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2C2 Multivariate Calculus
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- Contents
- Chapter 1 Introduction
- Chapter 2 Optimisation
- 2.1 The Second Derivative Test
- Chapter 3 Constrained Optimisation
- 3.1 Lagrangian Multipliers
- Chapter 4 Fields and Forms
- 4.1 Definitions Galore
- 4.2 Integrating 1-forms (vector fields) over curves.
- 4.3 Independence of Parametrisation
- 4.4 Conservative Fields/Exact Forms
- 4.5 Closed Loops and Conservatism
- Chapter 5 Green’s Theorem
- 5.1 Motivation
- 5.2 Green’s Theorem (Classical Version)
- 5.3 Spin fields and Differential 2-forms
- 5.4 More on Differential Stretching
- 5.5 Green’s Theorem Again
- Chapter 6 Stokes’ Theorem (Classical and Modern)
- 6.1 Classical
- 6.2 Modern Theorem
- 6.3 Divergence
- Chapter 7 Fourier Theory
- 7.1 Various Kinds of Spaces
- 7.2 Function Spaces
- 7.3 Applications
- 7.4 Fiddly Things
- 7.5 Odd and Even Functions
- 7.6 Fourier Series
- 7.7 Differentiation and Integration of Fourier Series
- 7.8 Functions of several variables
- Chapter 8 Partial Differential Equations
- 8.1 Introduction
- 8.2 The Diffusion Equation
- 8.3 Laplace’s Equation
- 8.4 The Wave Equation
- 8.5 Schr¨odinger’s Equation
- 8.6 The Dirichlet Problem for Laplace’s Equation
- 8.7 Laplace on Disks
- 8.8 Solving the Heat Equation
- 8.9 Solving the Wave Equation
- 8.10 And in Conclusion..