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Differential Equations Part I Basic Theory · LearnSpace
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Differential Equations Part I Basic Theory

Курс от Korea Advanced Institute of Science and Technology(KAIST)
Начальный≈ 14.5 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications. The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.

Навыки, которые вы освоите

Differential EquationsMathematical ModelingCalculusApplied MathematicsMechanics

Программа курса

9 модулей · 72 учебных материалов

01Introduction10 материалов

1. Basic Terminologies

1-1 What is a Differentiable Equation?Видео1-2 Order and Normal FormВидео1-3 Linear and Nonlinear EquationsВидео

2. Solutions and Examples

1-4 SolutionВидео1-5 Implicit Solution

Учитесь у экспертов

Kwon, Kil Hyun

Professor

Kil Hyun Kwon

Professor

Differential Equations Part I Basic Theory
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≈ 14.5 ч

9 модулей

Язык: Английский

Субтитры: Арабский, Французский, Бенгальский, 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

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Видео

3. Various Solutions, Initial Value Problem

1-6 Types of SolutionsВидео1-7 Initial Value ProblemВидео

4. Picard Theorem and Examples

1-8 Picard’s Theorem IВидео1-9 Picard’s Theorem IIВидео

Quiz1

Quiz1Задание
02First Order Differential Equation 110 материалов

1. Separable Equations

2-1 Separable EquationsВидео2-2 Separable Equations - Ex’s 1 & 2Видео

2. Separable and Linear Equations

2-3 Separable Equations - Ex’s 3 & 4Видео2-4 Integrating FactorВидео

3. Exact Equations I

2-5 Does IVP Have a Unique Solution?Видео2-6 Exact Equations IВидео

4. Exact Equations II

2-7 Exact Equations IIВидео

5. Examples

2-8 Exact Equations – Ex. 1Видео2-9 Exact Equations – Ex. 2Видео

Quiz2

Quiz2Задание
03FIRST ORDER DEFERENTIAL EQUATION 213 материалов

1. Integrating Factor I & II

3-1 Integrating Factor IВидео3-2 Integrating Factor IIВидео

2. Integrating Factor III, Substitutions

3.3 Integrating Factor IIIВидео3-4 Substitutions, Ex 1Видео

3. Homogeneous Equations

3-5 Homogeneous EquationsВидео3-6 Substitutions Ex's 2 & 3Видео

4. Bernoulli’s equations

3-7 Bernoulli EquationВидео

5. Equations with linear coefficients

3-8 Equations with Linear CoefficientsВидео3-9 Equations with Linear Coefficients - Ex. 5Видео

6. Ricatti’s Equation and Clairaut's Equation

3-10 Ricatti's Equation - Ex. 6Видео3-11 Clairaut's EquationВидео3-12 Clairaut's Equation - Ex. 7Видео

Quiz3

Quiz 3Задание
04Mathematical Modeling and Applications6 материалов

1. Radioactive Decay, Population Dynamics I

4-1 Radioactive DecayВидео4-2 Population Dynamics IВидео

2. Population Dynamics II & III

4-3 Population Dynamics IIВидео4-4 Population Dynamics IIIВидео

3. Population Dynamics IV

4-5 Population Dynamics IVВидео

Quiz4

Quiz4Задание
05LINEAR SECOND ORDER EQUATIONS 16 материалов

1. Linear Differential Equations, Superposition Principle

5-1 Linear differential equationsВидео5-2 Superposition PrincipleВидео

2. Unique Existence of Solution to IVP, Linear Independence, Wronskian Test

5-3 Unique Existence of SolutionВидео5-4 Linear independenceВидео5-5 Wronskian testВидео

Quiz5

Quiz5Задание
06Linear Second order equations 210 материалов

1. Fundamental set of Solutions, General solution of linear homogeneous equations

6-1 Fundamental set of solutionsВидео6-2 General solutionsВидео

2. Nonhomogeneous Equations I & II

6-3 Nonhomogeneous equations IВидео6-4 Nonhomogeneous equations IIВидео

3. Reduction of Order I & II

6-5 Reduction of order IВидео6-6 Reduction of order IIВидео

4. Homogeneous Linear Equations with Constant Coefficients

6-7 Homogeneous linear equations with constant coefficientsВидео

5. Homogeneous Linear Equations with Constant Coefficients, Extension to Higher Order Equations

6-8 Homogeneous linear equations – ExampleВидео6-9 Higher order equationsВидео

Quiz6

Quiz6Задание
07Linear Second order equations 36 материалов

1. Method of Undetermined Coefficients I

7-1 Differential polynomials – Ex. 1Видео7-2 Annihilator – Ex. 2Видео7-3 Method of undetermined coefficients IВидео

2. Method of Undetermined Coefficients II

7-4 Method of undetermined coefficients II – Ex. 3Видео7-5 Method of undetermined coefficients - Ex. 4Видео

Quiz7

Quiz7Задание
08Linear Second order equations 45 материалов

1. Variation of Parameters I & II

8-1 Variation of parameters IВидео8-2 Variation of parameters IIВидео

2. Variation of Parameters III & IV

8-3 Variation of parameters III – Ex. 1Видео8-4 Variation of parameters IV – Ex. 2Видео

Quiz8

Quiz8Задание
09APPLICATIONS OF SECOND ORDER EQUATIONS6 материалов

1. Spring mass system, Free Undamped Motion

9-1 Spring-mass systemВидео9-2 Free undamped motion – Ex. 1Видео

2. Free and Forced Damped Motion

9-3 Free & Forced damped motionВидео

3. Spring Mass System Example, Pendulum

9-4 Spring-mass system – Ex’s 2 & 3Видео9-5 PendulumВидео

Quiz9

Quiz9Задание