Handbook of Mathematics and Computational Science

by Harris, John W.; Stocker, Horst

• ISBN13: 9780387947464
• ISBN10: 0387947469
• Format: Hardcover
• Copyright: 1998-07-01
• Publisher: Springer Verlag

Summary

"It is the best text of its type that I have come across to date...an excellent resource for anyone involved in mathematical practice up to and including degree standard...it is a pleasant experience to flick through it at leisure, dropping in here and there on some of the thousands of results the book holds. It is beautifully illustrated and set out...we have here a comprehensive volume whose worth will not readily fade with time...If you feel the need to own a mathematical reference to see you through school and university mathematics to graduation, you couldn't do much better than to buy this one." --Mathematics Today A complete desk-top reference for working scientists, engineers, and students, this handbook serves as a veritable math toolbox for rapid access to a wealth of mathematics information for everyday use in problem solving, examinations, homework, etc. Compiled by professional scientists, engineers, and lecturers and internationally renowned for its clarity and completeness, The Handbook includes hundreds of tables of frequently used functions, formulae, transformations, and series, plus many applications. The layout, structured table of contents, and index make finding the relevant information quick and painless.

Table of Contents

Introduction	v
1 Numerical computation (arithmetics and numerics)	1	(36)
1.1 Sets	1	(3)
1.1.1 Representation of sets	1	(1)
1.1.2 Operations on sets	2	(2)
1.1.3 Laws of the algebra of sets	4	(1)
1.1.4 Mapping and function	4	(1)
1.2 Number systems	4	(3)
1.2.1 Decimal number system	5	(1)
1.2.2 Other number systems	6	(1)
1.2.3 Computer representation	6	(1)
1.2.4 Horner's scheme for the representation of numbers	7	(1)
1.3 Natural numbers	7	(4)
1.3.1 Mathematical induction	8	(1)
1.3.2 Vectors and fields, indexing	8	(1)
1.3.3 Calculating with natural numbers	9	(2)
1.4 Integers	11	(1)
1.5 Rational numbers (fractional numbers)	11	(3)
1.5.1 Decimal fractions	11	(2)
1.5.2 Fractions	13	(1)
1.5.3 Calculating with fractions	13	(1)
1.6 Calculating with quotients	14	(1)
1.6.1 Proportion	14	(1)
1.6.2 Rule of three	15	(1)
1.7 Mathematics of finance	15	(5)
1.7.1 Calculations of percentage	16	(1)
1.7.2 Interest and compound interest	16	(1)
1.7.3 Amortization	17	(1)
1.7.4 Annuities	18	(1)
1.7.5 Depreciation	19	(1)
1.8 Irrational numbers	20	(1)
1.9 Real numbers	20	(1)
1.10 Complex numbers	20	(2)
1.10.1 Field of complex numbers	21	(1)
1.11 Calculating with real numbers	22	(11)
1.11.1 Sign and absolute value	22	(1)
1.11.2 Ordering relations	23	(1)
1.11.3 Intervals	23	(1)
1.11.4 Rounding and truncating	24	(1)
1.11.5 Calculating with intervals	25	(1)
1.11.6 Brackets	25	(1)
1.11.7 Addition and subtraction	26	(1)
1.11.8 Summation sign	27	(1)
1.11.9 Multiplication and division	28	(1)
1.11.10 Product sign	29	(1)
1.11.11 Powers and roots	30	(2)
1.11.12 Exponentiation and logarithms	32	(1)
1.12 Binomial theorem	33	(4)
1.12.1 Binomial formulas	33	(1)
1.12.2 Binomial coefficients	34	(1)
1.12.3 Pascal's triangle	34	(1)
1.12.4 Properties of binomial coefficients	35	(1)
1.12.5 Expansion of powers of sums	36	(1)
2 Equations and inequalities (algebra)	37	(22)
2.1 Fundamental algebraic laws	37	(4)
2.1.1 Nomenclature	37	(2)
2.1.2 Group	39	(1)
2.1.3 Ring	39	(1)
2.1.4 Field	39	(1)
2.1.5 Vector space	40	(1)
2.1.6 Algebra	40	(1)
2.2 Equations with one unknown	41	(1)
2.2.1 Elementary equivalence transformations	41	(1)
2.2.2 Overview of the different kinds of equations	41	(1)
2.3 Linear equations	42	(1)
2.3.1 Ordinary linear equations	42	(1)
2.3.2 Linear equations in fractional form	42	(1)
2.3.3 Linear equations in irrational form	43	(1)
2.4 Quadratic equations	43	(1)
2.4.1 Quadratic equations in fractional form	44	(1)
2.4.2 Quadratic equations in irrational form	44	(1)
2.5 Cubic equations	44	(2)
2.6 Quartic equations	46	(1)
2.6.1 General quartic equations	46	(1)
2.6.2 Biquadratic equations	46	(1)
2.6.3 Symmetric quartic equations	46	(1)
2.7 Equations of arbitrary degree	47	(1)
2.7.1 Polynomial division	47	(1)
2.8 Fractional rational equations	48	(1)
2.9 Irrational equations	48	(1)
2.9.1 Radical equations	48	(1)
2.9.2 Power equations	49	(1)
2.10 Transcendental equations	49	(2)
2.10.1 Exponential equations	49	(1)
2.10.2 Logarithmic equations	50	(1)
2.10.3 Trigonometric (goniometric) equations	51	(1)
2.11 Equations with absolute values	51	(2)
2.11.1 Equations with one absolute value	51	(1)
2.11.2 Equations with several absolute values	52	(1)
2.12 Inequalities	53	(1)
2.12.1 Equivalence transformations for inequalities	53	(1)
2.13 Numerical solution of equations	54	(5)
2.13.1 Graphical solution	54	(1)
2.13.2 Nesting of intervals	54	(1)
2.13.3 Secant methods and method of false position	55	(1)
2.13.4 Newton's method	56	(1)
2.13.5 Successive approximation	57	(2)
3 Geometry and trigonometry in the plane	59	(36)
3.1 Point curves	60	(1)
3.2 Basic constructions	60	(2)
3.2.1 Construction of the midpoint of a segment	60	(1)
3.2.2 Construction of the bisector of an angle	61	(1)
3.2.3 Construction of perpendiculars	61	(1)
3.2.4 To drop a perpendicular	61	(1)
3.2.5 Construction of parallels at a given distance	61	(1)
3.2.6 Parallels through a given point	62	(1)
3.3 Angles	62	(2)
3.3.1 Specification of angles	62	(1)
3.3.2 Types of angles	63	(1)
3.3.3 Angles between two parallels	64	(1)
3.4 Similarity and intercept theorems	64	(3)
3.4.1 Intercept theorems	64	(1)
3.4.2 Division of a segment	65	(1)
3.4.3 Mean values	66	(1)
3.4.4 Golden Section	66	(1)
3.5 Triangles	67	(15)
3.5.1 Congruence theorems	67	(1)
3.5.2 Similarity of triangles	68	(1)
3.5.3 Construction of triangles	68	(2)
3.5.4 Calculation of a right triangle	70	(1)
3.5.5 Calculation of an arbitrary triangle	70	(2)
3.5.6 Relations between angles and sides of a triangle	72	(1)
3.5.7 Altitude	73	(1)
3.5.8 Angle-bisectors	74	(1)
3.5.9 Medians	74	(1)
3.5.10 Mid-perpendiculars, incircle, circumcircle, excircle	75	(1)
3.5.11 Area of a triangle	76	(1)
3.5.12 Generalized Pythagorean theorem	76	(1)
3.5.13 Angular relations	76	(1)
3.5.14 Sine theorem	76	(1)
3.5.15 Cosine theorem	77	(1)
3.5.16 Tangent theorem	77	(1)
3.5.17 Half-angle theorems	77	(1)
3.5.18 Mollweide's formulas	77	(1)
3.5.19 Theorems of sides	78	(1)
3.5.20 Isosceles triangle	78	(1)
3.5.21 Equilateral triangle	79	(1)
3.5.22 Right triangle	80	(1)
3.5.23 Theorem of Thales	81	(1)
3.5.24 Pythagorean theorem	81	(1)
3.5.25 Theorem of Euclid	81	(1)
3.5.26 Altitude theorem	81	(1)
3.6 Quadrilaterals	82	(4)
3.6.1 General quadrilateral	82	(1)
3.6.2 Trapezoid	82	(1)
3.6.3 Parallelogram	83	(1)
3.6.4 Rhombus	83	(1)
3.6.5 Rectangle	84	(1)
3.6.6 Square	84	(1)
3.6.7 Quadrilateral of chords	85	(1)
3.6.8 Quadrilateral of tangents	86	(1)
3.6.9 Kite	86	(1)
3.7 Regular n-gons (polygons)	86	(3)
3.7.1 General regular n-gons	87	(1)
3.7.2 Particular regular n-gons (polygons)	87	(2)
3.8 Circular objects	89	(6)
3.8.1 Circle	89	(1)
3.8.2 Circular areas	90	(1)
3.8.3 Annulus, circular ring	91	(1)
3.8.4 Sector of a circle	91	(1)
3.8.5 Sector of an annulus	92	(1)
3.8.6 Segment of a circle	92	(1)
3.8.7 Ellipse	93	(2)
4 Solid geometry	95	(22)
4.1 General theorems	95	(1)
4.1.1 Cavalieri's theorem	95	(1)
4.1.2 Simpson's rule	95	(1)
4.1.3 Guldin's rules	96	(1)
4.2 Prism	96	(2)
4.2.1 Oblique prism	96	(1)
4.2.2 Right prism	97	(1)
4.2.3 Cuboid	97	(1)
4.2.4 Cube	97	(1)
4.2.5 Obliquely truncated n-sided prism	98	(1)
4.3 Pyramid	98	(1)
4.3.1 Tetrahedron	98	(1)
4.3.2 Frustum of a pyramid	99	(1)
4.4 Regular polyhedron	99	(3)
4.4.1 Euler's theorem for polyhedrons	99	(1)
4.4.2 Tetrahedron	99	(1)
4.4.3 Cube (hexahedron)	100	(1)
4.4.4 Octahedron	100	(1)
4.4.5 Dodecahedron	101	(1)
4.4.6 Icosahedron	101	(1)
4.5 Other solids	102	(1)
4.5.1 Prismoid, prismatoid	102	(1)
4.5.2 Wedge	102	(1)
4.5.3 Obelisk	102	(1)
4.6 Cylinder	102	(2)
4.6.1 General cylinder	103	(1)
4.6.2 Right circular cylinder	103	(1)
4.6.3 Obliquely cut circular cylinder	103	(1)
4.6.4 Segment of a cylinder	104	(1)
4.6.5 Hollow cylinder (tube)	104	(1)
4.7 Cone	104	(2)
4.7.1 Right circular cone	105	(1)
4.7.2 Frustum of a right circular cone	105	(1)
4.8 Sphere	106	(2)
4.8.1 Solid sphere	106	(1)
4.8.2 Hollow sphere	106	(1)
4.8.3 Spherical sector	106	(1)
4.8.4 Spherical segment (spherical cap)	107	(1)
4.8.5 Spherical zone (spherical layer)	107	(1)
4.8.6 Spherical wedge	108	(1)
4.9 Spherical geometry	108	(3)
4.9.1 General spherical triangle (Euler's triangle)	108	(1)
4.9.2 Right-angled spherical triangle	109	(1)
4.9.3 Oblique spherical triangle	110	(1)
4.10 Solids of rotation	111	(2)
4.10.1 Ellipsoid	111	(1)
4.10.2 Paraboloid of revolution	112	(1)
4.10.3 Hyperboloid of revolution	112	(1)
4.10.4 Barrel	112	(1)
4.10.5 Torus	113	(1)
4.11 Fractal geometry	113	(4)
4.11.1 Scaling invariance and self-similarity	113	(1)
4.11.2 Construction of self-similar objects	113	(1)
4.11.3 Hausdorff dimension	113	(1)
4.11.4 Cantor set	114	(1)
4.11.5 Koch's curve	114	(1)
4.11.6 Koch's snowflake	115	(1)
4.11.7 Sierpinski gasket	115	(1)
4.11.8 Box-counting algorithm	116	(1)
5 Functions	117	(214)
5.1 Sequences, series, and functions	117	(7)
5.1.1 Sequences and series	117	(2)
5.1.2 Properties of sequences, limits	119	(1)
5.1.3 Functions	120	(2)
5.1.4 Classification of functions	122	(1)
5.1.5 Limit and continuity	123	(1)
5.2 Discussion of curves	124	(6)
5.2.1 Domain of definition	124	(1)
5.2.2 Symmetry	124	(1)
5.2.3 Behavior at infinity	125	(1)
5.2.4 Gaps of definition and points of discontinuity	126	(1)
5.2.5 Zeros	127	(1)
5.2.6 Behavior of sign	127	(1)
5.2.7 Behavior of slope, extremes	128	(1)
5.2.8 Curvature	129	(1)
5.2.9 Point of inflection	129	(1)
5.3 Basic properties of functions	130	(7)
Simple functions	137	(18)
5.4 Constant function	137	(2)
5.5 Step function	139	(4)
5.6 Absolute value function	143	(4)
5.7 Delta function	147	(3)
5.8 Integer-part function, fractional-part function	150	(5)
Integral rational functions	155	(34)
5.9 Linear function-straight line	155	(3)
5.10 Quadratic function-parabola	158	(4)
5.11 Cubic equation	162	(4)
5.12 Power function of higher degree	166	(4)
5.13 Polynomials of higher degree	170	(4)
5.14 Representation of polynomials and particular polynomials	174	(15)
5.14.1 Representation by sums and products	174	(1)
5.14.2 Taylor series	175	(1)
5.14.3 Horner's scheme	176	(3)
5.14.4 Newton's interpolation polynomial	179	(1)
5.14.5 Lagrange polynomials	180	(1)
5.14.6 Bezier polynomials and splines	181	(6)
5.14.7 Particular polynomials	187	(2)
Fractional rational functions	189	(20)
5.15 Hyperbola	189	(3)
5.16 Reciprocal quadratic function	192	(4)
5.17 Power functions with a negative exponent	196	(4)
5.18 Quotient of two polynomials	200	(3)
5.18.1 Polynomial division and partial fraction decomposition	203	(2)
5.18.2 Pade's approximation	205	(4)
Irrational algebraic functions	209	(19)
5.19 Square-root function	209	(3)
5.20 Root function	212	(4)
5.21 Power functions with fractional exponents	216	(3)
5.22 Roots of rational functions	219	(9)
Transcendental functions	228	(17)
5.23 Logarithmic function	228	(5)
5.24 Expansion function	233	(6)
5.25 Exponential functions of powers	239	(6)
Hyperbolic functions	245	(18)
5.26 Hyperbolic sine and cosine functions	247	(5)
5.27 Hyperbolic tangent and cotangent function	252	(6)
5.28 Hyperbolic secant and hyperbolic cosecant functions	258	(5)
Area hyperbolic functions	263	(11)
5.29 Area hyperbolic sine and hyperbolic cosine	264	(3)
5.30 Area-hyperbolic tangent and hyperbolic cotangent	267	(4)
5.31 Area-hyperbolic secant and hyperbolic cosecant	271	(3)
Trigonometric functions	274	(32)
5.32 Sine and cosine functions	278	(16)
5.32.1 Superpositions of oscillations	287	(5)
5.32.2 Periodic functions	292	(2)
5.33 Tangent and cotangent functions	294	(6)
5.34 Secant and cosecant	300	(6)
Inverse trigonometric functions	306	(13)
5.35 Inverse sine and cosine functions	307	(4)
5.36 Inverse tangent and cotangent functions	311	(4)
5.37 Inverse secant and cosecant functions	315	(4)
Plane curves	319	(12)
5.38 Algebraic curves of the n-th order	319	(5)
5.38.1 Curves of the second order	319	(2)
5.38.2 Curves of the third order	321	(2)
5.38.3 Curves of the fourth and higher order	323	(1)
5.39 Cycloidal curves	324	(3)
5.40 Spirals	327	(1)
5.41 Other curves	328	(3)
6 Vector analysis	331	(18)
6.1 Vector algebra	331	(7)
6.1.1 Vector and scalar	331	(1)
6.1.2 Particular vectors	332	(1)
6.1.3 Multiplication of a vector by a scalar	332	(1)
6.1.4 Vector addition	333	(1)
6.1.5 Vector subtraction	333	(1)
6.1.6 Calculating laws	333	(1)
6.1.7 Linear dependence/independence of vectors	334	(1)
6.1.8 Basis	335	(3)
6.2 Scalar product or inner product	338	(5)
6.2.1 Calculating laws	339	(1)
6.2.2 Properties and applications of the scalar product	339	(2)
6.2.3 Schmidt's orthonormalization method	341	(1)
6.2.4 Direction cosine	341	(1)
6.2.5 Application hypercubes of vector analysis	342	(1)
6.3 Vector product of two vectors	343	(2)
6.3.1 Properties of the vector product	344	(1)
6.4 Multiple products of vectors	345	(4)
6.4.1 Scalar triple product	345	(4)
7 Coordinate systems	349	(28)
7.1 Coordinate systems in two dimensions	349	(1)
7.1.1 Cartesian coordinates	349	(1)
7.1.2 Polar coordinates	350	(1)
7.1.3 Conversions between two-dimensional coordinate systems	350	(1)
7.2 Two-dimensional coordinate transformation	350	(4)
7.2.1 Parallel displacement (translation)	351	(1)
7.2.2 Rotation	352	(1)
7.2.3 Reflection	353	(1)
7.2.4 Scaling	353	(1)
7.3 Coordinate systems in three dimensions	354	(2)
7.3.1 Cartesian coordinates	354	(1)
7.3.2 Cylindrical coordinates	354	(1)
7.3.3 Spherical coordinates	355	(1)
7.3.4 Conversions between three-dimensional coordinate systems	355	(1)
7.4 Coordinate transformation in three dimensions	356	(1)
7.4.1 Parallel displacement (translation)	356	(1)
7.4.2 Rotation	357	(1)
7.5 Application in computer graphics	357	(1)
7.6 Transformations	358	(12)
7.6.1 Object representation and object description	358	(1)
7.6.2 Homogeneous coordinates	359	(1)
7.6.3 Two-dimensional translations with homogeneous coordinates	360	(1)
7.6.4 Two-dimensional scaling with homogenous coordinates	360	(1)
7.6.5 Three-dimensional translation with homogeneous coordinates	361	(1)
7.6.6 Three-dimensional scaling with homogeneous coordinates	361	(1)
7.6.7 Three-dimensional rotation of points with homogeneous coordinates	362	(1)
7.6.8 Positioning of an object in space	363	(1)
7.6.9 Rotation of objects about an arbitrary axis in space	364	(2)
7.6.10 Animation	366	(1)
7.6.11 Reflections	366	(1)
7.6.12 Transformation of coordinate systems	367	(1)
7.6.13 Translation of coordinate systems	367	(1)
7.6.14 Rotation of a coordinate system about a principal axis	368	(2)
7.7 Projections	370	(6)
7.7.1 Fundamental principles	370	(1)
7.7.2 Parallel projection	370	(3)
7.7.3 Central projection	373	(1)
7.7.4 General formulation of projections	374	(2)
7.8 Window/viewport transformation	376	(1)
8 Analytic geometry	377	(32)
8.1 Elements of the plane	377	(1)
8.1.1 Distance between two points	377	(1)
8.1.2 Division of a segment	377	(1)
8.1.3 Area of a triangle	378	(1)
8.1.4 Equation of a curve	378	(1)
8.2 Straight line	378	(4)
8.2.1 Forms of straight-line equations	379	(1)
8.2.2 Hessian normal form	380	(1)
8.2.3 Point of intersection of straight lines	381	(1)
8.2.4 Angle between straight lines	381	(1)
8.2.5 Parallel and perpendicular straight lines	382	(1)
8.3 Circle	382	(2)
8.3.1 Equations of a circle	382	(1)
8.3.2 Circle and straight line	383	(1)
8.3.3 Intersection of two circles	383	(1)
8.3.4 Equation of the tangent to a circle	384	(1)
8.4 Ellipse	384	(3)
8.4.1 Equations of the ellipse	384	(1)
8.4.2 Focal properties of the ellipse	385	(1)
8.4.3 Diameters of the ellipse	385	(1)
8.4.4 Tangent and normal to the ellipse	385	(1)
8.4.5 Curvature of the ellipse	386	(1)
8.4.6 Areas and circumference of the ellipse	386	(1)
8.5 Parabola	387	(3)
8.5.1 Equations of the parabola	387	(1)
8.5.2 Focal properties of the parabola	388	(1)
8.5.3 Diameters of the parabola	388	(1)
8.5.4 Tangent and normal of the parabola	388	(1)
8.5.5 Curvature of a parabola	389	(1)
8.5.6 Areas and arc lengths of the parabola	389	(1)
8.5.7 Parabola and straight line	389	(1)
8.6 Hyperbola	390	(3)
8.6.1 Equations of the hyperbola	390	(1)
8.6.2 Focal properties of the hyperbola	391	(1)
8.6.3 Tangent and normal to the hyperbola	392	(1)
8.6.4 Conjugate hyperbolas and diameter	392	(1)
8.6.5 Curvature of a hyperbola	392	(1)
8.6.6 Areas of hyperbola	393	(1)
8.6.7 Hyperbola and straight line	393	(1)
8.7 General equation of conics	393	(3)
8.7.1 Form of conics	394	(1)
8.7.2 Transformation to principal axes	394	(1)
8.7.3 Geometric construction (conic section)	395	(1)
8.7.4 Directrix property	395	(1)
8.7.5 Polar equation	396	(1)
8.8 Elements in space	396	(1)
8.8.1 Distance between two points	396	(1)
8.8.2 Division of a segment	396	(1)
8.8.3 Volume of a tetrahedron	396	(1)
8.9 Straight lines in space	397	(2)
8.9.1 Parametric representation of a straight line	397	(1)
8.9.2 Point of intersection of two straight lines	397	(1)
8.9.3 Angle of intersection between two intersecting straight lines	398	(1)
8.9.4 Foot of a perpendicular (perpendicular line)	398	(1)
8.9.5 Distance between a point and a straight line	398	(1)
8.9.6 Distance between two lines	399	(1)
8.10 Planes in space	399	(4)
8.10.1 Parametric representation of the plane	399	(1)
8.10.2 Coordinate representation of the plane	399	(1)
8.10.3 Hessian normal form of the plane	400	(1)
8.10.4 Conversions	400	(1)
8.10.5 Distance between a point and a plane	401	(1)
8.10.6 Point of intersection of a line and a plane	401	(1)
8.10.7 Angle of intersection between two intersecting planes	401	(1)
8.10.8 Foot of the perpendicular (perpendicular line)	401	(1)
8.10.9 Reflection	402	(1)
8.10.10 Distance between two parallel planes	402	(1)
8.10.11 Cut set of two planes	402	(1)
8.11 Plane of the second order in normal form	403	(3)
8.11.1 Ellipsoid	403	(1)
8.11.2 Hyperboloid	403	(1)
8.11.3 Cone	404	(1)
8.11.4 Paraboloid	404	(1)
8.11.5 Cylinder	405	(1)
8.12 General plane of the second order	406	(3)
8.12.1 General equation	406	(1)
8.12.2 Transformation to principal axes	406	(1)
8.12.3 Shape of a surface of the second order	407	(2)
9 Matrices, determinants, and systems of linear equations	409	(58)
9.1 Matrices	409	(3)
9.1.1 Row and column vectors	411	(1)
9.2 Special matrices	412	(6)
9.2.1 Transposed, conjugate, and adjoint matrices	412	(1)
9.2.2 Square matrices	412	(2)
9.2.3 Triangular matrices	414	(1)
9.2.4 Diagonal matrices	415	(3)
9.3 Operations with matrices	418	(8)
9.3.1 Addition and subtraction of matrices	418	(1)
9.3.2 Multiplication of a matrix by a scalar factor c	418	(1)
9.3.3 Multiplication of vectors, scalar product	419	(2)
9.3.4 Multiplication of a matrix by a vector	421	(1)
9.3.5 Multiplication of matrices	421	(1)
9.3.6 Calculating rules of matrix multiplication	422	(2)
9.3.7 Multiplication by a diagonal matrix	424	(1)
9.3.8 Matrix multiplication according to Falk's scheme	424	(1)
9.3.9 Checking of row and column sums	425	(1)
9.4 Determinants	426	(11)
9.4.1 Two-row determinants	427	(1)
9.4.2 General computational rules for determinants	427	(2)
9.4.3 Zero value of the determinant	429	(1)
9.4.4 Three-row determinants	430	(2)
9.4.5 Determinants of higher (n-th) order	432	(1)
9.4.6 Calculation of n-row determinants	433	(1)
9.4.7 Regular and inverse matrix	434	(1)
9.4.8 Calculation of the inverse matrix in terms of determinants	435	(1)
9.4.9 Rank of a matrix	436	(1)
9.4.10 Determination of the rank by means of minor determinants	437	(1)
9.5 Systems of linear equations	437	(4)
9.5.1 Systems of two equations with two unknowns	439	(2)
9.6 Numerical solution methods	441	(13)
9.6.1 Gaussian algorithm for systems of linear equations	441	(1)
9.6.2 Forward elimination	441	(2)
9.6.3 Pivoting	443	(1)
9.6.4 Backsubstitution	444	(1)
9.6.5 LU-decompostion	445	(3)
9.6.6 Solvability of (m x n) systems of equations	448	(2)
9.6.7 Gauss-Jordan method for matrix inversion	450	(2)
9.6.8 Calculation of the inverse matrix A(-1)	452	(2)
9.7 Iterative solution of systems of linear equations	454	(5)
9.7.1 Total-step methods (Jacobi)	456	(1)
9.7.2 Single-step methods (Gauss-Seidel)	456	(1)
9.7.3 Criteria of convergence for iterative methods	457	(1)
9.7.4 Storage of the coefficient matrix	458	(1)
9.8 Table of solution methods	459	(2)
9.9 Eigenvalue equations	461	(2)
9.10 Tensors	463	(4)
9.10.1 Algebraic operations with tensors	465	(2)
10 Boolean algebra-application in switching algebra	467	(16)
10.1 Basic notions	467	(1)
10.1.1 Propositions and truth values	467	(1)
10.1.2 Proposition variables	468	(1)
10.2 Boolean connectives	468	(3)
10.2.1 Negation: not	469	(1)
10.2.2 Conjunction: and	469	(1)
10.2.3 Disjunction (inclusive): or	469	(1)
10.2.4 Calculating rules	470	(1)
10.3 Boolean functions	471	(1)
10.3.1 Operator basis	472	(1)
10.4 Normal forms	472	(3)
10.4.1 Disjunctive normal forms	472	(1)
10.4.2 Conjunctive normal form	473	(1)
10.4.3 Representation of functions by normal forms	473	(2)
10.5 Karnaugh-Veitch diagrams	475	(3)
10.5.1 Producing a KV-diagram	476	(1)
10.5.2 Entering a function in a KV-diagram	476	(1)
10.5.3 Minimization with the help of KV-diagrams	477	(1)
10.6 Minimization according to Quine and McCluskey	478	(3)
10.7 Multi-valued logic and fuzzy logic	481	(2)
10.7.1 Multi-valued logic	481	(1)
10.7.2 Fuzzy logic	481	(2)
11 Graphs and Algorithms	483	(6)
11.1 Graphs	483	(3)
11.1.1 Basic definitions	483	(3)
11.1.2 Representation of graphs	485	(1)
11.1.3 Trees	485	(1)
11.2 Matchings	486	(1)
11.3 Networks	487	(2)
11.3.1 Flows in networks	487	(1)
11.3.2 Eulerian line and Hamiltonian circuit	487	(2)
12 Differential calculus	489	(28)
12.1 Derivative of a function	489	(3)
12.1.1 Differential	490	(1)
12.1.2 Differentiability	491	(1)
12.2 Differentiation rules	492	(7)
12.2.1 Derivatives of elementary functions	492	(1)
12.2.2 Derivatives of trigonometric functions	492	(1)
12.2.3 Derivatives of hyperbolic functions	492	(1)
12.2.4 Constant rule	493	(1)
12.2.5 Factor rule	493	(1)
12.2.6 Power rule	493	(1)
12.2.7 Sum rule	493	(1)
12.2.8 Product rule	493	(1)
12.2.9 Quotient rule	494	(1)
12.2.10 Chain rule	494	(1)
12.2.11 Logarithmic differentiation of functions	495	(1)
12.2.12 Differentiation of functions in parametric representation	495	(1)
12.2.13 Differentiation of functions in polar coordinates	496	(1)
12.2.14 Differentiation of an implicit function	496	(1)
12.2.15 Differentiation of the inverse function	497	(1)
12.2.16 Table of differentiation rules	498	(1)
12.3 Mean value theorems	499	(1)
12.3.1 Rolle's theorem	499	(1)
12.3.2 Mean value theorem of differential calculus	499	(1)
12.3.3 Extended mean value theorem of differential calculus	500	(1)
12.4 Higher derivatives	500	(4)
12.4.1 Slope, extremes	502	(1)
12.4.2 Curvature	503	(1)
12.4.3 Point of inflection	503	(1)
12.5 Approximation method of differentiation	504	(2)
12.5.1 Graphical differentiation	504	(1)
12.5.2 Numerical differentiation	505	(1)
12.6 Differentiation of functions with several variables	506	(4)
12.6.1 Partial derivative	506	(2)
12.6.2 Total differential	508	(1)
12.6.3 Extremes of functions in two dimensions	508	(1)
12.6.4 Extremes with constraints	509	(1)
12.7 Application of differential calculus	510	(7)
12.7.1 Calculation of indefinite expressions	510	(1)
12.7.2 Discussion of curves	511	(1)
12.7.3 Extreme value problems	512	(1)
12.7.4 Calculus of errors	513	(1)
12.7.5 Determination of zeros according to Newton's method	514	(3)
13 Differential geometry	517	(14)
13.1 Plane curves	517	(7)
13.1.1 Representation of curves	517	(1)
13.1.2 Differentiation by implicit representation	517	(1)
13.1.3 Differentiation by parametric representation	518	(1)
13.1.4 Differentiation by polar coordinates	518	(1)
13.1.5 Differential of arc of a curve	518	(1)
13.1.6 Tangent, normal	519	(1)
13.1.7 Curvature of a curve	520	(2)
13.1.8 Evolutes and evolvents	522	(1)
13.1.9 Points of inflection, vertices	522	(1)
13.1.10 Singular points	522	(1)
13.1.11 Asymptotes	523	(1)
13.1.12 Envelope of a family of curves	524	(1)
13.2 Space curves	524	(4)
13.2.1 Representation of space curves	524	(1)
13.2.2 Moving trihedral	525	(2)
13.2.3 Curvature	527	(1)
13.2.4 Torsion of a curve	527	(1)
13.2.5 Frenet formulas	528	(1)
13.3 Surfaces	528	(3)
13.3.1 Representation of a surface	528	(1)
13.3.2 Tangent plane and normal to the surface	529	(1)
13.3.3 Singular points of the surface	530	(1)
14 Infinite series	531	(16)
14.1 Series	531	(1)
14.2 Criteria of convergence	532	(3)
14.2.1 Special number series	535	(1)
14.3 Taylor and MacLaurin series	535	(2)
14.3.1 Taylor's formula	535	(1)
14.3.2 Taylor series	536	(1)
14.4 Power series	537	(3)
14.4.1 Test of convergence for power series	537	(1)
14.4.2 Properties of convergent power series	538	(2)
14.4.3 Inversion of power series	540	(1)
14.5 Special expansions of series and products	540	(7)
14.5.1 Binomial series	540	(1)
14.5.2 Special binomial series	540	(1)
14.5.3 Series of exponential functions	541	(1)
14.5.4 Series of logarithmic functions	542	(1)
14.5.5 Series of trigonometric functions	542	(1)
14.5.6 Series of inverse trigonometric functions	543	(1)
14.5.7 Series of hyperbolic functions	544	(1)
14.5.8 Series of area hyperbolic functions	544	(1)
14.5.9 Partial fraction expansions	544	(1)
14.5.10 Infinite products	545	(2)
15 Integral calculus	547	(44)
15.1 Definition and integrability	547	(5)
15.1.1 Primitive	547	(1)
15.1.2 Definite and indefinite integrals	548	(1)
15.1.3 Geometrical interpretation	549	(1)
15.1.4 Rules for integrability	550	(1)
15.1.5 Improper integrals	551	(1)
15.2 Integration rules	552	(5)
15.2.1 Rules for indefinite integrals	552	(1)
15.2.2 Rules for definite integrals	553	(1)
15.2.3 Table of integration rules	554	(1)
15.2.4 Integrals of some elementary functions	555	(2)
15.3 Integration methods	557	(10)
15.3.1 Integration by substitution	557	(3)
15.3.2 Integration by parts	560	(2)
15.3.3 Integration by partial fraction decomposition	562	(3)
15.3.4 Integration by series expansion	565	(2)
15.4 Numerical integration	567	(7)
15.4.1 Rectangular rule	567	(1)
15.4.2 Trapezoidal rule	568	(1)
15.4.3 Simpson's rule	568	(1)
15.4.4 Romberg integration	569	(1)
15.4.5 Gaussian quadrature	570	(2)
15.4.6 Table of numerical integration methods	572	(2)
15.5 Mean value theorem of integral calculus	574	(1)
15.6 Line, surface, and volume integrals	574	(3)
15.6.1 Arc length (rectification)	574	(1)
15.6.2 Area	575	(1)
15.6.3 Solid of rotation (solid of revolution)	576	(1)
15.7 Functions in parametric representation	577	(2)
15.7.1 Arc length in parametric representation	577	(1)
15.7.2 Sector formula	578	(1)
15.7.3 Solids of rotation in parametric representation	578	(1)
15.8 Multiple integrals and their applications	579	(5)
15.8.1 Definition of multiple integrals	579	(1)
15.8.2 Calculation of areas	580	(1)
15.8.3 Center of mass of arcs	581	(1)
15.8.4 Moment of inertia of an area	581	(1)
15.8.5 Center of mass of areas	582	(1)
15.8.6 Moment of inertia of planes	582	(1)
15.8.7 Center of mass of a body	582	(1)
15.8.8 Moment of inertia of a body	583	(1)
15.8.9 Center of mass of rotational solids	583	(1)
15.8.10 Moment of inertia of rotational solids	583	(1)
15.9 Technical applications of integral calculus	584	(7)
15.9.1 Static moment, center of mass	584	(1)
15.9.2 Mass moment of inertia	585	(3)
15.9.3 Statics	588	(1)
15.9.4 Calculation of work	588	(1)
15.9.5 Mean values	589	(2)
16 Vector analysis	591	(22)
16.1 Fields	591	(3)
16.1.1 Symmetries of fields	592	(2)
16.2 Differentiation and integration of vectors	594	(4)
16.2.1 Scale factors in general orthogonal coordinates	596	(1)
16.2.2 Differential operators	597	(1)
16.3 Gradient and potential	598	(2)
16.4 Directional derivative and vector gradient	600	(1)
16.5 Divergence and Gaussian integral theorem	601	(3)
16.6 Rotation and Stokes's theorem	604	(3)
16.7 Laplace operator and Green's formulas	607	(3)
16.7.1 Combinations of div, rot, and grad; calculation of fields	609	(1)
16.8 Summary	610	(3)
17 Complex variables and functions	613	(34)
17.1 Complex numbers	613	(6)
17.1.1 Imaginary numbers	613	(1)
17.1.2 Algebraic representation of complex numbers	614	(1)
17.1.3 Cartesian representation of complex numbers	614	(1)
17.1.4 Conjugate complex numbers	615	(1)
17.1.5 Absolute value of a complex number	615	(1)
17.1.6 Trigonometric representation of complex numbers	616	(1)
17.1.7 Exponential representation of complex numbers	616	(1)
17.1.8 Transformation from Cartesian to trigonometric representation	617	(1)
17.1.9 Riemann sphere	618	(1)
17.2 Elementary arithmetical operations with complex numbers	619	(4)
17.2.1 Addition and subtraction of complex numbers	619	(1)
17.2.2 Multiplication and division of complex numbers	619	(3)
17.2.3 Exponentiation in the complex domain	622	(1)
17.2.4 Taking the root in the complex domain	623	(1)
17.3 Elementary functions of a complex variable	623	(8)
17.3.1 Sequences in the complex domain	624	(1)
17.3.2 Series in the complex domain	625	(1)
17.3.3 Exponential function in the complex domain	626	(1)
17.3.4 Natural logarithm in the complex domain	626	(1)
17.3.5 General power in the complex domain	627	(1)
17.3.6 Trigonometric functions in the complex domain	627	(2)
17.3.7 Hyperbolic functions in the complex domain	629	(1)
17.3.8 Inverse trigonometric, inverse hyperbolic functions in the complex domain	630	(1)
17.4 Applications of complex functions	631	(4)
17.4.1 Representation of oscillations in the complex plane	631	(1)
17.4.2 Superposition of oscillations of equal frequency	632	(1)
17.4.3 Loci	633	(1)
17.4.4 Inversion of loci	634	(1)
17.5 Differentiation of functions of a complex variable	635	(4)
17.5.1 Definition of the derivative in the complex domain	635	(1)
17.5.2 Differentiation rules in the complex domain	636	(1)
17.5.3 Cauchy-Riemann differentiability conditions	637	(1)
17.5.4 Conformal mapping	637	(2)
17.6 Integration in the complex plane	639	(8)
17.6.1 Complex curvilinear integrals	639	(1)
17.6.2 Cauchy's integral theorem	640	(1)
17.6.3 Primitive functions in the complex domain	641	(1)
17.6.4 Cauchy's integral formulas	641	(1)
17.6.5 Taylor series of an analytic function	642	(1)
17.6.6 Laurent series	643	(1)
17.6.7 Classification of singular points	643	(1)
17.6.8 Residue theorem	644	(1)
17.6.9 Inverse Laplace transformation	645	(2)
18 Differential equations	647	(44)
18.1 General definitions	647	(2)
18.2 Geometric interpretation	649	(1)
18.3 Solution methods for first-order differential equations	650	(2)
18.3.1 Separation of variables	650	(1)
18.3.2 Substitution	651	(1)
18.3.3 Exact differential equations	651	(1)
18.3.4 Integrating factor	651	(1)
18.4 Linear differential equations of the first order	652	(2)
18.4.1 Variation of the constants	652	(1)
18.4.2 General solution	653	(1)
18.4.3 Determination of a particular solution	653	(1)
18.4.4 Linear differential equations of the first order with constant coefficients	653	(1)
18.5 Some specific equations	654	(1)
18.5.1 Bernoulli differential equation	654	(1)
18.5.2 Riccati differential equation	654	(1)
18.6 Differential equations of the second order	655	(1)
18.6.1 Simple special cases	655	(1)
18.7 Linear differential equations of the second order	656	(6)
18.7.1 Homogeneous linear differential equation of the second order	657	(1)
18.7.2 Inhomogeneous linear differential equations of the second order	657	(2)
18.7.3 Reduction of special differential equations of the second order to differential equations of the first order	659	(1)
18.7.4 Linear differential equations of the second order with constant coefficients	659	(3)
18.8 Differential equations of the n-th order	662	(6)
18.9 Systems of coupled differential equations of the first order	668	(2)
18.10 Systems of linear homogeneous differential equations with constant coefficients	670	(2)
18.11 Partial differential equations	672	(4)
18.11.1 Solution by separation	673	(3)
18.12 Numerical integration of differential equations	676	(15)
18.12.1 Euler method	676	(1)
18.12.2 Heun method	677	(2)
18.12.3 Modified Euler method	679	(1)
18.12.4 Runge-Kutta methods	679	(6)
18.12.5 Runge-Kutta method for systems of differential equations	685	(1)
18.12.6 Difference method for the solution of partial differential equations	685	(3)
18.12.7 Method of finite elements	688	(3)
19 Fourier transformation	691	(44)
19.1 Fourier series	691	(16)
19.1.1 Introduction	691	(1)
19.1.2 Definition and coefficients	691	(2)
19.1.3 Condition of convergence	693	(1)
19.1.4 Extended interval	694	(2)
19.1.5 Symmetries	696	(2)
19.1.6 Fourier series in complex and spectral representation	698	(1)
19.1.7 Formulas for the calculation of Fourier series	699	(1)
19.1.8 Fourier expansion of simple periodic functions	699	(6)
19.1.9 Fourier series (table)	705	(2)
19.2 Fourier integrals	707	(5)
19.2.1 Introduction	707	(1)
19.2.2 Definition and coefficients	707	(1)
19.2.3 Conditions for convergence	708	(1)
19.2.4 Complex representation, Fourier sine and cosine transformation	708	(2)
19.2.5 Symmetries	710	(1)
19.2.6 Convolution and some calculating rules	710	(2)
19.3 Discrete Fourier transformation (DFT)	712	(12)
19.3.1 Definition and coefficients	712	(1)
19.3.2 Shannon scanning theorem	713	(1)
19.3.3 Discrete sine and cosine transformation	714	(1)
19.3.4 Fast Fourier transformation (FFT)	715	(5)
19.3.5 Particular pairs of Fourier transforms	720	(1)
19.3.6 Fourier transforms (table)	720	(2)
19.3.7 Particular Fourier sine transforms	722	(1)
19.3.8 Particular Fourier cosine transforms	723	(1)
19.4 Wavelet transformation	724	(11)
19.4.1 Signals	724	(1)
19.4.2 Linear signal analysis	725	(1)
19.4.3 Symmetry transformations	726	(1)
19.4.4 Time-frequency analysis and Gabor transformation	727	(1)
19.4.5 Wavelet transformation	728	(4)
19.4.6 Discrete wavelet transformation	732	(3)
20 Laplace and z transformations	735	(38)
20.1 Introduction	735	(1)
20.2 Definition of the Laplace transformation	736	(1)
20.3 Transformation theorems	737	(8)
20.4 Partial fraction separation	745	(3)
20.4.1 Partial fraction separation with simple real zeros	745	(1)
20.4.2 Partial fraction decomposition with multiple real zeros	746	(1)
20.4.3 Partial fraction decomposition with complex zeros	747	(1)
20.5 Linear differential equations with constant coefficients	748	(16)
20.5.1 Laplace transformation: linear differential equation of the first order with constant coefficients	749	(2)
20.5.2 Laplace transformation: linear differential equation of the second order with constant coefficients	751	(2)
20.5.3 Example: linear differential equations	753	(3)
20.5.4 Laplace transforms (table)	756	(8)
20.6 z transformation	764	(9)
20.6.1 Definition of the z transformation	764	(2)
20.6.2 Convergence conditions for the z transformation	766	(1)
20.6.3 Inversion of the z transformation	767	(1)
20.6.4 Calculating rules	767	(3)
20.6.5 Calculating rules for the z transformation	770	(1)
20.6.6 Table of z transforms	770	(3)
21 Probability theory and mathematical statistics	773	(74)
21.1 Combinatorics	773	(1)
21.2 Random events	774	(4)
21.2.1 Basic notions	774	(1)
21.2.2 Event relations and event operations	775	(2)
21.2.3 Structural representation of events	777	(1)
21.3 Probability of events	778	(3)
21.3.1 Properties of probabilities	778	(1)
21.3.2 Methods to calculate probabilities	778	(1)
21.3.3 Conditional probabilities	779	(1)
21.3.4 Calculating with probabilities	779	(2)
21.4 Random variables and their distributions	781	(19)
21.4.1 Individual probability, density function and distribution function	782	(1)
21.4.2 Parameters of distributions	783	(2)
21.4.3 Special discrete distribution	785	(8)
21.4.4 Special continuous distributions	793	(7)
21.5 Limit theorems	800	(2)
21.5.1 Laws of large numbers	800	(1)
21.5.2 Limit theorems	801	(1)
21.6 Multidimensional random variables	802	(6)
21.6.1 Distribution functions of two-dimensional random variables	802	(1)
21.6.2 Two-dimensional discrete random variables	803	(1)
21.6.3 Two-dimensional continuous random variables	804	(1)
21.6.4 Independence of random variables	805	(1)
21.6.5 Parameters of two-dimensional random variables	806	(1)
21.6.6 Two-dimensional normal distribution	807	(1)
21.7 Basics of mathematical statistics	808	(4)
21.7.1 Description of measurements	809	(1)
21.7.2 Types of error	810	(2)
21.8 Parameters for describing distributions of measured values	812	(3)
21.8.1 Position parameter, means of series of measurements	812	(2)
21.8.2 Dispersion parameter	814	(1)
21.9 Special distributions	815	(5)
21.9.1 Frequency distributions	815	(1)
21.9.2 Distribution of random sample functions	816	(4)
21.10 Analysis by means of random sampling (theory of testing and estimating)	820	(19)
21.10.1 Estimation methods	821	(2)
21.10.2 Construction principles for estimators	823	(1)
21.10.3 Method of moments	823	(1)
21.10.4 Maximum likelihood method	824	(1)
21.10.5 Method of least squares	824	(1)
21.10.6 X(2) minimum method	825	(1)
21.10.7 Method of quantiles, percentiles	825	(1)
21.10.8 Interval estimation	826	(2)
21.10.9 Interval bounds for normal distribution	828	(1)
21.10.10 Prediction and confidence interval bounds for binomial and hypergeometric distributions	829	(1)
21.10.11 Interval bounds for a Poisson distribution	830	(1)
21.10.12 Determination of sample sizes n	830	(1)
21.10.13 Test methods	831	(3)
21.10.14 Parameter tests	834	(1)
21.10.15 Parameter tests for a normal distribution	834	(2)
21.10.16 Hypotheses about the mean value of arbitrary distributions	836	(1)
21.10.17 Hypotheses about p of binomial and hypergeometric distributions	837	(1)
21.10.18 Tests of goodness of fit	837	(1)
21.10.19 Application: acceptance/rejection test	838	(1)
21.11 Reliability	839	(2)
21.12 Computation of adjustment, regression	841	(6)
21.12.1 Linear regression, least squares method	843	(1)
21.12.2 Regression of the n-th order	844	(3)
22 Fuzzy logic	847	(24)
22.1 Fuzzy sets	847	(1)
22.2 Fuzzy concept	848	(1)
22.3 Functional graphs for the modeling of fuzzy sets	849	(3)
22.4 Combination of fuzzy sets	852	(9)
22.4.1 Elementary operations	852	(3)
22.4.2 Calculating rules for fuzzy sets	855	(1)
22.4.3 Rules for families of fuzzy sets	856	(1)
22.4.4 t norm and t conorm	856	(2)
22.4.5 Non-parametrized operators: t norms and s norms (t conorms)	858	(1)
22.4.6 Parametrized t and s norms	859	(1)
22.4.7 Compensatory operators	860	(1)
22.5 Fuzzy relations	861	(2)
22.6 Fuzzy inference	863	(1)
22.7 Defuzzification methods	864	(2)
22.8 Example: erect pendulum	866	(4)
22.9 Fuzzy realizations	870	(1)
23 Neural networks	871	(12)
23.1 Function and structure	871	(2)
23.1.1 Function	871	(1)
23.1.2 Structure	872	(1)
23.2 Implementation of the neuron model	873	(1)
23.2.1 Time-independent systems	873	(1)
23.2.2 Time-dependent systems	873	(1)
23.2.3 Application	874	(1)
23.3 Supervised learning	874	(7)
23.3.1 Principle of supervised learning	874	(2)
23.3.2 Standard backpropagation	876	(1)
23.3.3 Backpropagation through time	877	(1)
23.3.4 Improved learning methods	878	(1)
23.3.5 Hopfield network	879	(2)
23.4 Unsupervised learning	881	(2)
23.4.1 Principle of unsupervised learning	881	(1)
23.4.2 Kohonen model	881	(2)
24 Computers	883	(68)
24.1 Operating systems	883	(6)
24.1.1 Introduction to MS-DOS	885	(1)
24.1.2 Introduction to UNIX	886	(3)
24.2 High-level programming languages	889	(4)
24.2.1 Program structures	890	(2)
24.2.2 Object-oriented programming (OOP)	892	(1)
Introduction to PASCAL	893	(21)
24.3 Basic structure	894	(1)
24.4 Variables and types	894	(6)
24.4.1 Integers	895	(1)
24.4.2 Real numbers	895	(1)
24.4.3 Boolean values	895	(1)
24.4.4 ARRAYs	895	(1)
24.4.5 Characters and character strings	896	(1)
24.4.6 RECORD	897	(1)
24.4.7 Pointers	898	(1)
24.4.8 Self-defined types	899	(1)
24.5 Statements	900	(5)
24.5.1 Assignments and expressions	900	(1)
24.5.2 Input and output	901	(1)
24.5.3 Compound statements	902	(1)
24.5.4 Conditional statements IF and CASE	903	(1)
24.5.5 Loops FOR, WHILE, and REPEAT	904	(1)
24.6 Procedures and functions	905	(3)
24.6.1 Procedures	905	(1)
24.6.2 Functions	906	(1)
24.6.3 Local and global variables, parameter passing	906	(2)
24.7 Recursion	908	(11)
24.8 Basic algorithms	909	(4)
24.8.1 Dynamic data structures	909	(1)
24.8.2 Search	910	(1)
24.8.3 Sorting	911	(2)
24.9 Computer graphics	913	(1)
24.9.1 Basic functions	913	(1)
Introduction to C	914	(10)
24.9.2 Basic structures	914	(2)
24.9.3 Operators	916	(2)
24.9.4 Data structures	918	(3)
24.9.5 Loops and branches	921	(3)
Introduction to C++	924	(6)
24.9.6 Variables and constants	924	(1)
24.9.7 Overloading of functions	924	(1)
24.9.8 Overloading of operators	924	(1)
24.9.9 Classes	925	(1)
24.9.10 Instantiation of classes	926	(1)
24.9.11 friend functions	926	(1)
24.9.12 Operators as member functions	926	(1)
24.9.13 Constructors	927	(1)
24.9.14 Derived classes (inheritance)	928	(1)
24.9.15 Class libraries	929	(1)
Introduction to FORTRAN	930	(7)
24.9.16 Program structure	930	(1)
24.9.17 Data structures	930	(1)
24.9.18 Type conversion	931	(2)
24.9.19 Operators	933	(1)
24.9.20 Loops and branches	933	(1)
24.9.21 Subprograms	934	(3)
Computer algebra	937	(14)
24.9.22 Structural elements of Mathematica	937	(3)
24.9.23 Structural elements of Maple	940	(2)
24.9.24 Algebraic expressions	942	(1)
24.9.25 Equations and systems of equations	943	(1)
24.9.26 Linear algebra	944	(1)
24.9.27 Differential and integral calculus	945	(2)
24.9.28 Programming	947	(1)
24.9.29 Fitting curves and interpolation with Mathematica	948	(1)
24.9.30 Graphics	949	(2)
25 Tables of integrals	951	(48)
25.1 Integrals of rational functions	951	(12)
25.1.1 Integrals with P = ax + b, a is not equal to 0	951	(1)
25.1.2 Integrals with x(m)/(ax + b)(n), P = ax + b, a is not equal to 0, P is not equal to 0	952	(1)
25.1.3 Integrals with 1/(x)(n)(ax + b)(m), P = ax + b b is not equal to 0	953	(2)
25.1.4 Integrals with ax + b and cx + d c is not equal to 0	955	(1)
25.1.5 Integrals with a + x and b + x a is not equal to b	955	(1)
25.1.6 Integrals with P = ax(2)+ bx + c a is not equal to 0	956	(1)
25.1.7 Integrals with x(n)/(ax)(2) + bx + c(m), P = ax(2) + bx + c a is not equal to 0	956	(1)
25.1.8 Integrals with 1/(x)(n)/(ax)(2) + bx + c)(m), P = ax(2) + bx + c c is not equal to 0	957	(1)
25.1.9 Integrals with P = a(2) XXX x (2)	958	(1)
25.1.10 Integrals with 1/(a)(2) XXX x(2)(n), P = a(2) XXX x(2) a is not equal to 0	958	(1)
25.1.11 Integrals with x(n)/(a)(2) XXX x(2)(m), P = a(2) XXX x(2) a is not equal to 0	958	(2)
25.1.12 Integrals with 1/(x)(n)(a)(2) XXX x(2)(m) P = a(2) XXX x(2) a is not equal to 0	960	(1)
25.1.13 Integrals with P = a(3) XXX x(3) a is not equal to 0	961	(1)
25.1.14 Integrals with a(4) + x(4) a is greater than 0	962	(1)
25.1.15 Integrals with a(4) - x(4) a is greater than 0	962	(1)
25.2 Integrals of irrational functions	963	(10)
25.2.1 Integrals with x(1/2) and P = ax + b a, b is not equal to 0	963	(1)
25.2.2 Integrals with (ax + b)(1/2) P = ax + b a is not equal to 0	964	(2)
25.2.3 Integrals with (ax + b)(1/2) and (cx + d)(1/2), a, c is not equal to 0	966	(1)
25.2.4 Integrals with R = (a)(2) + x(2)(1)(2) a is not equal to 0	966	(2)
25.2.5 Integrals with S = (x)(2) - a(2)(1)(2) a is not equal to 0	968	(2)
25.2.6 Integrals with T = (a)(2) - x(2)(1)(2) a is not equal to 0	970	(2)
25.2.7 Integrals with (ax)(2) + bx + c(1)(2) X = ax(2) + bx + c a is not equal to 0	972	(1)
25.3 Integrals of transcendental functions	973	(19)
25.3.1 Integrals with exponential functions	973	(2)
25.3.2 Integrals with logarithmic functions (x is greater than 0)	975	(2)
25.3.3 Integrals with hyperbolic functions (a is not equal to 0)	977	(2)
25.3.4 Integrals with inverse hyperbolic functions	979	(1)
25.3.5 Integrals with sine and cosine functions (a is not equal to 0)	979	(5)
25.3.6 Integrals with sine and cosine functions (a is not equal to 0)	984	(5)
25.3.7 Integrals with tangent or cotangent functions (a is not equal to 0)	989	(1)
25.3.8 Integrals with inverse trigonometric functions (a is not equal to 0)	990	(2)
25.4 Definite integrals	992	(7)
25.4.1 Definite integrals with algebraic functions	992	(1)
25.4.2 Definite integrals with exponential functions	992	(2)
25.4.3 Definite integrals with logarithmic functions	994	(1)
25.4.4 Definite integrals with trigonometric functions	995	(4)
Index	999