University Maths Notes

University Maths Notes: Calculus

L'Hospital's Rule	Variation of Parameters Method – Solving Nonhomogeneous Differential Equations
Variation of Parameters Method – Solving Nonhomogeneous Differential Equations - Examples	Partial Differentiation
The Total Derivative	The Mean Value Theorem
Rolle's Theorem	Cauchy – Euler Equations (1)
Exact Differential Equations	Solving Constant Coefficient Linear Second Order Differential Equations
Green's Theorem	Using Green's Theorem to Find an Area
Series Solutions of Differential Equations	Transforming Variables and Integration – The Jacobian
Transforming Variables and Integration – The Jacobian – An Example	Fourier Series
Finding Fourier Series - Theory	Finding Fourier Series - Examples
Some Basic Fourier Series	The Legendre Equation – Legendre Polynomials
Where Does the Power Series Method for Solving Differential Equations Break Down?	Linearity and Superposition
The Laplacian Operator – A Discussion	Table of Laplace Transforms
Classifying Second Partial Differential Equations in Two Dimensions	Maxima, Minima and Turning Points – the Scond Partials Test
The Laplace Transform	The Equality of Mixed Partial Derivatives
Solving Differential Equations With the Laplace Transformation	Solving Partial Differntial Equations Using the Separation of Variables Method
Differentiating Under the Integral Sign	Level Curves
Lagrange Multipliers	Properties of the Laplace Transformation