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Differential Equations Part II Series Solutions
  • Level Foundation
  • Duration 14 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

Introduction Video

    • 1 Videos
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1 Videos

  • Introduction Video

Euler Equations

    • 4 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 1

4 Videos

  • 1-1 Euler Equations 1
  • 1-2 Euler Equations 2
  • 1-3 Euler Equations 3
  • 1-4 Power Series 1

1 Readings

  • Lecture Note

Power Series

    • 3 Videos
    • 1 Assignment
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1 Assignment

  • Quiz 2

3 Videos

  • 2-1 Power Series 2
  • 2-2 Power Series 3
  • 2-3 Power Series 4

Solutions about ordinary points

    • 5 Videos
    • 1 Assignment
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1 Assignment

  • Quiz 3

5 Videos

  • 3-1 Power Series 5
  • 3-2 Analyticity
  • 3-3 Singular and Ordinary Points 1
  • 3-4 Solutions about Ordinary Points 2
  • 3-5 Solutions about Ordinary Points 3

Frobenius Theorem

    • 4 Videos
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4 Videos

  • 4-1 Solutions about Ordinary Points 4
  • 4-2 Frobenius Theorem 1
  • 4-3 Frobenius Theorem 2
  • 4-4 Frobenius Theorem 3

Finding a Second Solution

    • 6 Videos
    • 1 Assignment
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1 Assignment

  • Quiz 4

6 Videos

  • 5-1 Frobenius Theorem 4
  • 5-2 Finding a Second Solution 1
  • 5-3 Finding a Second Solution 2
  • 5-4 Finding a Second Solution 3
  • 5-5 Finding a Second Solution 4
  • 5-6 Finding a Second Solution 5

Bessel Functions

    • 5 Videos
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5 Videos

  • 6-1 Bessel Functions 1
  • 6-2 Bessel Functions 2
  • 6-3 Bessel Functions 3
  • 6-4 Bessel Functions 4
  • 6-5 Bessel Functions 5

Legendre Polynomials

    • 5 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Quiz 5

5 Videos

  • 7-1 Bessel Functions 6
  • 7-2 Legendre Polynomials 1
  • 7-3 Legendre Polynomials 2
  • 7-4 Legendre Polynomials 3
  • 7-5 Legendre Polynomials 4

1 Readings

  • Lecture Note

Auto Summary

Explore the foundational concepts and practical applications of Ordinary Differential Equations in this engaging course. Ideal for those with basic calculus and matrix theory knowledge, this 840-minute course offers essential terminologies, methods, and applications. Available on Coursera, with Starter and Professional subscription options. Perfect for learners in Maths & Statistics looking to deepen their understanding.

Kil Hyun Kwon
Instructor

Kil Hyun Kwon