Numerical Methods - Advanced Calculus

Numerical solution of non-linear equations, integration.

43

9 hrs

$ 8.58

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.
MTH 201: Mathematical Methods I
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.

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.

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.