DIV GRAD CURL ARE DEAD

Table of Contents

VERSION 2.0--October--, 1995

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• Preface
• Introduction

CHAPTER ZERO. PROLEGOMENA

• Patterns
• Linear Algebra
• Affine Algebra
• Computer Algebra Systems

CHAPTER ONE. CALCULUS

• Vectors
• Calculus of Curves
• What is Calculus?
• Linear Transformations
• The Differential in Optics

CHAPTER TWO. GRADIENTS AND FLOW

• The Differential of a Function
• The algebra of 1--forms
• 1--forms in mechanics
• Flow in 2D
• Density
• Flow in 3D
• Drawing Vectors: The Eight Icons

CHAPTER THREE. DIFFERENTIAL FORMS

• Ordinary Differential Forms
• Twisted Forms
• Maps and Pullback

CHAPTER FOUR. CALCULUS OF FORMS

• Exterior Derivatives
• Integrals
• Stokes' theorem
• Symmetries and conservation laws
• Inverse of Stokes' theorem
• Delta Functions

CHAPTER FIVE. GEOMETRY WITH FORMS

• Tensor algebra
• Star Operator
• Symmetry and Lie Derivatives
• Old Vector Calculus
• Simplicial Calculus

CHAPTER SIX. ELECTRODYNAMICS

• Maxwell's equations
• Electrostatics
• Energy in Electrostatics
• Magnetism
• Maxwell's equations in spacetime

CHAPTER SEVEN. MECHANICS

• Hamiltonian Mechanics
• Lagrangian Mechanics
• Fluid Mechanics

CHAPTER EIGHT. WAVES

• Dispersive Waves
• Group Velocity
• Water Waves

APPENDICES

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