Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)

This course provides a complete guide to solving ordinary differential equations (ODEs). It covers the classification of differential equations and details the solution methods for first-order equations, including separable, homogeneous, exact, and linear types. The course then moves to second-order linear equations with constant coefficients and covers the methods of undetermined coefficients and variation of parameters. Differential equations are the mathematical language used to model dynamic systems in science and engineering. They are used to describe the motion of objects, the flow of electric circuits, population growth, radioactive decay, and chemical reaction rates. A command of this subject is a non-negotiable requirement for any serious study in physics, engineering, or applied mathematics. By the end of this course, you will be able to classify any ordinary differential equation by its order, degree, and linearity. You will be able to solve a wide variety of first-order ODEs and constant-coefficient second-order ODEs. You will also be able to model and solve real-world problems, such as orthogonal trajectories, exponential growth and decay, and simple electric circuits. This course is for undergraduate students in mathematics, physics, engineering, and chemistry. It is a standard module in any mathematical methods curriculum and assumes a full prerequisite knowledge of single and multivariable calculus. It is an essential foundation for the study of partial differential equations, control theory, and advanced physics.

130

40 hrs

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.
[OAU, Ife] CHE 306: Engineering Analysis II
[OAU, Ife] 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.

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.

[OAU, Ife] MTH 201: Mathematical Methods I
[OAU, Ife] MTH 201: Mathematical Methods I
This learning track delivers the complete mathematical toolkit required for a university-level science, engineering, or computing degree. It systematically covers the entire MTH 201 curriculum, building from the foundational principles of single-variable calculus - functions, limits, continuity, and differentiability - to the advanced methods of multivariable calculus, infinite series, numerical methods, and ordinary differential equations. This is the definitive preparation for advanced quantitative study. This programme is designed for second-year students offering MTH 201 at Obafemi Awolowo University, Ile-Ife, Nigeria. It is also helpful for any student in a STEM field - including physics, engineering, and computer science - who requires a rigorous and comprehensive command of calculus and its applications. This track delivers a full skill set in mathematical analysis and applied problem-solving. Graduates will be able to solve a wide range of problems, from optimising multivariable functions to modelling dynamic systems with differential equations and testing the convergence of infinite series. This programme directly prepares students for success in advanced courses in vector calculus, partial differential equations, and real analysis, providing the necessary foundation for a career in engineering, data science, or theoretical physics.

This learning track delivers the complete mathematical toolkit required for a university-level science, engineering, or computing degree. It systematically covers the entire MTH 201 curriculum, building from the foundational principles of single-variable calculus - functions, limits, continuity, and differentiability - to the advanced methods of multivariable calculus, infinite series, numerical methods, and ordinary differential equations. This is the definitive preparation for advanced quantitative study. This programme is designed for second-year students offering MTH 201 at Obafemi Awolowo University, Ile-Ife, Nigeria. It is also helpful for any student in a STEM field - including physics, engineering, and computer science - who requires a rigorous and comprehensive command of calculus and its applications. This track delivers a full skill set in mathematical analysis and applied problem-solving. Graduates will be able to solve a wide range of problems, from optimising multivariable functions to modelling dynamic systems with differential equations and testing the convergence of infinite series. This programme directly prepares students for success in advanced courses in vector calculus, partial differential equations, and real analysis, providing the necessary foundation for a career in engineering, data science, or theoretical physics.

Course Chapters

1. Introduction
9
3

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

Chapter lessons

1-1. Definition
17:23

What are differential equations?

1-2. Ordinary and partial differential equations
28:07

Classification of differential equations into ordinary and partial differential equations.

1-3. Order of differential equations
7:45

Meaning of the order of differential equations.

1-4. Linear and non-linear differential equations
32:46

Identifying linear and non-linear differential equations.

1-5. Degree of differential equations
15:37

Identifying the degree of differential equations.

1-6. Solution of differential equations (1)
21:29

Meaning of the solution of differential equations.

1-7. Solution of differential equations (2)
8:06

How to obtain a differential equation from its known general solution.

1-8. Initial-value and boundary-value problems
34:45

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

1-9. Notations
6:21

An overview of common notations for derivatives.

2. Solutions of First-Order Ordinary Differential Equations
9
3

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

2-1. Introduction
46:24

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

2-2. Variable-separable equations
51:28

Solution of variable-separable differential equations.

2-3. Homogeneous equations
1:01:35

Solution of homogeneous differential equations.

2-4. Non-homogeneous equations
1:24:14

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

2-5. Exact differential equations
58:33

Solution of exact differential equations.

2-6. Inexact differential equations
1:26:19

Inexact differential equations and their solutions with integrating factors.

2-7. Linear differential equations
1:09:04

Solution linear differential equations with integrating factors.

2-8. Simple non-linear equations (1)
48:16

Solution of Bernoulli's ordinary differential equation.

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

Solution of Riccati's ordinary differential equation.

3. Applications of First-Order Ordinary Differential Equations
9
1

Applications of first-order ordinary differential equations.

Chapter lessons

3-1. Orthogonal trajectories
1:33:26

Determining the orthogonal trajectories of a family of curves.

3-2. Oblique trajectories
1:13:15

Determining the oblique trajectories of a family of curves.

3-3. Newton's second law of motion
1:00:15

Worked examples on Newton's second law of motion.

3-4. Exponential growth and decay
28:09

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

3-5. Population growth
31:21

Modelling population growth with first-order ordinary differential equations.

3-6. Radioactive decay
37:44

Modelling radioactive decay with first-order ordinary differential equations.

3-7. Newton's law of cooling
58:42

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

3-8. Rate of chemical reactions
1:24:20

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

3-9. Electric circuits
1:19:58

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

4. Solutions of Second-Order Ordinary Differential Equations (1)
6
2

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

Chapter lessons

4-1. Introduction
11:13

Meaning of homogeneous and non-homogeneous linear differential equations.

4-2. Linear dependence
29:47

Understanding linear dependence of functions and the Wronskian.

4-3. General solution of homogeneous equations
25:32

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

4-4. General solution of non-homogeneous equations
13:57

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

4-5. Solving homogeneous equations with constant coefficients (1)
20:18

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

4-6. 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.

5. Solutions of Second-Order Ordinary Differential Equations (2)
3
4

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

Chapter lessons

5-1. Introduction
17:24

An overview of methods of determining the particular integral.

5-2. Undetermined coefficients
48:31

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

5-3. Variation of parameters
33:53

More worked examples on the method of undetermined coefficients.