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The Mathematics Companion: Mathematical Methods for Physicists and Engineers 2005 book

The Mathematics Companion: Mathematical Methods for Physicists and Engineers

Details Of The Book

The Mathematics Companion: Mathematical Methods for Physicists and Engineers

edition:  
Authors:   
serie:  
ISBN : 0750310200, 9780750310208 
publisher: Taylor & Francis 
publish year: 2005 
pages: 204 
language: English  
ebook format : PDF (It will be converted to PDF, EPUB OR AZW3 if requested by the user) 
file size: 17 MB 

price : $11.76 14 With 16% OFF



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Abstract Of The Book



Table Of Contents

The Mathematics Companion......Page 2
Contents......Page 5
Preface......Page 6
Part 1: Mathematics Essentials......Page 7
1.1 Numbers, Trigonometry and Analytical Geometry......Page 8
1.1.1 Real Numbers......Page 9
1.1.2 Complex numbers......Page 10
1.1.3 Coordinate systems......Page 12
1.1.4 Vectors......Page 13
1.1.5 The unit vectors......Page 14
1.1.6 Trigonometry......Page 15
1.1.7 Straight line......Page 16
1.1.8 Circle and ellipse......Page 17
1.1.9 Parabola......Page 18
1.1.10 Hyperbola......Page 19
1.2 Limits and Functions......Page 20
1.2.1 Functions......Page 21
1.2.2 Quadratic function......Page 22
1.2.3 Limits......Page 23
1.2.4 Theorems on limits......Page 24
1.3 Differentiation......Page 25
1.3.1 Derivative......Page 26
1.3.2 Rules for calculating the derivative......Page 27
1.3.3 Higher order derivatives......Page 29
1.3.4 Maxima and minima......Page 30
1.3.5 The 2nd derivative......Page 31
1.3.6 Curve sketching......Page 32
1.3.7 Time rate of change......Page 33
1.3.8 Anti-derivatives......Page 34
1.4 Integration......Page 35
1.4.1 Definite integral......Page 36
1.4.2 Fundamental theorem of calculus......Page 37
1.4.3 Properties of the definite integral......Page 38
1.4.4 Indefinite integral......Page 39
1.4.5 Numerical integration......Page 40
1.5 Exponential and Logarithmic Functions......Page 41
1.5.1 Logarithms......Page 42
1.5.2 The natural logarithm......Page 43
1.5.3 The natural exponential......Page 44
1.5.4 Differentiation and integration of ex......Page 45
1.5.5 Exponential law of growth and decay......Page 46
1.6 Trigonometric and Hyperbolic Functions......Page 47
1.6.1 Circular measure......Page 48
1.6.2 Derivatives and integrals of trigonometric functions......Page 49
1.6.3 Inverse trigonometric functions......Page 50
1.6.4 Derivatives of trigonometric functions......Page 51
1.6.5 Hyperbolic functions......Page 52
1.6.6 Properties of hyperbolic functions......Page 53
1.6.7 Derivative of hyperbolic functions......Page 54
1.6.8 Inverse hyperbolic functions......Page 55
1.7 Methods of Integration......Page 56
1.7.1 Integration by substitution......Page 57
1.7.2 Integration by parts......Page 58
1.7.3 Trigonometric substitutions......Page 59
1.7.4 Integration by partial fractions......Page 60
1.7.5 Quadratic expressions......Page 61
1.7.6 Indeterminate forms......Page 62
1.7.7 Improper integrals......Page 63
1.8 Infinite Series Summary......Page 64
1.8.1 Sequences......Page 65
1.8.2 Series......Page 66
1.8.3 d’Alembert’s ratio test......Page 67
1.8.4 Power series......Page 68
1.8.5 Binomial series......Page 69
1.9 Probability......Page 70
1.9.1 Mean, median, mode......Page 71
1.9.2 Permutations and combinations......Page 72
1.9.3 Probabilities, odds and expectation......Page 73
1.9.4 Probability distribution......Page 74
1.9.5 Expected value......Page 75
1.9.6 Binomial distribution......Page 76
1.9.7 Normal distribution......Page 77
1.9.8 Sampling......Page 79
1.9.9 t distribution......Page 80
1.9.10 Chi-squared distribution......Page 81
1.10 Matrices......Page 82
1.10.1 Matrices......Page 83
1.10.2 Determinants......Page 84
1.10.3 Systems of equations......Page 85
1.10.4 Eigenvalues and eigenvectors......Page 86
1.10.5 Cayley-Hamilton theorem......Page 87
1.10.6 Tensors......Page 88
Part 2: Advanced Mathematics......Page 91
2.1 Ordinary Differential Equations......Page 92
2.1.1 Ordinary differential equations......Page 93
2.1.2 Separation of variables......Page 94
2.1.3 Homogenous equations......Page 95
2.1.4 Exact equations......Page 97
2.1.5 Linear equations......Page 98
2.1.6 Linear equations with constant coefficients......Page 100
2.1.7 Method of undetermined coefficients......Page 102
2.1.8 Systems of equations......Page 104
2.1.9 Complex eigenvalues......Page 107
2.1.10 Power series......Page 108
2.2 Laplace Transforms......Page 110
2.2.1 Laplace transform......Page 111
2.2.2 Laplace transform of derivatives......Page 112
2.2.3 Step functions......Page 113
2.2.4 Laplace transforms to solve differential equations......Page 114
2.2.5 Laplace transforms and partial fractions......Page 115
2.3 Vector Analysis......Page 118
2.3.1 Vectors......Page 119
2.3.2 Direction cosines......Page 120
2.3.4 Vector dot product......Page 121
2.3.5 Equation of a line in space......Page 122
2.3.6 Equation of a plane......Page 123
2.3.7 Distance from a point to a plane......Page 124
2.3.8 Vector cross product......Page 125
2.3.9 Distance from a point to a line......Page 126
2.3.10 Distance between two skew lines......Page 127
2.3.11 Vector differentiation......Page 128
2.3.12 Motion of a body......Page 129
2.4 Partial Derivatives......Page 130
2.4.1 Partial differentiation......Page 131
2.4.2 Chain rule for partial derivatives......Page 132
2.4.3 Increments and differentials......Page 133
2.4.4 Directional derivatives......Page 134
2.4.5 Tangent planes and normal vector......Page 135
2.4.6 Gradient, divergence and curl......Page 136
2.4.7 Maxima and minima......Page 138
2.4.8 Lagrange multipliers......Page 139
2.4.9 Multiple least squares analysis......Page 140
2.4.10 Constraints......Page 142
2.5 Multiple Integrals......Page 144
2.5.1 Line integrals......Page 145
2.5.2 Electrical potential......Page 148
2.5.3 Work done by a force......Page 149
2.5.4 Double integral......Page 150
2.5.5 Triple integral......Page 151
2.5.6 Surface integrals......Page 152
2.5.7 Gauss’ law......Page 155
2.5.8 Divergence theorem......Page 156
2.5.9 Stokes’ theorem......Page 157
2.5.10 Green’s theorem......Page 158
2.5.11 Vector representations of Green’s theorem......Page 159
2.5.12 Application of Green’s theorem......Page 160
2.5.13 Maxwell’s equations (integral form)......Page 161
2.5.14 Maxwell’s equations (differential form)......Page 162
2.6 Fourier Series......Page 163
2.6.1 Fourier series......Page 164
2.6.2 Fourier transform......Page 165
2.6.3 Sampling......Page 166
2.6.4 Discrete Fourier transform......Page 167
2.6.5 Odd and even functions......Page 168
2.6.6 Convolution......Page 169
2.7 Partial Differential Equations......Page 171
2.7.1 Partial differential equations......Page 172
2.7.2 General wave equation......Page 173
2.7.3 Solution to the general wave equation......Page 174
2.7.4 d’Alembert’s solution to the wave equation......Page 177
2.7.5 Heat conduction equation......Page 178
2.7.6 Solution to the heat conduction equation......Page 179
2.7.7 Heat equation for a thin rod of infinite length......Page 180
2.8 Complex Functions......Page 181
2.8.1 Complex functions......Page 182
2.8.2 Quantum mechanics......Page 183
2.8.3 Solutions to the wave equation......Page 184
2.8.4 Zero potential......Page 185
2.8.5 Infinite square well......Page 186
2.8.6 Harmonic oscillator......Page 188
2.9 Numerical methods......Page 189
2.9.1 Newton’s method......Page 190
2.9.2 Interpolating polynomial......Page 191
2.9.3 Linear least squares......Page 192
2.9.4 Non-linear least squares......Page 193
2.9.5 Error propagation through equations......Page 194
2.9.6 Cubic spline......Page 195
2.9.7 Differentiation......Page 196
2.9.8 Integration......Page 197
2.9.9 1st Order ordinarydifferential equations......Page 198
2.9.10 Runge-Kutta method......Page 199
2.9.11 Finite element method......Page 200
Appendix......Page 201
A.1 Useful information......Page 202
A.2 Some standard integrals......Page 203
A.3 Special functions......Page 204


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