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

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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.

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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.

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Comprehensive treatise of advanced calculus covering ordinary differential equations, finite differences, difference equations and numerical integration. Curated for second-year students of engineering and physical sciences at University of Ibadan, Nigeria. Students and professionals with a 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.