Introduction to Ordinary Differential Equations
- Offered byCoursera
Introduction to Ordinary Differential Equations at Coursera Overview
Duration | 15 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
Introduction to Ordinary Differential Equations at Coursera Highlights
- 25% got a tangible career benefit from this course.
- Earn a shareable certificate upon completion.
Introduction to Ordinary Differential Equations at Coursera Course details
- In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course.
- The lecture is self contained. However, if necessary, you may consult any introductory level text
- on ordinary differential equations. For example, "Elementary Differential Equations and Boundary Value Problems
- by W. E. Boyce and R. C. DiPrima from John Wiley & Sons" is a good source for further study on the subject.
- The course is mainly delivered through video lectures. At the end of each module, there will be a quiz consisting of several problems related to the lecture of the week.
Introduction to Ordinary Differential Equations at Coursera Curriculum
Introduction
1-1 What is a Differentiable Equations?
1-2 Order and Normal Form
1-3 Linear and Nonlinear Equations
1-4 Solution
1-5 Implicit Solution
1-6 Types of Solutions
1-7 Initial Value Problem
1-8 Picard?s Theorem I
1-9 Picard?s Theorem II
Quiz1
First Order Differential Equation 1
2-1 Separable Equations
2-2 Separable Equations - Ex?s 1 & 2
2-3 Separable Equations - Ex?s 3 & 4
2-4 Integrating Factor
2-5 Does IVP Have a Unique Solution?
2-6 Exact Equations I
2-7 Exact Equations II
2-8 Exact Equations ? Ex. 1
2-9 Exact Equations ? Ex. 2
Quiz2
FIRST ORDER DEFERENTIAL EQUATION 2
3-1 Integrating Factor I
3-2 Integrating Factor II
3.3 Integrating Factor III
3-4 Substitutions, Ex 1
3-5 Homogeneous Equations
3-6 Substitutions Ex's 2 & 3
3-7 Bernoulli Equation
3-8 Equations with Linear Coefficients
3-9 Equations with Linear Coefficients - Ex. 5
3-10 Ricatti's Equation - Ex. 6
3-11 Clairaut's Equation
3-12 Clairaut's Equation - Ex. 7
Quiz 3
Mathematical Modeling and Applications
4-1 Radioactive Decay
4-2 Population Dynamics I
4-3 Population Dynamics II
4-4 Population Dynamics III
4-5 Population Dynamics IV
Quiz4
LINEAR SECOND ORDER EQUATIONS 1
5-1 Linear differential equations
5-2 Superposition Principle
5-3 Unique Existence of Solution
5-4 Linear independence
5-5 Wronskian test
Quiz5
Linear Second order equations 2
6-1 Fundamental set of solutions
6-2 General solutions
6-3 Nonhomogeneous equations I
6-4 Nonhomogeneous equations II
6-5 Reduction of order I
6-6 Reduction of order II
6-7 Homogeneous linear equations with constant coefficients
6-8 Homogeneous linear equations ? Example
6-9 Higher order equations
Quiz6
Linear Second order equations 3
7-1 Differential polynomials ? Ex. 1
7-2 Annihilator ? Ex. 2
7-3 Method of undetermined coefficients I
7-4 Method of undetermined coefficients II ? Ex. 3
7-5 Method of undetermined coefficients - Ex. 4
Quiz7
Linear Second order equations 4
8-1 Variation of parameters I
8-2 Variation of parameters II
8-3 Variation of parameters III ? Ex. 1
8-4 Variation of parameters IV ? Ex. 2
Quiz8
APPLICATIONS OF SECOND ORDER EQUATIONS
9-1 Spring-mass system
9-2 Free undamped motion ? Ex. 1
9-3 Free & Forced damped motion
9-4 Spring-mass system ? Ex?s 2 & 3
9-5 Pendulum
Quiz9
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