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Differential Equations Part III Systems of Equations
  • Level Professional
  • المدة 10 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. Table of Contents Differential Equations Part I Basic Theory Chapter 1 Introduction Chapter 2 First Order Differential Equations Chapter 3 Mathematical Modelling and Applications Chapter 4 Linear Second Order Equations Chapter 5 Applications of Second Order Equations Differential Equations Part II Series Solutions Chapter 1 Euler Equations Chapter 2 Series Solutions of Linear Equations Chapter 3 Special Functions: Bessel Functions and Legendre Polynomials Differential Equations Part III Systems of Differential Equations Chapter 1 Systems of Linear Equations Chapter 2 Stability of Autonomous Systems

الوحدات

Introduction

    • 6 Videos
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6 Videos

  • Introduction
  • 1-1 Basic Theory 1
  • 1-2 Basic Theory 2
  • 1-3 Basic Theory 3
  • 1-4 Basic Theory 4
  • 1-5 Basic Theory 5

Week 2

    • 7 Videos
    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz 1

7 Videos

  • 2-1 Homogeneous Linear Systems 1
  • 2-2 Homogeneous Linear Systems 2
  • 2-3 Homogeneous Linear Systems 3
  • 2-4 Homogeneous Linear Systems 4
  • 2-5 Homogeneous Linear Systems 5
  • 2-6 Homogeneous Linear Systems 6
  • 2-7 Homogeneous Linear Systems 7

Week 3

    • 6 Videos
    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz 2

6 Videos

  • 3-1 Nonhomogeneous Linear Systems 1
  • 3-2 Nonhomogeneous Linear Systems 2
  • 3-3 Nonhomogeneous Linear Systems 3
  • 3-4 Nonhomogeneous Linear Systems 4
  • 3-5 Nonhomogeneous Linear Systems 5
  • 3-6 Nonhomogeneous Linear Systems 6

1 Readings

  • Lecture Note

Untitled Lesson

    • 5 Videos
Show info about module content

5 Videos

  • 4-1 Introduction 1
  • 4-2 Introduction 2
  • 4-3 Introduction 3
  • 4-4 Linear Systems 1
  • 4-5 Linear Systems 2

Untitled Lesson

    • 5 Videos
Show info about module content

5 Videos

  • 5-1 Linear Systems 3
  • 5-2 Linear Systems 4
  • 5-3 Nonlinear Systems 1
  • 5-4 Nonlinear Systems 2
  • 5-5 Nonlinear Systems 3

Untitled Lesson

    • 5 Videos
    • 1 Readings
    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz 3

5 Videos

  • 6-1 Nonlinear Systems 4
  • 6-2 Nonlinear Systems 5
  • 6-3 Nonlinear Systems 6
  • 6-4 Nonlinear Systems 7
  • 6-5 Nonlinear Systems 8

1 Readings

  • Lecture Note

Auto Summary

Explore the practical world of differential equations with this comprehensive course tailored for professionals needing hands-on applications in their fields. Delve into essential terminologies, concepts, and solution methods, guided by the expert instructor. With a focus on systems of equations, this course covers linear systems, stability of autonomous systems, and more. Spanning 600 minutes, it’s ideal for those with a calculus and basic matrix theory background. Available via Coursera, the course offers a flexible starter subscription. Perfect for professionals aiming to deepen their mathematical expertise.

Kil Hyun Kwon
Instructor

Kil Hyun Kwon