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9780387947464

Handbook of Mathematics and Computational Science

by ;
  • ISBN13:

    9780387947464

  • ISBN10:

    0387947469

  • Format: Hardcover
  • Copyright: 1998-07-01
  • Publisher: Springer Verlag
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List Price: $179.99

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

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