К содержимому
learnspaceYOUR NEXT CHAPTER
ПРОСТРАНСТВО ОБУЧЕНИЯ
ГлавнаяКаталог курсовМоё обучениеCoursera

Знания без границ

Учитесь у лучших университетов и компаний мира.

Открыть Coursera
Интеграция
Пространство университета
Моё пространствоСтраница курса
↵
ЯЛичный кабинетСтудент
© 2026 LearnSpaceКаждый день — возможность узнать больше.Помощь
Differential Equations for Engineers · LearnSpace
Назад в каталог
courseraМатематика

Differential Equations for Engineers

Курс от The Hong Kong University of Science and Technology
Начальный≈ 26.8 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This course is all about differential equations and covers both theory and applications. In the first five weeks, students will learn about ordinary differential equations, while the sixth week is an introduction to partial differential equations. The course includes 56 concise lecture videos, with a few problems to solve after each lecture. After each major topic, there is a short practice quiz. At the end of each week, there is an assessed quiz. Solutions to the problems and practice quizzes can be found in the instructor-provided lecture notes. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/differential-equations-for-engineers.pdf Watch the promotional video from the link https://youtu.be/eSty7oo09ZI

Навыки, которые вы освоите

Differential EquationsLinear AlgebraVibrationsApplied MathematicsIntegral CalculusCalculusAlgebraMathematical ModelingNumerical AnalysisAdvanced Mathematics

Программа курса

6 модулей · 162 учебных материалов

01First-Order Differential Equations33 материалов

Welcome to Differential Equations for Engineers

Welcome and Course InformationЧтениеCourse OverviewВидеоDiagnostic Quiz ЗаданиеHow to Write Math in the Discussion Forums Using MathJaxЧтение

Учитесь у экспертов

Jeffrey R. Chasnov

Professor

Differential Equations for Engineers
В каталоге вашей программы

Инвестируйте в себя

Новые знания — в удобное для вас время.

Начать на Coursera

Обучение откроется на Coursera
в новой вкладке

Обучение на Coursera

≈ 26.8 ч

6 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, Узбекский, Украинский, Китайский (Китай), Греческий, Итальянский, Бразильский португальский, Вьетнамский, Нидерландский, Корейский, Немецкий, Пушту, Урду, Русский, Тайский, Индонезийский, Шведский, Турецкий, Азербайджанский, Испанский, Дари, Хинди, Японский, Казахский, Венгерский, Польский

Часть программы вашего университета
Introduction to Differential Equations | Lecture 1Видео
Classify Differential Equations Задание

Introduction to Week One

Week One IntroductionВидео

Numerical Methods

Euler Method | Lecture 2ВидеоRunge-Kutta MethodsЧтение

Separable Equations

Separable First-order Equations | Lecture 3ВидеоSeparable First-order EquationsЧтениеSeparable First-order Equation: Example | Lecture 4ВидеоSeparable First-order Equation ExamplesЧтениеSeparable First-order ODEsЗадание

Linear Equations

Linear First-order Equations | Lecture 5ВидеоLinear First-order EquationsЧтениеChange of Variables Transforms a Nonlinear to a Linear EquationЧтениеLinear First-order Equation: Example | Lecture 6ВидеоLinear First-order Equation: ExamplesЧтениеLinear First-order ODEsЗадание

Applications

Application: Compound Interest | Lecture 7ВидеоSaving for RetirementЧтениеBorrowing for a MortgageЧтениеApplication: Terminal Velocity | Lecture 8ВидеоTerminal Velocity of a SkydiverЧтениеHow Fast Can You Skydive? ЧтениеApplication: RC Circuit | Lecture 9ВидеоThe Current in an RC CircuitЧтениеApplicationsЗадание

Quiz

Week One AssessmentЗадание

Additional Videos: The SIR Epidemic Model of Infectious Disease

The SIR ModelВидеоThe Basic Reproductive RatioВидеоSolution of the SIR ModelВидео
02Homogeneous Linear Differential Equations26 материалов

Introduction to Week Two

Week Two IntroductionВидео

Numerical Methods

Euler Method for Higher-order ODEs | Lecture 10ВидеоSecond-order Equation as System of First-order EquationsЧтениеSecond-order Runge-Kutta MethodЧтение

Theory

The Principle of Superposition | Lecture 11ВидеоLinear Superposition for Inhomogeneous ODEsЧтениеThe Wronskian | Lecture 12ВидеоWronskian of Exponential FunctionЧтениеHomogeneous Second-order ODE with Constant Coefficients| Lecture 13ВидеоRoots of the Characteristic EquationЧтениеTheory of ODEЗадание

Distinct Real Roots

Case 1: Distinct Real Roots | Lecture 14ВидеоDistinct Real RootsЧтениеHyperbolic Sine and Cosine FunctionsЧтение

Complex-Conjugate Roots

Do You Know Complex Numbers?ЧтениеCase 2: Complex-Conjugate Roots (Part A) | Lecture 15ВидеоCase 2: Complex-Conjugate Roots (Part B) | Lecture 16ВидеоComplex-Conjugate RootsЧтениеSine and Cosine FunctionsЧтение

Repeated Roots

Case 3: Repeated Roots (Part A) | Lecture 17ВидеоCase 3: Repeated Roots (Part B) | Lecture 18ВидеоRepeated RootsЧтениеHomogeneous EquationsЗадание

The Amazing Equation y' = y

Defining the Exponential, Logarithm, Sine, and Cosine Functions using ODEsPLUGIN

Supplemental Videos

Complex NumbersВидео

Quiz

Week Two AssessmentЗадание
03Inhomogeneous Linear Differential Equations25 материалов

Introduction to Week Three

Week Three IntroductionВидео

Theory and Exponential Inhomogeneous Terms

Inhomogeneous Second-order ODE | Lecture 19ВидеоMultiple Inhomogeneous TermsЧтениеInhomogeneous Term: Exponential Function | Lecture 20ВидеоExponential Inhomogeneous TermЧтениеSolving Inhomogeneous EquationsЗадание

Particular Solutions for Sine/Cosine and Polynomials

Inhomogeneous Term: Sine or Cosine (Part A) | Lecture 21ВидеоInhomogeneous Term: Sine or Cosine (Part B) | Lecture 22ВидеоSine or Cosine Inhomogeneous TermЧтениеInhomogeneous Term: Polynomials | Lecture 23ВидеоPolynomial Inhomogeneous TermЧтениеParticular SolutionsЗадание

Resonance

Resonance | Lecture 24ВидеоWhen the Inhomogeneous Term is a Solution of the Homogeneous EquationЧтение

Applications and Damped Resonance

Do You Know Dimensional Analysis?ЧтениеRLC Circuit | Lecture 25ВидеоAnother Nondimensionalization of the RLC Circuit EquationЧтениеMass on a Spring | Lecture 26ВидеоAnother Nondimensionalization of the Mass on a Spring EquationЧтениеPendulum | Lecture 27Видео

Supplemental Videos

NondimensionalizationВидео

Quiz

Week Three AssessmentЗадание
04The Laplace Transform and Series Solution Methods25 материалов

Introduction to Week Four

Week Four IntroductionВидео

The Laplace Transform Method

Definition of the Laplace Transform | Lecture 29ВидеоThe Laplace Transform of SineЧтениеLaplace Transform of a Constant Coefficient ODE | Lecture 30ВидеоLaplace Transform of an ODEЧтениеSolution of an Initial Value Problem | Lecture 31ВидеоSolution of an Initial Value ProblemЧтениеThe Laplace Transform MethodЗадание

Heaviside Step Function and Dirac Delta function

The Heaviside Step Function | Lecture 32ВидеоHeaviside Step FunctionЧтениеThe Dirac Delta Function | Lecture 33ВидеоThe Dirac Delta FunctionЧтениеSolution of a Discontinuous Inhomogeneous Term | Lecture 34ВидеоDiscontinuous Inhomogeneous TermЧтение

Series Solution Method

The Series Solution Method | Lecture 36ВидеоSeries Solution MethodЧтениеSeries Solution of the Airy's Equation (Part A) | Lecture 37ВидеоSeries Solution of a Nonconstant Coefficient ODEЧтениеSeries Solution of the Airy's Equation (Part B) | Lecture 38ВидеоSolution of the Airy's EquationЧтение

Quiz

Week Four AssessmentЗадание
05Systems of Differential Equations27 материалов

Introduction to Week Five

Week Five IntroductionВидео

Systems of First-order Linear Differential Equations

Do You Know Matrix Algebra?ЧтениеSystems of Homogeneous Linear First-Order ODEs | Lecture 39ВидеоEigenvalues of a Symmetric MatrixЧтениеDistinct Real Eigenvalues | Lecture 40ВидеоDistinct Real EigenvaluesЧтениеComplex-Conjugate Eigenvalues | Lecture 41ВидеоComplex-Conjugate EigenvaluesЧтениеSystems of Differential EquationsЗадание

Phase Portraits

Phase Portraits | Lecture 42ВидеоPhase PortraitsЧтениеStable and Unstable Nodes | Lecture 43ВидеоNodesЧтениеSaddle points | Lecture 44ВидеоSaddle PointsЧтениеSpirals | Lecture 45

Normal Modes

Coupled Oscillators | Lecture 46ВидеоCoupled OscillatorsЧтениеNormal Modes (Eigenvalues) | Lecture 47ВидеоNormal Modes (Eigenvectors) | Lecture 48ВидеоNormal Modes of Coupled OscillatorsЧтениеNormal Modes Задание

Supplemental Videos

Matrices and DeterminantsВидеоEigenvalues and EigenvectorsВидео

Quiz

Week Five AssessmentЗадание
06Partial Differential Equations26 материалов

Introduction to Week Six

Week Six IntroductionВидео

Fourier Series

Fourier Series | Lecture 49ВидеоFourier SeriesЧтениеFourier Sine and Cosine Series |Lecture 50ВидеоFourier series at x=0ЧтениеFourier Series: Example | Lecture 51ВидеоFourier Series of a Square WaveЧтениеFourier SeriesЗадание

The Diffusion Equation

Do You Know Partial Derivatives?ЧтениеThe Diffusion Equation | Lecture 52ВидеоNondimensionalization of the Diffusion EquationЧтение

Separation of Variables

Solution of the Diffusion Equation: Separation of Variables | Lecture 53ВидеоBoundary Conditions with Closed Pipe EndsЧтениеSolution of the Diffusion Equation: Eigenvalues | Lecture 54ВидеоODE Eigenvalue ProblemsЧтениеSeparable Partial Differential EquationsЗадание

Diffusion of a Dye

Solution of the Diffusion Equation: Fourier Series | Lecture 55ВидеоSolution of the Diffusion Equation with Closed Pipe EndsЧтениеDiffusion Equation: Example | Lecture 56ВидеоConcentration of a Dye in a Pipe with Closed EndsЧтениеThe Diffusion EquationЗадание

Supplemental Videos

Partial DerivativesВидео

Quiz

Week Six AssessmentЗадание

Farewell

Concluding RemarksВидеоPlease Rate this CourseЧтениеAcknowledgementsЧтение
Damped Resonance | Lecture 28Видео
Find the Amplitude of OscillationЧтение
Applications and ResonanceЗадание
Solution of an Impulsive Inhomogeneous Term | Lecture 35Видео
Impulsive Inhomogeneous TermЧтение
Discontinuous and Impulsive Inhomogeneous TermsЗадание
Series SolutionsЗадание
Видео
SpiralsЧтение
Phase portraitsЗадание