Separable Partial Differential Equations20分钟
The Diffusion Equation20分钟
Week Four1小时
4.8
37 个审阅Chevron Right

来自Differential Equations for Engineers的热门评论

创建者 AKSep 8th 2019

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.

创建者 YHApr 3rd 2019

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

讲师

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

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