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Guide to essential math: a review for physics, chemistry and engineering students
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Edition
1st ed.
Language
English
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Table of Contents
From the Book - 1st ed.
To the Reader
1. Mathematical Thinking
1.1. The NCAA March Madness Problem
1.2. Gauss and the Arithmetic Series
1.3. The Pythagorean Theorem
1.4. Torus Area and Volume
1.5. Einstein's Velocity Addition Law
1.6. The Birthday Problem
1.7. Fibonacci Numbers and the Golden Ratio
1.8. [characters not reproducible] [pi] in the Gaussian Integral
1.9. Function Equal to Its Derivative
1.10. Log of N Factorial for Large N
1.11. Potential and Kinetic Energies
1.12. Riemann Zeta Function and Prime Numbers
1.13. How to Solve It
1.14. A Note on Mathematical Rigor
2. Numbers
2.1. Integers
2.2. Primes
2.3. Divisibility
2.4. Rational Numbers
2.5. Exponential Notation
2.6. Powers of 10
2.7. Binary Number System
2.8. Infinity
3. Algebra
3.1. Symbolic Variables
3.2. Legal and Illegal Algebraic Manipulations
3.3. Factor-Label Method
3.4. Powers and Roots
3.5. Logarithms
3.6. The Quadratic Formula
3.7. Imagining i
3.8. Factorials, Permutations, and Combinations
3.9. The Binomial Theorem
3.10. e Is for Euler
4. Trigonometry
4.1. What Use Is Trigonometry?
4.2. The Pythagorean Theorem
4.3. [pi] in the Sky
4.4. Sine and Cosine
4.5. Tangent and Secant
4.6. Trigonometry in the Complex Plane
4.7. de Moivre's Theorem
4.8. Euler's Theorem
4.9. Hyperbolic Functions
5. Analytic Geometry
5.1. Functions and Graphs
5.2. Linear Functions
5.3. Conic Sections
5.4. Conic Sections in Polar Coordinates
6. Calculus
6.1. A Little Road Trip
6.2. A Speedboat Ride
6.3. Differential and Integral Calculus
6.4. Basic Formulas of Differential Calculus
6.5. More on Derivatives
6.6. Indefinite Integrals
6.7. Techniques of Integration
6.8. Curvature, Maxima, and Minima
6.9. The Gamma Function
6.10. Gaussian and Error Functions
7. Series and Integrals
7.1. Some Elementary Series
7.2. Power Series
7.3. Convergence of Series
7.4. Taylor Series
7.5. L'Hopital's Rule
7.6. Fourier Series
7.7. Dirac Deltafunction
7.8. Fourier Integrals
7.9. Generalized Fourier Expansions
7.10. Asymptotic Series
8. Differential Equations
8.1. First-Order Differential Equations
8.2. AC Circuits
8.3. Second-Order Differential Equations
8.4. Some Examples from Physics
8.5. Boundary Conditions
8.6. Series Solutions
8.7. Bessel Functions
8.8. Second Solution
9. Matrix Algebra
9.1. Matrix Multiplication
9.2. Further Properties of Matrices
9.3. Determinants
9.4. Matrix Inverse
9.5. Wronskian Determinant
9.6. Special Matrices
9.7. Similarity Transformations
9.8. Eigenvalue Problems
9.9. Group Theory
9.10. Minkowski Spacetime
10. Multivariable Calculus
10.1. Partial Derivatives
10.2. Multiple Integration
10.3. Polar Coordinates
10.4. Cylindrical Coordinates
10.5. Spherical Polar Coordinates
10.6. Differential Expressions
10.7. Line Integrals
10.8. Green's Theorem
11. Vector Analysis
11.1. Scalars and Vectors
11.2. Scalar or Dot Product
11.3. Vector or Cross Product
11.4. Triple Products of Vectors
11.5. Vector Velocity and Acceleration
11.6. Circular Motion
11.7. Angular Momentum
11.8. Gradient of a Scalar Field
11.9. Divergence of a Vector Field
11.10. Curl of a Vector Field
11.11. Maxwell's Equations
11.12. Covariant Electrodynamics
11.13. Curvilinear Coordinates
11.14. Vector Identities
12. Partial Differential Equations and Special Functions
12.1. Partial Differential Equations
12.2. Separation of Variables
12.3. Special Functions
12.4. Leibniz's Formula
12.5. Vibration of a Circular Membrane
12.6. Bessel Functions
12.7. Laplace's Equation in Spherical Coordinates
12.8. Legendre Polynomials
12.9. Spherical Harmonics
12.10. Spherical Bessel Functions
12.11. Hermite Polynomials
12.12. Laguerre Polynomials
13. Complex Variables
13.1. Analytic Functions
13.2. Derivative of an Analytic Function
13.3. Contour Integrals
13.4. Cauchy's Theorem
13.5. Cauchy's Integral Formula
13.6. Taylor Series
13.7. Laurent Expansions
13.8. Calculus of Residues
13.9. Multivalued Functions
13.10. Integral Representations for Special Functions
About the Author
Index
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ISBN
9780124071636
9780124071582
9780123742643
9780124071582
9780123742643
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