We use the result for inverse Laplace transform of a derivative to find the inverse transforms of g(s)/(s^2+a^2)^2 with g(s) constant, linear or quadratic in s.

We solve a 2nd order, constant coefficient, non-homogeneous ODE with boundary conditions at t = 0 for y and y'.

We use the result for inverse Laplace transform of a derivative to find the inverse transforms of g(s)/(s^2+a^2)^2 with g(s) constant, linear or quadratic in s.

We solve a 2nd order, constant coefficient, non-homogeneous ODE with boundary conditions at t = 0 for y and y'.

This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is an irreducible quadratic function. We complete the square on the denominator, then we integrate by substitution to find the answer.

This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is a linear function. Integration by substitution is used.

This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is a linear function. Integration by substitution is used.

This recording demonstrates how to integrate rational functions where the numerator is a constant and the denominator is an irreducible quadratic function. We complete the square on the denominator, then we integrate by substitution to find the answer.

We prove the formula for sin(A-B) using right-angled triangles then we show how the corresponding formulae for cos(A-B) and sin and cos of A+B can be deduced as a result.

We prove the formula for sin(A-B) using right-angled triangles then we show how the corresponding formulae for cos(A-B) and sin and cos of A+B can be deduced as a result.