Chapter 1. Mathematical Thinking
1.1 The NCAA March Madness Problem
1.2 Gauss and the Arithmetic Series
1.5 Einstein’s Velocity Addition Law
1.7 Fibonacci Numbers and the Golden Ratio
1.9 Function Equal to Its Derivative
1.10 Stirling’s Approximation for!
1.11 Potential and Kinetic Energies
1.12 Riemann Zeta Function and Prime Numbers
1.14 A Note on Mathematical Rigor
3.2 Legal and Illegal Algebraic Manipulations
3.8 Factorials, Permutations and Combinations
4.7 Trigonometry in the Complex Plane
5.4 Conic Sections in Polar Coordinates
6.3 Differential and Integral Calculus
6.4 Basic Formulas of Differential Calculus
6.8 Curvature, Maxima and Minima
6.10 Gaussian and Error Functions
Chapter 7. Series and Integrals
7.5 Bernoulli and Euler Numbers
7.10 Generalized Fourier Expansions
Chapter 8. Differential Equations
8.1 First-Order Differential Equations
8.4 Second-Order Differential Equations
8.5 Some Examples from Physics
9.2 Further Properties of Matrices
9.7 Similarity Transformations
9.8 Matrix Eigenvalue Problems
9.9 Diagonalization of Matrices
9.10 Four-Vectors and Minkowski Spacetime
10.3 Mathematical Theory of Groups
10.4 Representations of Groups
10.6 Group Theory in Quantum Mechanics
10.7 Molecular Symmetry Operations
Chapter 11. Multivariable Calculus
11.5 Spherical Polar Coordinates
12.4 Triple Products of Vectors
12.5 Vector Velocity and Acceleration
12.8 Gradient of a Scalar Field
12.9 Divergence of a Vector Field
12.12 Covariant Electrodynamics
Chapter 13. Partial Differential Equations and Special Functions
13.1 Partial Differential Equations
13.5 Vibration of a Circular Membrane
13.7 Laplace’s Equation in Spherical Coordinates
13.10 Spherical Bessel Functions
13.13 Hypergeometric Functions
14.2 Derivative of an Analytic Function
14.5 Cauchy’s Integral Formula
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