Preface Notation 1 Introduction 1.1 Vector （linear） spaces 1.2 The scalar product 1.3 Complex numbers 1.4 Quaternions 1.5 The cross product 1.6 The outer product 1.7 Notes 1.8 Exercises 2 Geometric algebra in two and three dimensions 2.1 A new product for vectors 2.2 An outline of geometric algebra 2.3 Geometric algebra of the plane 2.4 The geometric algebra of space 2.5 Conventions 2.6 Reflections 2.7 Rotations 2.8 Notes 2.9 Exercises 3 Classical mechanics 3.1 Elementary principles 3.2 Two-body central force interactions 3.3 Celestial mechanics and perturbations 3.4 Rotating systems and rigid-body motion 3.5 Notes 3.6 Exercises 4 Foundations of geometric algebra 4.1 Axiomatic development 4.2 Rotations and refiections 4.3 Bases， frames and components 4.4 Linear algebra 4.5 Tensors and components 4.6 Notes 4.7 Exercises 5 Relativity and spacetime 5.1 An algebra for spacetime 5.2 Observers, trajectories and frames 5.3 Lorentz transformations 5.4 The Lorentz group 5.5 Spacetime dynamics 5.6 Notes 5.7 Exercises 6 Geometric calculus 6.1 The vector derivative 6.2 Curvilinear coordinates 6.3 Analytic functions 6.4 Directed integration theory 6.5 Embedded surfaces and vector manifolds
6.6 Elasticity 6.7 Notes 6.8 Exercises 7 Classical electrodynamics 7.1 Maxwell's equations 7.2 Integral and conservation theorems 7.3 The electromagnetic field of a point charge 7.4 Electromagnetic waves 7.5 Scattering and diffraction 7.6 Scattering 7.7 Notes 7.8 Exercises 8 Quantum theory and spinors 8.1 Non-relativistic quantum spin 8.2 Relativistic quantum states 8.3 The Dirac equation 8.4 Central potentials 8.5 Scattering theory 8.6 Notes 8.7 Exercises 9 Multiparticle states and quantum entanglement 9.1 Many-body quantum theory 9.2 Multiparticle spacetime algebra 9.3 Systems of two particles 9.4 Relativistic states and operators 9.5 Two-spinor calculus 9.6 Notes 9.7 Exercises 10 Geometry 10.1 Projective geometry 10.2 Conformal geometry 10.3 Conformal transformations 10.4 Geometric primitives in conformal space 10.5 Intersection and reflection in conformal space 10.6 Non-Euclidean geometry 10.7 Spacetime conformal geometry 10.8 Notes 10.9 Exercises 11 Further topics in calculus and group theory 11.1 Multivector calculus 11.2 Grassmann calculus 11.3 Lie groups 11.4 Complex structures and unitary groups 11.5 The generallinear group 11.6 Notes 11.7 Exercises 12 Lagrangian and Hamiltonian techniques 12.1 The Euler-Lagrange equations 12.2 Classical models for spin-1／2 particles 12.3 Hamiltonian techniques
12.4 Lagrangian field theory 12.5 Notes 12.6 Exercises 13 Symmetry and gauge theory 13.1 Conservation laws in field theory 13.2 Electromagnetism 13.3 Dirac theory 13.4 Gauge principles for gravitation 13.5 The gravitational field equations 13.6 The structure of the Riemann tensor 13.7 Notes 13.8 Exercises 14 Gravitation 14.1 Solving the field equations 14.2 Spherically-symmetric systems 14.3 Schwarzschild black holes 14.4 Quantum mechanics in a black hole background 14.5 Cosmology 14.6 Cylindrical systems 14.7 Axially-symmetric systems 14.8 Notes 14.9 Exercises Bibliography Index
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