The meaning and need for numerical methods.

Definition and use

Introduction

Numerical solutions of equations in one variable.

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

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

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

Bisection method of solution of equations in one variable.

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

Condition for the existence of a solution within an interval.

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

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

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

Introduction to numerical methods  for interpolation and polynomial approximation.

Numerical differentiation using finite differences.

Introduction to numerical methods  for differentiation.

Numerical integration of single-variable functions.

An overview of the theory of numerical integration methods.

More worked examples on numerical integration.

Worked examples on integration by the trapezoidal rule.

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

Numerical solutions of initial-value problems.

Introduction to numerical methods  for ordinary differential equations.

Numerical solution of non-linear equations, integration.

Tutorials for undergraduates in engineering and physical sciences.