Alder M.D. Multivariate Calculus

2002. — 197 pages.Introduction
Optimisation
The Second Derivative Test
Constrained Optimisation
Lagrangian Multipliers
Fields and Forms
Definitions Galore
Integrating 1-forms (vector fields) over curves
Independence of Parametrisation
Conservative Fields/Exact Forms
Closed Loops and Conservatism
Green’s Theorem
Motivation
Functions as transformations
Change of Variables in Integration
Spin Fields
Green’s Theorem (Classical Version)
Spin fields and Differential 2-forms
The Exterior Derivative
For the Pure Mathematicians
Return to the (relatively) mundane
More on Differential Stretching
Green’s Theorem Again
Stokes’ Theorem (Classical and Modern)
Classical
Modern
Divergence
Fourier Theory
Various Kinds of Spaces
Function Spaces
Applications
Fiddly Things
Odd and Even Functions
Fourier Series
Differentiation and Integration of Fourier Series
Functions of several variables
Partial Differential EquationsThe Diffusion Equation
Intuitive
Saying it in Algebra
Laplace’s Equation
The Wave Equation
Schrodinger’s Equation
The Dirichlet Problem for Laplace’s Equation
Laplace on Disks
Solving the Heat Equation
Solving the Wave Equation
And in Conclusion