A review of the methods of integration of single-variable functions.

A review of the techniques of integration of single-variable real-valued functions.

Techniques of integration (2)

Overview of common functions and their integrals.

Standard integrals

Techniques of integration (1)

Meaning of integration and its associated symbols.

Definition

Welcome to the course and overview of course content.

Welcome

Techniques of integration (3)

Properties of integrals of real-valued single-variable functions.

Properties of integrals

Introduction

Meaning and methods of evaluation of line integrals.

Meaning of line integral, in contrast to a definite integral along the x-axis.

How to evaluate line integrals in two and three dimensions.

Evaluation

Properties

Worked examples on evaluating line integrals in two and three dimensions.

Worked examples (1)

More worked examples on evaluating line integrals in two and three dimensions.

Worked examples (2)

Worked examples (3)

Line Integrals

Meaning, methods of evaluation and applications of double integrals.

Meaning and symbols for double integrals.

How to evaluate double integrals by change of variables.

Change of variables

Worked examples on evaluation of double integrals.

More worked examples on evaluation of double integrals.

Double Integrals

Applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.

Calculation of areas in Cartesian and polar coordinates by double integration.

Areas

Calculation of volume beneath a surface and above a region by double integration.

Volumes

Calculation of total mass and centre of gravity by double integration.

Mass and centre of gravity

Meaning and calculation of moments of inertia by double integration.

Moments of inertia

Worked examples on applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.

More worked examples on applications of double integrals to areas, volumes, total masses, centres of gravity, moments of inertia, etc.

Applications of Double Integrals

Meaning and methods of evaluation of surface integrals.

Meaning and symbols for surface integrals, in contrast to line integrals.

Parametric representation of common surfaces.

Parametric representation (1)

Parametric representation (2)

Worked examples on evaluation and applications of surface integrals.

More worked examples on evaluation and applications of surface integrals.

Surface Integrals

Meaning and methods of evaluation of triple integrals.

Meaning and symbols for triple integrals, in contrast to double integrals.

Worked examples on evaluation and applications of triple integrals.

More worked examples on evaluation and applications of triple integrals.

Triple Integrals

Multiple integration; line, surface and volume integrals.

Tutorials for undergraduates in engineering and physical sciences.

Multiple Integration and Its Applications

One-time payment