Part I: Newtonian Mechanics; 1 Introduction; 2 Newton's Three Laws; 3 Energy and Work; 4 Introductory Rotational Dynamics; 5 The Harmonic Oscillator; 6 Wave Mechanics & Elements of Mathematical Physics; Part II: Langrangian Mechanics; 7 Introduction; 8 Coordinates & Constraints; 9 The Stationary Action Principle; 10 Constrained Langrangian Mechanics; 11 Point Transformations in Langrangian Mechanics; 12 The Jacobi Energy Function; 13 Symmetries & Langrangian-Hamiltonian-Jacobi Theory; 14 Near-Equilibrium Oscillations; 15 Virtual Work & d'Alembert's Principle; Part III: Canonical Mechanics; 16 Introduction; 17 The Hamiltonian & Phase Space; 18 Hamiltonian's equations & Routhian Reduction; 19 Poisson Brackets & Angular momentum; 20 Canonical & Gauge Transformations; 21 Hamilton-Jacobi Theory; 22 Liouville's Theorem & Classical Statistical Mechanics; 23 Constrained Hamiltonian Dynamics; 24 Autonomous Geometrical Mehcanics; 25 The Structure of Phase Space; 26 Near-Integrable Systems; Part IV: Classical Field Theory; 27 Introduction; 28 Langrangian Field Theory; 29 Hamiltonian Field Theory; 30 Clssical Electromagnetism; 31 Neother's Theorem for Fields; 32 Classical Path-Integrals; Part V: Preliminary Mathematics; 33 The (Not so?) Basics; 34 Matrices; 35 Partial Differentiation; 36 Legendre Transformations; 37 Vector Calculus; 38 Differential equations; 39 Calculus of Variations; Part VI: Advanced Mathematics; 40 Linear Algebra; 41 Differential Geometry; Part VII: Exam Style Questions; Appendix A Noether's Theorem Explored; Appendix B The Action Principle Explored; Appendix C Useful Relations; Appendxi D Poisson & Nambu Brackets Explored; Appendix Canonical Transformations Explored; Appendix F Action-Angle Variables Explored; Appendix G Statistical Mechanics Explored; Appendix H Biographies
Part I: Newtonian Mechanics; 1 Introduction; 2 Newton's Three Laws; 3 Energy and Work; 4 Introductory Rotational Dynamics; 5 The Harmonic Oscillator; 6 Wave Mechanics & Elements of Mathematical Physics; Part II: Langrangian Mechanics; 7 Introduction; 8 Coordinates & Constraints; 9 The Stationary Action Principle; 10 Constrained Langrangian Mechanics; 11 Point Transformations in Langrangian Mechanics; 12 The Jacobi Energy Function; 13 Symmetries & Langrangian-Hamiltonian-Jacobi Theory; 14 Near-Equilibrium Oscillations; 15 Virtual Work & d'Alembert's Principle; Part III: Canonical Mechanics; 16 Introduction; 17 The Hamiltonian & Phase Space; 18 Hamiltonian's equations & Routhian Reduction; 19 Poisson Brackets & Angular momentum; 20 Canonical & Gauge Transformations; 21 Hamilton-Jacobi Theory; 22 Liouville's Theorem & Classical Statistical Mechanics; 23 Constrained Hamiltonian Dynamics; 24 Autonomous Geometrical Mehcanics; 25 The Structure of Phase Space; 26 Near-Integrable Systems; Part IV: Classical Field Theory; 27 Introduction; 28 Langrangian Field Theory; 29 Hamiltonian Field Theory; 30 Clssical Electromagnetism; 31 Neother's Theorem for Fields; 32 Classical Path-Integrals; Part V: Preliminary Mathematics; 33 The (Not so?) Basics; 34 Matrices; 35 Partial Differentiation; 36 Legendre Transformations; 37 Vector Calculus; 38 Differential equations; 39 Calculus of Variations; Part VI: Advanced Mathematics; 40 Linear Algebra; 41 Differential Geometry; Part VII: Exam Style Questions; Appendix A Noether's Theorem Explored; Appendix B The Action Principle Explored; Appendix C Useful Relations; Appendxi D Poisson & Nambu Brackets Explored; Appendix Canonical Transformations Explored; Appendix F Action-Angle Variables Explored; Appendix G Statistical Mechanics Explored; Appendix H Biographies
