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Differential Equations Part I Basic Theory
  • Level Foundation
  • Duration 15 hours
  • Course by Korea Advanced Institute of Science and Technology(KAIST)
  • Offered by

About

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.

Modules

1. Basic Terminologies

    • 3 Videos
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3 Videos

  • 1-1 What is a Differentiable Equation?
  • 1-2 Order and Normal Form
  • 1-3 Linear and Nonlinear Equations

2. Solutions and Examples

    • 2 Videos
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2 Videos

  • 1-4 Solution
  • 1-5 Implicit Solution

3. Various Solutions, Initial Value Problem

    • 2 Videos
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2 Videos

  • 1-6 Types of Solutions
  • 1-7 Initial Value Problem

4. Picard Theorem and Examples

    • 2 Videos
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2 Videos

  • 1-8 Picard’s Theorem I
  • 1-9 Picard’s Theorem II

Quiz1

    • 1 Assignment
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1 Assignment

  • Quiz1

1. Separable Equations

    • 2 Videos
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2 Videos

  • 2-1 Separable Equations
  • 2-2 Separable Equations - Ex’s 1 & 2

2. Separable and Linear Equations

    • 2 Videos
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2 Videos

  • 2-3 Separable Equations - Ex’s 3 & 4
  • 2-4 Integrating Factor

3. Exact Equations I

    • 2 Videos
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2 Videos

  • 2-5 Does IVP Have a Unique Solution?
  • 2-6 Exact Equations I

4. Exact Equations II

    • 1 Videos
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1 Videos

  • 2-7 Exact Equations II

5. Examples

    • 2 Videos
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2 Videos

  • 2-8 Exact Equations – Ex. 1
  • 2-9 Exact Equations – Ex. 2

Quiz2

    • 1 Assignment
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1 Assignment

  • Quiz2

1. Integrating Factor I & II

    • 2 Videos
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2 Videos

  • 3-1 Integrating Factor I
  • 3-2 Integrating Factor II

2. Integrating Factor III, Substitutions

    • 2 Videos
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2 Videos

  • 3.3 Integrating Factor III
  • 3-4 Substitutions, Ex 1

3. Homogeneous Equations

    • 2 Videos
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2 Videos

  • 3-5 Homogeneous Equations
  • 3-6 Substitutions Ex's 2 & 3

4. Bernoulli’s equations

    • 1 Videos
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1 Videos

  • 3-7 Bernoulli Equation

5. Equations with linear coefficients

    • 2 Videos
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2 Videos

  • 3-8 Equations with Linear Coefficients
  • 3-9 Equations with Linear Coefficients - Ex. 5

6. Ricatti’s Equation and Clairaut's Equation

    • 3 Videos
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3 Videos

  • 3-10 Ricatti's Equation - Ex. 6
  • 3-11 Clairaut's Equation
  • 3-12 Clairaut's Equation - Ex. 7

Quiz3

    • 1 Assignment
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1 Assignment

  • Quiz 3

1. Radioactive Decay, Population Dynamics I

    • 2 Videos
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2 Videos

  • 4-1 Radioactive Decay
  • 4-2 Population Dynamics I

2. Population Dynamics II & III

    • 2 Videos
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2 Videos

  • 4-3 Population Dynamics II
  • 4-4 Population Dynamics III

3. Population Dynamics IV

    • 1 Videos
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1 Videos

  • 4-5 Population Dynamics IV

Quiz4

    • 1 Assignment
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1 Assignment

  • Quiz4

1. Linear Differential Equations, Superposition Principle

    • 2 Videos
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2 Videos

  • 5-1 Linear differential equations
  • 5-2 Superposition Principle

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

    • 3 Videos
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3 Videos

  • 5-3 Unique Existence of Solution
  • 5-4 Linear independence
  • 5-5 Wronskian test

Quiz5

    • 1 Assignment
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1 Assignment

  • Quiz5

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

    • 2 Videos
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2 Videos

  • 6-1 Fundamental set of solutions
  • 6-2 General solutions

2. Nonhomogeneous Equations I & II

    • 2 Videos
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2 Videos

  • 6-3 Nonhomogeneous equations I
  • 6-4 Nonhomogeneous equations II

3. Reduction of Order I & II

    • 2 Videos
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2 Videos

  • 6-5 Reduction of order I
  • 6-6 Reduction of order II

4. Homogeneous Linear Equations with Constant Coefficients

    • 1 Videos
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1 Videos

  • 6-7 Homogeneous linear equations with constant coefficients

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

    • 2 Videos
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2 Videos

  • 6-8 Homogeneous linear equations – Example
  • 6-9 Higher order equations

Quiz6

    • 1 Assignment
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1 Assignment

  • Quiz6

1. Method of Undetermined Coefficients I

    • 3 Videos
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3 Videos

  • 7-1 Differential polynomials – Ex. 1
  • 7-2 Annihilator – Ex. 2
  • 7-3 Method of undetermined coefficients I

2. Method of Undetermined Coefficients II

    • 2 Videos
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2 Videos

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

Quiz7

    • 1 Assignment
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1 Assignment

  • Quiz7

1. Variation of Parameters I & II

    • 2 Videos
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2 Videos

  • 8-1 Variation of parameters I
  • 8-2 Variation of parameters II

2. Variation of Parameters III & IV

    • 2 Videos
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2 Videos

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

Quiz8

    • 1 Assignment
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1 Assignment

  • Quiz8

1. Spring mass system, Free Undamped Motion

    • 2 Videos
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2 Videos

  • 9-1 Spring-mass system
  • 9-2 Free undamped motion – Ex. 1

2. Free and Forced Damped Motion

    • 1 Videos
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1 Videos

  • 9-3 Free & Forced damped motion

3. Spring Mass System Example, Pendulum

    • 2 Videos
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2 Videos

  • 9-4 Spring-mass system – Ex’s 2 & 3
  • 9-5 Pendulum

Quiz9

    • 1 Assignment
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1 Assignment

  • Quiz9

Auto Summary

Immerse yourself in the foundational study of Differential Equations with "Differential Equations Part I: Basic Theory," a course designed for practical application across various fields. This engaging program, offered by Coursera, provides essential terminologies, concepts, and methods for solving different types of differential equations, alongside an indispensable understanding of the underlying theory and related applications. Ideal for learners with a background in calculus and basic matrix theory, this course covers determinants, Cramer’s Rule, eigenvalues, and eigenvectors. Over 900 minutes of content, you'll build a solid foundation in these critical mathematical tools, equipping you with the skills needed for practical problem-solving in your field. Available through Coursera's Starter subscription, this foundational level course is perfect for those looking to enhance their mathematical toolkit with a comprehensive introduction to differential equations. Join now and take the first step towards mastering this essential area of mathematics and statistics.

Kwon, Kil Hyun
Instructors

Kwon, Kil Hyun

Kil Hyun Kwon
Instructors

Kil Hyun Kwon