Table Of ContentMathematics Advances in Applied Mathematics
Mathematics 5th
Pocket Book of Integrals and Mathematical Formulas, 5th Edition covers
Edition
topics ranging from precalculus to vector analysis and from Fourier series to
BstCaCtistics, presenting numerous worked examples to demonstrate the application
of the formulas and methods. This popular pocket book is an essential source
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for students of calculus and higher mathematics courses. It also provides an n o
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• Includes several classic calculus applications that illustrate the power m o
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• Discusses an interesting offshoot of Fermat’s last theorem, namely, “near t o
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• Contains the most important mathematical formulas for engineering and
scientific applications
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Fourier series to statistics
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K24730
www.crcpress.com
A CHAPMAN & HALL BOOK
K24730_cover.indd 1 2/20/15 11:10 AM
Pocket Book of
Integrals and
Mathematical
Formulas
5th Edition
Advances in Applied Mathematics
Series Editor: Daniel Zwillinger
Published Titles
Stochastic Partial Differential Equations, Second Edition Pao-Liu Chow
Markov Processes James R. Kirkwood
Green’s Functions with Applications, Second Edition Dean G. Duffy
Pocket Book of Integrals and Mathematical Formulas, 5th Edition
Ronald J. Tallarida
Advances in Applied Mathematics
Pocket Book of
Integrals and
Mathematical
Formulas
5th Edition
Ronald J. Tallarida
Temple University
Philadelphia, Pennsylvania, USA
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
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Contents
Preface to the Fifth Edition ................................xiii
Preface to the Fourth Edition ..............................xv
Preface to the Third Edition .............................xvii
Preface to the Second Edition ............................xix
Preface to the First Edition .................................xxi
Author .................................................................xxiii
Greek Letters.......................................................xxv
1. Elementary Algebra and Geometry ............1
1.1 Fundamental Properties
(Real Numbers) ......................................1
1.2 Exponents ...............................................2
1.3 Fractional Exponents ............................2
1.4 Irrational Exponents .............................3
1.5 Logarithms .............................................3
1.6 Factorials ................................................4
1.7 Binomial Theorem ................................4
1.8 Factors and Expansion .........................5
1.9 Progression.............................................5
1.10 Complex Numbers ................................6
1.11 Polar Form ..............................................7
1.12 Permutations ..........................................8
1.13 Combinations.........................................9
1.14 Algebraic Equations ..............................9
1.15 Geometry ..............................................11
1.16 Pythagorean Theorem ........................16
v
vi Contents
2. Determinants, Matrices, and Linear
Systems of Equations ...................................17
2.1 Determinants .......................................17
2.2 Evaluation by Cofactors .....................19
2.3 Properties of Determinants ...............19
2.4 Matrices ................................................20
2.5 Operations ............................................21
2.6 Properties .............................................22
2.7 Transpose .............................................23
2.8 Identity Matrix.....................................23
2.9 Adjoint ..................................................24
2.10 Inverse Matrix......................................24
2.11 Systems of Linear Equations .............26
2.12 Matrix Solution ....................................27
3. Trigonometry .................................................29
3.1 Triangles ...............................................29
3.2 Trigonometric Functions of an
Angle .....................................................30
3.3 Trigonometric Identities .....................32
3.4 Inverse Trigonometric Functions ......35
4. Analytic Geometry .......................................37
4.1 Rectangular Coordinates ...................37
4.2 Distance between Two Points: Slope ....38
4.3 Equations of Straight Lines ................40
4.4 Distance from a Point to a Line .........43
4.5 Circle .....................................................43
4.6 Parabola ................................................43
4.7 Ellipse ...................................................47
4.8 Hyperbola (e > 1) .................................48
4.9 Change of Axes....................................51
4.10 General Equation of Degree 2 ...........53
Contents vii
4.11 Polar Coordinates ................................54
4.12 Curves and Equations ........................57
4.13 Exponential Function (Half-Life) ......63
5. Series, Number Facts, and Theory ............65
5.1 Bernoulli and Euler Numbers ...........65
5.2 Series of Functions ..............................66
5.3 Error Function .....................................72
5.4 Fermat’s Little Theorem .....................73
5.5 Fermat’s Last Theorem .......................73
5.6 Beatty’s Theorem .................................75
5.7 An Interesting Prime ..........................76
5.8 Goldbach Conjecture ..........................76
5.9 Twin Primes .........................................76
5.10 Collatz Conjecture...............................77
6. Differential Calculus ...................................79
6.1 Notation ................................................79
6.2 Slope of a Curve ..................................80
6.3 Angle of Intersection of Two
Curves .................................................80
6.4 Radius of Curvature ...........................81
6.5 Relative Maxima and Minima ..........81
6.6 Points of Inflection of a Curve ...........82
6.7 Taylor’s Formula ..................................83
6.8 Indeterminant Forms .........................84
6.9 Numerical Methods ............................85
6.10 Functions of Two Variables ................87
6.11 Partial Derivatives ...............................88
6.12 Application of Derivatives .................89
6.12.1 Related Rate Problems...........89
6.12.2 Rectilinear Motion .................92
6.12.3 Applied Problem in
Maximum and Minimum ....94
viii Contents
7. Integral Calculus ..........................................99
7.1 Indefinite Integral ...............................99
7.2 Definite Integral ................................100
7.3 Properties ...........................................100
7.4 Common Applications of the
Definite Integral ................................101
7.5 Cylindrical and Spherical
Coordinates ........................................104
7.6 Double Integration ............................106
7.7 Surface Area and Volume by
Double Integration ............................107
7.8 Centroid ..............................................108
7.9 Applications of Integration ..............110
7.9.1 Indefinite Integral ................110
7.9.2 The Definite Integral ...........113
8. Vector Analysis ...........................................119
8.1 Vectors ................................................119
8.2 Vector Differentiation .......................121
8.3 Divergence Theorem (Gauss) ..........123
8.4 Stokes’ Theorem ................................123
8.5 Planar Motion in Polar
Coordinates ........................................123
8.6 Geostationary Satellite Orbit ...........124
9. Special Functions ........................................127
9.1 Hyperbolic Functions .......................127
9.2 Gamma Function (Generalized
Factorial Function) ............................128
9.3 Laplace Transforms ...........................129
9.4 z-Transform ........................................133
9.5 Fourier Series .....................................136
