Introduction to Numerical Methods (Undergraduate Foundation)

This course covers numerical methods for solving problems that have no exact analytical solution. It is a practical study of iterative approximation techniques. The material is focused on two core areas: finding the roots of single-variable equations using the Bisection and Newton's methods, and approximating definite integrals using the Trapezoidal and Simpson's rules. Numerical methods are the foundation of all modern computational problem-solving in science, engineering, and finance. These are the algorithms that power computer simulations, engineering design software, and financial modelling tools. The ability to find approximate solutions to complex equations is a fundamental skill for any technical or scientific professional. By the end of this course, you will be able to apply the Bisection and Newton's methods to find the roots of single-variable equations. You will also be able to use the Trapezoidal and Simpson's rules to calculate the approximate value of definite integrals, providing a core toolkit for numerical approximation. This course is for undergraduate foundation students in engineering, physics, and computer science. It is an essential topic for anyone who will use computational tools to solve mathematical problems. A solid understanding of single-variable calculus is a prerequisite.

9 hrs

Payment required for enrolment

Enrolment valid for 12 months

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

[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.

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.