Explore

Introduction to Ordinary Differential Equations

Approx. 15 hours to complete

Save Course

Go to Course

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

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

Intermediate

Course 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.

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.

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

Recommended for you

Differential Equations in Action

By the end of this course, you'll develop an intuition for the use of differential equations in the applied sciences. Symplectic Euler Method....

Save Course

Neuronal Dynamics

The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail....

Save Course

Robotics: Mobility

How can robots use their motors and sensors to move around in an unstructured environment? Introduction: Motivation and Background 0. 0....

Save Course

Introduction to Calculus

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce....

Save Course