Numerical Methods - Advanced Calculus

Numerical solution of non-linear equations, integration.

48

9 hrs

$ 20.00

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.
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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.

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.

Course Chapters

1
Introduction

Meaning and use of numerical methods.

Chapter lessons

1.Welcome6:52

Welcome to the course and course outline.

2.Definition10:25

The meaning and need for numerical methods.

2
Equations in One Variable (1)

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

Chapter lessons

1.Introduction10:11

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

2.Existence of a solution19:03

Condition for the existence of a solution within an interval.

3.Bisection method24:37

Bisection method of solution of equations in one variable.

4.Worked examples (1)42:06

Worked examples on the bisection method of solution of equations in one variable.

5.Worked examples (2)29:32

More worked examples on the bisection method of solution of equations in one variable.

6.Overview of the bisection method7:11

Advantages and disadvantages of the 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

1.Newton's method28:57

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

2.Worked examples (1)26:46

More worked examples on Newton's method of solution of equations in one variable.

3.Worked examples (2)39:48

More worked examples on Newton's method of solution of equations in one variable.

4.Worked examples (3)26:02

More worked examples on Newton's method of solution of equations in one variable.

5.Overview of Newton's method6:17

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

1.Introduction17:23

An overview of the theory of numerical integration methods.

2.Trapezoidal rule9:48

Integration by the trapezoidal rule.

3.Worked examples (1)34:17

Worked examples on integration by the trapezoidal rule.

5
Integration (2)

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

Chapter lessons

1.Simpson's rule6:50

Integration by Simpson's 1/3 rule.

2.Worked examples (1)32:12

Worked examples on integration by Simpson's 1/3 rule.

3.Worked examples (2)18:35

More worked examples on numerical integration.

4.Worked examples (3)15:48

More worked examples on numerical integration.