Ordinary Differential Equations

Ordinary Differential Equations - Advanced Calculus

A comprehensive treatise of ordinary differential equations covering solutions of first-order and second-order ordinary differential equations, and applications of first-order ordinary differential equations.

40 hrs

$ 10.00

Payment required for enrolment

Enrolment valid for 12 months

This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.

MTH 201: Mathematical Methods I

Comprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

CHE 306: Engineering Analysis II

Advanced engineering mathematics covering numerical and analytical methods of engineering analysis. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

Introduction

Meaning of differential equations, order, degree, solutions, etc., of differential equations.

Chapter lessons

1.Definition17:23

What are differential equations?

2.Ordinary and partial differential equations28:07

Classification of differential equations into ordinary and partial differential equations.

3.Order of differential equations7:45

Meaning of the order of differential equations.

4.Linear and non-linear differential equations32:46

Identifying linear and non-linear differential equations.

5.Degree of differential equations15:37

Identifying the degree of differential equations.

6.Solution of differential equations21:29

Meaning of the solution of differential equations.

7.Worked examples (1)25:57

Worked examples on identifying differential equations and their solutions.

8.Initial-value and boundary-value problems34:45

Meaning of initial-value problems and boundary-value problems.

9.Worked examples (2)18:22

Worked examples on boundary-value and initial-value problems.

10.Notations6:21

An overview of common notations for derivatives.

Solutions of First-Order Ordinary Differential Equations

Analytical solutions of first-order ordinary differential equations, such as variable-separable equations, homogeneous equations, non-homogeneous equations convertible to homogeneous forms, exact differential equations, inexact differential equations, linear differential equations, Bernoulli equation, and Riccati equation.

Chapter lessons

1.Introduction46:24

An introduction to first-order differential equations and their solutions.

2.Variable-separable equations51:28

Solution of variable-separable differential equations.

3.Homogeneous equations1:01:35

Solution of homogeneous differential equations.

4.Non-homogeneous equations1:24:14

Solution of non-homogeneous differential equations reducible to homogeneous form.

5.Exact differential equations58:33

Solution of exact differential equations.

6.Inexact differential equations1:26:19

Inexact differential equations and their solutions with integrating factors.

7.Linear differential equations1:09:04

Solution linear differential equations with integrating factors.

8.Simple non-linear equations (1)48:16

Solution of Bernoulli's ordinary differential equation.

9.Simple non-linear equations (2)1:16:29

Solution of Riccati's ordinary differential equation.

10.More worked examples (1)47:41

More worked examples on solution of first-order ordinary differential equations.

11.More worked examples (2)1:22:30

More worked examples on solution of first-order ordinary differential equations.

12.More worked examples (3)29:18

More worked examples on solution of first-order ordinary differential equations.

Applications of First-Order Ordinary Differential Equations

Applications of first-order ordinary differential equations.

Chapter lessons

1.Orthogonal trajectories1:33:26

Determining the orthogonal trajectories of a family of curves.

2.Oblique trajectories1:13:15

Determining the oblique trajectories of a family of curves.

3.Newton's second law of motion1:00:15

Worked examples on Newton's second law of motion.

4.Exponential growth and decay28:09

Modelling exponential growth and decay with first-order ordinary differential equations.

5.Population growth31:21

Modelling population growth with first-order ordinary differential equations.

6.Radioactive decay37:44

Modelling radioactive decay with first-order ordinary differential equations.

7.Newton's law of cooling58:42

Modelling temperature change problems with first-order ordinary differential equations.

8.Rate of chemical reactions1:24:20

Modelling rate of chemical reactions with first-order ordinary differential equations.

9.Electric circuits1:19:58

Modelling electric circuit problems with first-order ordinary differential equations.

10.More worked examples (1)28:55

More examples on applications of first-order ordinary differential equations.

Solutions of Second-Order Ordinary Differential Equations (1)

Analytical solutions of homogeneous linear second-order ordinary differential equations with constant coefficients.

Chapter lessons

1.Introduction11:13

Meaning of homogeneous and non-homogeneous linear differential equations.

2.Linear dependence29:47

Understanding linear dependence of functions and the Wronskian.

3.General solution of homogeneous equations25:32

Linearly-independent solutions and the general solution of homogeneous linear second-order differential equations.

4.General solution of non-homogeneous equations13:57

General solution of non-homogeneous linear second-order differential equations.

5.Solving homogeneous equations with constant coefficients (1)20:18

How to obtain the auxiliary equation of homogeneous equations with constant coefficients.

6.Solving homogeneous equations with constant coefficients (2)32:24

How to obtain the general solution of homogeneous equations with constant coefficients from the roots of the auxiliary equation.

7.Worked examples (1)21:13

More worked examples on solving homogeneous linear ordinary differential equations with constant coefficients.

8.Worked examples (2)29:35

More worked examples on solving homogeneous linear ordinary differential equations with constant coefficients.

Solutions of Second-Order Ordinary Differential Equations (2)

Analytical solutions of non-homogeneous linear second-order ordinary differential equations by the methods of undetermined coefficients and variation of parameters.

Chapter lessons

1.Introduction17:24

An overview of methods of determining the particular integral.

2.Undetermined coefficients48:31

Solution of non-homogeneous second-order linear ordinary differential equations by the method of undetermined coefficients.

3.Worked examples (1)33:59

Worked examples on the method of undetermined coefficients.

4.Worked examples (2)41:05

More worked examples on the method of undetermined coefficients.

5.Worked examples (3)51:19

More worked examples on the method of undetermined coefficients.

6.Variation of parameters33:53

More worked examples on the method of undetermined coefficients.

7.Worked examples (4)20:49

Worked examples on the method of variation of parameters.