# Mathematics Hyper-Tutorials

Contents - Background | Vector Product Maths Tutorials | Integration Maths Tutorials | Ordinary Differential Equation Maths Tutorials | Power Series and Fourier Series Maths Tutorials

## Maths Tutorials - Background

Feel free to use and distribute these tutorials, keeping each intact. They were developed as part of the FDTL4 PPLATO (Promoting Physics Learning And Teaching Opportunities) project, led by Dr Mike Tinker. Some of the tutorials are co-authored with Dr Silvia Dalla. Click on any of the tutorials below to launch it. They are hyper-linked pdf files that use AcroTeX (by D.P. Story).

## Vector Product - Maths Tutorials

### Scalar product of vectors

Maths tutorial - scalar product of vectors

### Vector product of vectors

Maths tutorial - vector product of vectors

## Integration - Maths Tutorials

### Integration by substitution I

Integration by substitution - Tutorial 1

### Integration by substitution II

Integration by substitution - Tutorial 2

### Integration by substitution III

Integration by substitution - Tutorial 3

### Integration of algebraic fractions

Maths tutorial - integration of algebraic fractions

### Integration using trig identities

Maths tutorial - integration using trig identities

### Integration by parts

Maths tutorial - integration by parts

## Ordinary Differential Equation (ODE) - Maths Tutorials

### ODE solution by direct integration

Maths tutorial - direct integration (ODE's)

### ODE solution by separation of variables

Maths tutorial - separation of variables (ODE's)

### Solution of ODE's involving homogeneous functions

Maths tutorial - homogeneous functions (ODE's)

### ODE solution by integrating factor method

Maths tutorial - integrating factor method (ODE's)

### Bernoulli differential equations

Maths tutorial - Bernoulli differential equations

### Exact differential equations

Maths tutorial - exact differential equations

### Second order differential equations I

Maths tutorial - second order, RHS=0 (ODE's)

### Second order differential equations II

Maths tutorial - second order, RHS not 0 (ODE's)

## Power Series and Fourier Series - Maths Tutorials

### Power series tutorial

Maths tutorial - using power series

### Fourier series tutorial

Maths tutorial - using Fourier series