Introduction to Ordinary Differential Equations
- 4.7
Course Summary
This course covers the basic theory of ordinary differential equations and its applications in a wide range of fields.Key Learning Points
- Learn how to solve ordinary differential equations using various techniques
- Explore the applications of differential equations in various fields such as physics, engineering, and economics
- Gain a deeper understanding of the mathematical theory behind differential equations
Related Topics for further study
- Differential Equations
- Mathematical Modeling
- Numerical Methods
- Applied Mathematics
- Engineering Mathematics
Learning Outcomes
- Solve ordinary differential equations using various techniques
- Understand the applications of differential equations in various fields
- Develop a deeper understanding of the mathematical theory behind differential equations
Prerequisites or good to have knowledge before taking this course
- Calculus
- Linear Algebra
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
- Video Lectures
Similar Courses
- Introduction to Partial Differential Equations
- Differential Equations for Engineers
Related Education Paths
Notable People in This Field
- Dr. Jordan Ellenberg
- Dr. Hannah Fry
Related Books
Description
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.
Outline
- 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
Summary of User Reviews
Discover the world of Ordinary Differential Equations with this comprehensive Coursera course. Students praise the professor's clear explanations and the practical applications of the subject matter.Key Aspect Users Liked About This Course
Many users appreciated the practical applications of the subject matter.Pros from User Reviews
- Clear and concise explanations from the professor
- Good mix of theoretical and practical content
- Assignments and quizzes help reinforce the material
- Great course for beginners and those looking to refresh their knowledge
Cons from User Reviews
- Some users found the pace too slow
- Occasional technical difficulties with the platform
- Limited interaction with other students and the professor
- Some users would have liked more challenging problem sets