This course is about differential equations and covers material that all engineers should know. Both basic theory and applications are taught. In the first five weeks we will learn about ordinary differential equations, and in the final week, partial differential equations.

제공자:

## Differential Equations for Engineers

## About this Course

#### 100% 온라인

#### 유동적 마감일

#### 초급 단계

Knowledge of single variable calculus.

#### 완료하는 데 약 26시간 필요

#### 영어

### 배울 내용

First-order differential equations

Second-order differential equations

The Laplace transform and series solution methods

Systems of differential equations and partial differential equations

### 귀하가 습득할 기술

#### 100% 온라인

#### 유동적 마감일

#### 초급 단계

Knowledge of single variable calculus.

#### 완료하는 데 약 26시간 필요

#### 영어

### 제공자:

#### 홍콩과학기술대학

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.

## 강의 계획 - 이 강좌에서 배울 내용

**완료하는 데 5시간 필요**

## First-Order Differential Equations

A differential equation is an equation for a function with one or more of its derivatives. We introduce differential equations and classify them. We then learn about the Euler method for numerically solving a first-order ordinary differential equation (ode). Then we learn analytical methods for solving separable and linear first-order odes. An explanation of the theory is followed by illustrative solutions of some simple odes. Finally, we learn about three real-world examples of first-order odes: compound interest, terminal velocity of a falling mass, and the resistor-capacitor electrical circuit.

**완료하는 데 5시간 필요**

**15개의 동영상**

**11개의 읽기 자료**

**6개 연습문제**

**완료하는 데 4시간 필요**

## Homogeneous Linear Differential Equations

We generalize the Euler numerical method to a second-order ode. We then develop two theoretical concepts used for linear equations: the principle of superposition, and the Wronskian. Armed with these concepts, we can find analytical solutions to a homogeneous second-order ode with constant coefficients. We make use of an exponential ansatz, and transform the constant-coefficient ode to a second-order polynomial equation called the characteristic equation of the ode. The characteristic equation may have real or complex roots and we learn solution methods for the different cases.

**완료하는 데 4시간 필요**

**11개의 동영상**

**11개의 읽기 자료**

**3개 연습문제**

**완료하는 데 5시간 필요**

## Inhomogeneous Linear Differential Equations

We now add an inhomogeneous term to the constant-coefficient ode. The inhomogeneous term may be an exponential, a sine or cosine, or a polynomial. We also study the phenomena of resonance, when the forcing frequency is equal to the natural frequency of the oscillator. Finally, we learn about three important applications: the RLC electrical circuit, a mass on a spring, and the pendulum.

**완료하는 데 5시간 필요**

**12개의 동영상**

**9개의 읽기 자료**

**4개 연습문제**

**완료하는 데 4시간 필요**

## The Laplace Transform and Series Solution Methods

We present two new analytical solution methods for solving linear odes. The first is the Laplace transform method, which is used to solve the constant-coefficient ode with a discontinuous or impulsive inhomogeneous term. The Laplace transform is a good vehicle in general for introducing sophisticated integral transform techniques within an easily understandable context. We also introduce the solution of a linear ode by a series solution. Although we do not go deeply here, an introduction to this technique may be useful to students that encounter it again in more advanced courses.

**완료하는 데 4시간 필요**

**11개의 동영상**

**10개의 읽기 자료**

**4개 연습문제**

### 검토

#### 4.9

##### DIFFERENTIAL EQUATIONS FOR ENGINEERS의 최상위 리뷰

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.

Excellent course. I would recommend it very highly! The professor starts from the very basics and goes on to tackle highly intricate and interesting problems.

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.

## 자주 묻는 질문

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