About this Course
최근 조회 49,092

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

Knowledge of single variable calculus.

완료하는 데 약 13시간 필요

권장: 6 hours per week...

영어

자막: 영어

배울 내용

  • Check

    First-order differential equations

  • Check

    Second-order differential equations

  • Check

    The Laplace transform and series solution methods

  • Check

    Systems of differential equations and partial differential equations

귀하가 습득할 기술

Differential EquationsOrdinary Differential EquationPartial Differential Equation (PDE)Engineering Mathematics

100% 온라인

지금 바로 시작해 나만의 일정에 따라 학습을 진행하세요.

유동적 마감일

일정에 따라 마감일을 재설정합니다.

초급 단계

Knowledge of single variable calculus.

완료하는 데 약 13시간 필요

권장: 6 hours per week...

영어

자막: 영어

강의 계획 - 이 강좌에서 배울 내용

1
완료하는 데 6시간 필요

First-Order Differential Equations

12개 동영상 (총 98분), 12 readings, 6 quizzes
12개의 동영상
Course Overview3m
Introduction to Differential Equations9m
Week One Introduction59
Euler Method9m
Separable First-order Equations8m
Separable First-order Equation: Example6m
Linear First-order Equations13m
Linear First-order Equation: Example5m
Application: Compound Interest13m
Application: Terminal Velocity11m
Application: RC Circuit11m
12개의 읽기 자료
Welcome and Course Information5m
Get to Know Your Classmates10m
How to Write Math in the Discussions Using MathJax10m
Practice: Runge-Kutta Methods10m
Practice: Separable First-order Equations10m
Practice: Separable First-order Equation Examples10m
Practice: Linear First-order Equations5m
Change of Variables Transforms a Nonlinear to a Linear Equation10m
Practice: Linear First-order Equation: Examples10m
Practice: Compound Interest10m
Practice: Terminal Velocity10m
Practice: RC Circuit10m
6개 연습문제
Diagnostic Quiz15m
Classify Differential Equations10m
Separable First-order ODEs15m
Linear First-order ODEs15m
Applications20m
Week One1h
2
완료하는 데 5시간 필요

Linear Homogeneous Differential Equations

11개 동영상 (총 93분), 11 readings, 3 quizzes
11개의 동영상
Euler Method for Higher-order ODEs9m
The Principle of Superposition6m
The Wronskian8m
Homogeneous Second-order ODE with Constant Coefficients9m
Case 1: Distinct Real Roots7m
Case 2: Complex-Conjugate Roots (Part A)7m
Case 2: Complex-Conjugate Roots (Part B)8m
Case 3: Repeated Roots (Part A)12m
Case 3: Repeated Roots (Part B)4m
Complex Numbers17m
11개의 읽기 자료
Practice: Second-order Equation as System of First-order Equations10m
Practice: Second-order Runge-Kutta Method10m
Practice: Linear Superposition for Inhomogeneous ODEs10m
Practice: Wronskian of Exponential Function10m
Practice: Roots of the Characteristic Equation10m
Practice: Distinct Real Roots10m
Practice: Hyperbolic Sine and Cosine Functions10m
Do You Know Complex Numbers?
Practice: Complex-Conjugate Roots10m
Practice: Sine and Cosine Functions10m
Practice: Repeated Roots10m
3개 연습문제
Superposition, the Wronskian, and the Characteristic Equation20m
Homogeneous Equations30m
Week Two55m
3
완료하는 데 6시간 필요

Linear Inhomogeneous Differential Equations

12개 동영상 (총 127분), 9 readings, 4 quizzes
12개의 동영상
Inhomogeneous Second-order ODE9m
Inhomogeneous Term: Exponential Function11m
Inhomogeneous Term: Sine or Cosine (Part A)9m
Inhomogeneous Term: Sine or Cosine (Part B)8m
Inhomogeneous Term: Polynomials7m
Resonance13m
RLC Circuit11m
Mass on a Spring9m
Pendulum12m
Damped Resonance14m
Nondimensionalization17m
9개의 읽기 자료
Practice: Multiple Inhomogeneous Terms10m
Practice: Exponential Inhomogeneous Term10m
Practice: Sine or Cosine Inhomogeneous Term10m
Practice: Polynomial Inhomogeneous Term10m
When the Inhomogeneous Term is a Solution of the Homogeneous Equation10m
Do You Know Dimensional Analysis?
Another Nondimensionalization of the RLC Circuit Equation10m
Another Nondimensionalization of the Mass on a Spring Equation10m
Find the Amplitude of Oscillation10m
4개 연습문제
Solving Inhomogeneous Equations30m
Particular Solutions30m
Applications and Resonance30m
Week Three1h
4
완료하는 데 6시간 필요

The Laplace Transform and Series Solution Methods

11개 동영상 (총 123분), 10 readings, 4 quizzes
11개의 동영상
Definition of the Laplace Transform13m
Laplace Transform of a Constant Coefficient ODE11m
Solution of an Initial Value Problem13m
The Heaviside Step Function10m
The Dirac Delta Function12m
Solution of a Discontinuous Inhomogeneous Term13m
Solution of an Impulsive Inhomogeneous Term7m
The Series Solution Method17m
Series Solution of the Airy's Equation (Part A)14m
Series Solution of the Airy's Equation (Part B)7m
10개의 읽기 자료
Practice: The Laplace Transform of Sine10m
Practice: Laplace Transform of an ODE10m
Practice: Solution of an Initial Value Problem10m
Practice: Heaviside Step Function10m
Practice: The Dirac Delta Function15m
Practice: Discontinuous Inhomogeneous Term20m
Practice: Impulsive Inhomogeneous Term10m
Practice: Series Solution Method10m
Practice: Series Solution of a Nonconstant Coefficient ODE1m
Practice: Solution of the Airy's Equation10m
4개 연습문제
The Laplace Transform Method30m
Discontinuous and Impulsive Inhomogeneous Terms20m
Series Solutions20m
Week Four1h
4.9
49개의 리뷰Chevron Right

Differential Equations for Engineers의 최상위 리뷰

대학: 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.

대학: 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.

강사

Avatar

Jeffrey R. Chasnov

Professor
Department of Mathematics

홍콩과학기술대학 정보

HKUST - A dynamic, international research university, in relentless pursuit of excellence, leading the advance of science and technology, and educating the new generation of front-runners for Asia and the world....

자주 묻는 질문

  • 강좌에 등록하면 바로 모든 비디오, 테스트 및 프로그래밍 과제(해당하는 경우)에 접근할 수 있습니다. 상호 첨삭 과제는 이 세션이 시작된 경우에만 제출하고 검토할 수 있습니다. 강좌를 구매하지 않고 살펴보기만 하면 특정 과제에 접근하지 못할 수 있습니다.

  • 수료증을 구매하면 성적 평가 과제를 포함한 모든 강좌 자료에 접근할 수 있습니다. 강좌를 완료하면 전자 수료증이 성취도 페이지에 추가되며, 해당 페이지에서 수료증을 인쇄하거나 LinkedIn 프로필에 수료증을 추가할 수 있습니다. 강좌 콘텐츠만 읽고 살펴보려면 해당 강좌를 무료로 청강할 수 있습니다.

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