Monthly Subscription Starting at AED 99 + VAT

Differential Equations Part I Basic Theory
  • Level Foundation
  • المدة 15 ساعات hours
  • الطبع بواسطة Korea Advanced Institute of Science and Technology(KAIST)
  • Offered by

عن

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.

الوحدات

1. Basic Terminologies

    • 3 Videos
Show info about module content

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
Show info about module content

2 Videos

  • 1-4 Solution
  • 1-5 Implicit Solution

3. Various Solutions, Initial Value Problem

    • 2 Videos
Show info about module content

2 Videos

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

4. Picard Theorem and Examples

    • 2 Videos
Show info about module content

2 Videos

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

Quiz1

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz1

1. Separable Equations

    • 2 Videos
Show info about module content

2 Videos

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

2. Separable and Linear Equations

    • 2 Videos
Show info about module content

2 Videos

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

3. Exact Equations I

    • 2 Videos
Show info about module content

2 Videos

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

4. Exact Equations II

    • 1 Videos
Show info about module content

1 Videos

  • 2-7 Exact Equations II

5. Examples

    • 2 Videos
Show info about module content

2 Videos

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

Quiz2

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz2

1. Integrating Factor I & II

    • 2 Videos
Show info about module content

2 Videos

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

2. Integrating Factor III, Substitutions

    • 2 Videos
Show info about module content

2 Videos

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

3. Homogeneous Equations

    • 2 Videos
Show info about module content

2 Videos

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

4. Bernoulli’s equations

    • 1 Videos
Show info about module content

1 Videos

  • 3-7 Bernoulli Equation

5. Equations with linear coefficients

    • 2 Videos
Show info about module content

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
Show info about module content

3 Videos

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

Quiz3

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz 3

1. Radioactive Decay, Population Dynamics I

    • 2 Videos
Show info about module content

2 Videos

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

2. Population Dynamics II & III

    • 2 Videos
Show info about module content

2 Videos

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

3. Population Dynamics IV

    • 1 Videos
Show info about module content

1 Videos

  • 4-5 Population Dynamics IV

Quiz4

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz4

1. Linear Differential Equations, Superposition Principle

    • 2 Videos
Show info about module content

2 Videos

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

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

    • 3 Videos
Show info about module content

3 Videos

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

Quiz5

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz5

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

    • 2 Videos
Show info about module content

2 Videos

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

2. Nonhomogeneous Equations I & II

    • 2 Videos
Show info about module content

2 Videos

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

3. Reduction of Order I & II

    • 2 Videos
Show info about module content

2 Videos

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

4. Homogeneous Linear Equations with Constant Coefficients

    • 1 Videos
Show info about module content

1 Videos

  • 6-7 Homogeneous linear equations with constant coefficients

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

    • 2 Videos
Show info about module content

2 Videos

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

Quiz6

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz6

1. Method of Undetermined Coefficients I

    • 3 Videos
Show info about module content

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
Show info about module content

2 Videos

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

Quiz7

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz7

1. Variation of Parameters I & II

    • 2 Videos
Show info about module content

2 Videos

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

2. Variation of Parameters III & IV

    • 2 Videos
Show info about module content

2 Videos

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

Quiz8

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz8

1. Spring mass system, Free Undamped Motion

    • 2 Videos
Show info about module content

2 Videos

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

2. Free and Forced Damped Motion

    • 1 Videos
Show info about module content

1 Videos

  • 9-3 Free & Forced damped motion

3. Spring Mass System Example, Pendulum

    • 2 Videos
Show info about module content

2 Videos

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

Quiz9

    • 1 Assignment
Show info about module content

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