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Joule Physics Laboratory    

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

Scalar product of vectors Maths tutorial - scalar product of vectors

Vector 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 - Tutorial 1

Integration by substitution II

Integration by substitution - tutorial 2 Integration by substitution - Tutorial 2

Integration by substitution III

Integration by substitution - tutorial 3 Integration by substitution - Tutorial 3

Integration of algebraic fractions

Integration of algebraic fractions Maths tutorial - integration of algebraic fractions

Integration using trig identities

Integration using trig identities Maths tutorial - integration using trig identities

Integration by parts

Integration by parts Maths tutorial - integration by parts

 

Ordinary Differential Equation (ODE) - Maths Tutorials

ODE solution by direct integration

Ordinary differential equations - direct integration Maths tutorial - direct integration (ODE's)

ODE solution by separation of variables

Ordinary differential equations - separation of variables Maths tutorial - separation of variables (ODE's)

Solution of ODE's involving homogeneous functions

Ordinary differential equations - homogeneous functions Maths tutorial - homogeneous functions (ODE's)

ODE solution by integrating factor method

Ordinary differential equations - integrating factor Maths tutorial - integrating factor method (ODE's)

Bernoulli differential equations

Bernoulli differential equations Maths tutorial - Bernoulli differential equations

Exact differential equations

Exact differential equations Maths tutorial - exact differential equations

Second order differential equations I

Second order ordinary differential equations I Maths tutorial - second order, RHS=0 (ODE's)

Second order differential equations II

Second order ordinary differential equations II Maths tutorial - second order, RHS not 0 (ODE's)

 

Power Series and Fourier Series - Maths Tutorials

Power series tutorial

Power series tutorial Maths tutorial - using power series

Fourier series tutorial

Fourier series tutorial Maths tutorial - using Fourier series