Guide to essential math [electronic resource] : a review for physics, chemistry and engineering students / S.M. Blinder
- 2nd ed.
- London : Elsevier, 2013
- Elsevier insights Guide to essential math
1 online resource (285 p.)
- Electronic books.
- This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly), which is needed to succeed in science courses. The focus is on math actually used in physics, chemistry and engineering, and the approach to mathematics begins with 12 examples of increasing complexity, designed to hone the student's ability to think in mathematical terms and to apply quantitative methods to scientific problems. Detailed Illustrations and links to reference material online help further comprehension. The
- Half Title; Title Page; Copyright; Contents; To the Reader; Preface to Second Edition; 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 sqrtpi in the Gaussian Integral; 1.9 Function Equal to Its Derivative; 1.10 Stirling's Approximation for N!; 1.11 Potential and Kinetic Energies; 1.12 Riemann Zeta Function and Prime Numbers; 1.13 How to Solve It; 1.13.1 Understanding the Problem
1.13.2 Devising a Plan1.13.3 Carrying Out the Plan; 1.13.4 Looking Back; 1.14 A Note on Mathematical Rigor; 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; 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; Trigonometry; 4.1 What Use is Trigonometry?
4.2 Geometry of Triangles4.3 The Pythagorean Theorem; 4.4 π in the Sky; 4.5 Sine and Cosine; 4.6 Tangent and Secant; 4.7 Trigonometry in the Complex Plane; 4.8 de Moivre's Theorem; 4.9 Euler's Theorem; 4.10 Hyperbolic Functions; Analytic Geometry; 5.1 Functions and Graphs; 5.2 Linear Functions; 5.3 Conic Sections; 5.4 Conic Sections in Polar Coordinates; 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 Minima6.9 The Gamma Function; 6.10 Gaussian and Error Functions; 6.11 Numerical Integration; Series and Integrals; 7.1 Some Elementary Series; 7.2 Power Series; 7.3 Convergence of Series; 7.4 Taylor Series; 7.5 Bernoulli and Euler Numbers; 7.6 L'Hôpital's Rule; 7.7 Fourier Series; 7.8 Dirac Deltafunction; 7.9 Fourier Integrals; 7.10 Generalized Fourier Expansions; 7.11 Asymptotic Series; Differential Equations; 8.1 First-Order Differential Equations; 8.2 Numerical Solutions; 8.3 AC Circuits; 8.4 Second-Order Differential Equations; 8.5 Some Examples from Physics
8.6 Boundary Conditions8.7 Series Solutions; 8.8 Bessel Functions; 8.9 Second Solution; 8.10 Eigenvalue Problems; 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 Matrix Eigenvalue Problems; 9.9 Diagonalization of Matrices; 9.10 Four-Vectors and Minkowski Spacetime; Group Theory; 10.1 Introduction; 10.2 Symmetry Operations; 10.3 Mathematical Theory of Groups; 10.4 Representations of Groups; 10.5 Group Characters
10.6 Group Theory in Quantum Mechanics
- Description based upon print version of record
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