Introduction to Numerical Methods (Undergraduate Foundation)

Numerical solution of non-linear equations, integration.

9 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] 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.

[UNILAG, Akoka] MTH 102: Elementary Mathematics II

This learning track is designed to guide first-year students at the University Of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

[UI, Ibadan] MAT 241: Ordinary Differential Equations

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

1. Introduction

This chapter sets the foundation for the entire course. It defines what numerical methods are, explains why they matter, and outlines when and why they are used instead of analytical techniques. We establish the scope, assumptions, and limitations that shape all subsequent methods. If you skip this, you will misapply the rest. By the end of this chapter, you should be able to: – Distinguish between analytical and numerical solutions. – Identify problems best suited for numerical methods. – Recognise key sources of numerical error. – Understand the structure of a typical numerical method.

Chapter lessons

1-1. Welcome

6:52

Welcome to the course and course outline.

1-2. Definition

10:25

Numerical methods are algorithmic procedures that approximate solutions when closed-form answers are unavailable. They convert continuous problems into discrete computations. This lesson defines their scope and purpose.

2. Equations in One Variable (1)

Introduction, existence of solutions, and bisection method of numerical solutions of equations in one variable.

Chapter lessons

2-1. Introduction

10:11

Meaning and examples of equations in one variable, meaning root of an equation and zero of a function.

2-2. Existence of a solution

19:03

Condition for the existence of a solution within an interval.

2-3. Overview of the bisection method

7:11

Advantages and disadvantages of the bisection method of solution of equations in one variable.

2-4. Bisection method

24:37

Bisection method of solution of equations in one variable.

3. Equations in One Variable (2)

Numerical solutions of equations in one variable - Newton-Raphson's iterative method.

Chapter lessons

3-1. Newton's method

28:57

Newton's method of solution of equations in one variable.

3-2. Overview of Newton's method

6:17

Advantages and disadvantages of Newton's method solution of equations in one variable.

4. Integration (1)

Introduction to numerical integration of single-variable functions. Trapezoidal rule.

Chapter lessons

4-1. Introduction

17:23

An overview of the theory of numerical integration methods.

4-2. Trapezoidal rule

9:48

Integration by the trapezoidal rule.

5. Integration (2)

Simpson's 1/3 rule of numerical integration of single-variable functions.

Chapter lessons

5-1. Simpson's rule

6:50

Integration by Simpson's 1/3 rule.