Calculus and Algebra with Mathcad 2000

Title Page......Page 1
Copyright Page......Page 2
Table of contents......Page 3
Preface......Page 9
1.1 Elementary operations......Page 11
1.2.2 Starting a new file......Page 15
1.2.5 Printing a file......Page 16
1.3.2 Forcing symbolic calculation......Page 17
1.4 Mathcad\'s built-in functions......Page 19
1.5.1 Defining a variable......Page 20
1.5.2 Variable names......Page 21
1.5.3 Range variables......Page 22
1.5.4 Using dimensions......Page 23
1.6.1 Defining an array with [Ctrl]M......Page 25
1.6.3 The nth column vector of a matrix......Page 26
1.6.4 Defining an array by means of a formula......Page 27
1.6.7 Array operations......Page 28
1.6.9 Defining bigger arrays......Page 30
1.7.1 Defining your own functions......Page 32
1.7.2 Drawing the graph of a function......Page 33
1.7.4 Drawing a polar curve......Page 36
1.7.5 Functions as argument to a new function......Page 38
1.8.2 Using Mathcad\'s programming language......Page 40
1.9.2 Functions for rounding and truncating......Page 46
1.9.3 Prime numbers......Page 47
1.9.4 Numbers in various number bases......Page 49
1.10.1 The summation symbol......Page 50
1.10.2 The product symbol......Page 51
1.11.1 The graph of a function of two variables......Page 52
1.11.2 Contour plots and 3D bar charts.......Page 53
1.11.3 Parameter surfaces......Page 54
1.11.4 Space curves......Page 57
1.11.5 Drawing several three dimensional objects......Page 58
1.12.1 Text blocks......Page 60
1.12.2 Text variables......Page 62
1.12.3 Text on a two dimensional graph......Page 63
1.13 Animation......Page 65
2.1 Tools for symbolic algebra......Page 67
2.2.1 Evaluating an expression.......Page 68
2.2.2 Simplifying an expression......Page 69
2.2.3 Expanding an expression......Page 70
2.2.4 Factoring an expression......Page 71
2.2.5 Collecting on a subexpression......Page 72
2.2.6 Partial fractions......Page 73
2.2.7 Substituting an expression for a variable in another expression......Page 74
2.2.9 Polynomial coefficients......Page 76
2.3.1 Solving one equation with one unknown numerically......Page 77
2.3.2 Solving one equation with one unknown symbolically......Page 78
2.3.4 Several equations with several unknown solved numerically......Page 79
2.3.5 Linear equations......Page 80
2.3.6 Several simultaneous equations solved symbolically......Page 81
3.2.1 The derivative as a limit......Page 83
3.2.2 The built-in differentiation operator......Page 84
3.2.4 Differential formulae......Page 85
3.2.5 Differentiation of implicit functions......Page 86
3.2.6 Tangent and normal......Page 87
3.2.7 Curvature and evolute......Page 89
3.2.8 Envelope of a family of curves......Page 93
3.2.9 Extrema of functions......Page 94
3.2.11 Series......Page 96
3.2.12 Extrema of functions of two variables......Page 97
3.2.13 Extrema of functions with three or more variables......Page 99
3.2.14 Extrema with side conditions......Page 101
3.2.15 Linear optimization......Page 103
3.3.1 Indefinite integrals......Page 104
3.3.2 Definite Integrals......Page 106
3.3.3 Improper Integrals......Page 108
3.3.4 Plane areas......Page 109
3.3.5 Curve length......Page 112
3.3.6 Centroids and moments of inertia......Page 114
3.3.7 The volume of a surface of revolution......Page 116
3.3.8 Surface area of a surface of revolution......Page 119
3.3.9 Double integrals......Page 121
3.4.1 Vectors in Rn......Page 122
3.4.2 Vector valued functions R -- R3......Page 123
3.4.3 Differential geometry of space curves......Page 125
3.4.4 Vector fields and scalar fields......Page 127
3.4.5 Line integrals......Page 128
3.4.6 Surface integrals......Page 130
3.4.8 Triple Integrals......Page 132
4.1.2 Separable equations f(y) dy = g(x) dx......Page 135
4.1.4 Linear equations y\' - y = g(x), where a is a constant.......Page 136
4.1.6 Total differentials......Page 137
4.2.1 Homogeneous equations with constant coefficients......Page 138
4.2.2 Inhomogeneous equations with constant coefficients......Page 139
4.2.3 Solution by power series expansion......Page 142
4.3.2 Application to initial value problems......Page 144
4.4.1 Method of undetermined coefficients......Page 146
4.4.2 The z transform......Page 147
4.5.1 Fourier coefficients and Fourier series......Page 149
4.5.2 Step functions......Page 150
4.5.3 Fourier transforms......Page 151
4.5.4 Fourier transforms and the heat equation......Page 152
4.5.5 Discrete Fourier Transforms......Page 153
4.6.1 Drawing a two dimensional vector field......Page 155
4.6.2 Drawing a family of integral curves......Page 158
4.6.3 Runge-Kutta\'s fourth order method......Page 159
4.6.4 Drawing a family of numerically computed integral curves.......Page 161
4.6.5 ODEs of order two or higher......Page 163
4.6.7 Other differential equation solvers.......Page 165
4.6.8 A boundary value problem: Ballistics......Page 169
5.1.1 Elementary row operations......Page 173
5.1.3 Gauss elimination with pivoting......Page 175
5.2.1 The rank of a matrix......Page 177
5.2.3 Basis for the null space of a matrix......Page 178
5.2.4 Gram-Schmidt\'s orthonormalization process......Page 181
5.3.1 Eigenvalues and eigenvectors.......Page 182
Index......Page 187