Kooperativer Bibliotheksverbund

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Format: XV, 367 S.

ISBN: 0-86720-293-9

Series Statement: Jones and Bartlett books in mathematics

Language: English

Subjects: Mathematics

Keywords: Numerische Integration

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005430437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Inhaltsverzeichnis

URL: Inhaltsverzeichnis

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005430437&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

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Format: XX, 673 S.

ISBN: 0-12-784390-6

Language: English

Subjects: Mathematics

Keywords: Differentialgleichung ; Handbuch ; Beispielsammlung

URL: Inhaltsverzeichnis

URL: Inhaltstext

URL: Inhaltsverzeichnis

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Format: IX, 812 S.

Edition: 30. ed.

ISBN: 0-8493-2479-3

Language: English

Subjects: Mathematics

Keywords: Mathematik ; Tabelle ; Mathematik ; Formelsammlung ; Formelsammlung ; Formelsammlung ; Formelsammlung

URL: https://www.gbv.de/dms/ilmenau/toc/190707232.PDF

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Format: XX, 787 S.

Edition: 2nd ed.

ISBN: 0-12-784391-4

Subjects: Mathematics

Keywords: Handbuch ; Differentialgleichung ; Beispielsammlung

URL: Inhaltsverzeichnis

URL: Inhaltstext

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Format: 1 online resource.

Edition: Fourth edition.

ISBN: 9780429286834 , 042928683X , 9781000468168 , 100046816X , 9781000468182 , 1000468186

Series Statement: Advances in applied mathematics

Content: "Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition"--

Additional Edition: Print version: Zwillinger, Daniel, 1957- Handbook of differential equations Boca Raton : Chapman & Hall, CRC Press, 2022 ISBN 9780367252571

Language: English

Keywords: Electronic books.

URL: https://www.taylorfrancis.com/books/9780429286834

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Format: 1 online resource (1184 pages)

Edition: 8th edition.

Uniform Title: Tablitsy integralov, summ, riadov i proizvedenii.

Content: The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions. The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates. Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged. The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source. Over 10, 000 mathematical entries Most up to date listing of integrals, series and products (special functions) Provides accuracy and efficiency in industry work 25% of new material not including changes to the restrictions on results that revise the range of validity of results, which lend to approximately 35% of new updates

Note: Bibliographic Level Mode of Issuance: Monograph , Front Cover -- Table of Integrals, Series, and Products -- Copyright -- Contents -- Preface to the Eighth Edition -- Acknowledgments -- The Order of Presentation of the Formulas -- Use of the Tables -- Bernoulli and Euler Polynomials and Numbers -- Elliptic Functions and Elliptic Integrals -- The Jacobi Zeta Function and Theta Functions -- Exponential and Related Integrals -- Hermite and Chebyshev Orthogonal Polynomials -- Bessel Functions -- Parabolic Cylinder Functions and Whittaker Functions -- Mathieu Functions -- Index of Special Functions -- Notation -- Note on the Bibliographic References -- 0 Introduction -- 0.1 Finite sums -- 0.11 Progressions -- 0.12 Sums of powers of natural numbers -- 0.13 Sums of reciprocals of natural numbers -- 0.14 Sums of products of reciprocals of natural numbers -- 0.15 Sums of the binomial coefficients -- 0.2 Numerical series and infinite products -- 0.21 The convergence of numerical series -- 0.22 Convergence tests -- 0.23-0.24 Examples of numerical series -- 0.25 Infinite products -- 0.26 Examples of infinite products -- 0.3 Functional series -- 0.30 Definitions and theorems -- 0.31 Power series -- 0.32 Fourier series -- 0.33 Asymptotic series -- 0.4 Certain formulas from differential calculus -- 0.41 Differentiation of a definite integral with respect to a parameter -- 0.42 The nth derivative of a product (Leibniz's rule) -- 0.43 The nth derivative of a composite function -- 0.44 Integration by substitution -- 1 Elementary Functions -- 1.1 Power of Binomials -- 1.11 Power series -- 1.12 Series of rational fractions -- 1.2 The Exponential Function -- 1.21 Series representation -- 1.22 Functional relations -- 1.23 Series of exponentials -- 1.3-1.4 Trigonometric and Hyperbolic Functions -- 1.30 Introduction -- 1.31 The basic functional relations. , 1.32 The representation of powers of trigonometric and hyperbolic functions in terms of functions of multiples of the argu ... -- 1.33 The representation of trigonometric and hyperbolic functions of multiples of the argument (angle) in terms of powers... -- 1.34 Certain sums of trigonometric and hyperbolic functions -- 1.35 Sums of powers of trigonometric functions of multiple angles -- 1.36 Sums of products of trigonometric functions of multiple angles -- 1.37 Sums of tangents of multiple angles -- 1.38 Sums leading to hyperbolic tangents and cotangents -- 1.39 The representation of cosines and sines of multiples of the angle as finite products -- 1.41 The expansion of trigonometric and hyperbolic functions in power series -- 1.42 Expansion in series of simple fractions -- 1.43 Representation in the form of an infinite product -- 1.44-1.45 Trigonometric (Fourier) series -- 1.46 Series of products of exponential and trigonometric functions -- 1.47 Series of hyperbolic functions -- 1.48 Lobachevskiy's ``Angle of parallelism'' Π(x) -- 1.49 The hyperbolic amplitude (the Gudermannian) gd x -- 1.5 The Logarithm -- 1.51 Series representation -- 1.52 Series of logarithms (cf. 1.431) -- 1.6 The Inverse Trigonometric and Hyperbolic Functions -- 1.61 The domain of definition -- 1.62-1.63 Functional relations -- 1.64 Series representations -- 2 Indefinite Integrals of Elementary Functions -- 2.0 Introduction -- 2.00 General remarks -- 2.01 The basic integrals -- 2.02 General formulas -- 2.1 Rational Functions -- 2.10 General integration rules -- 2.11-2.13 Forms containing the binomial a+bxk -- 2.14 Forms containing the binomial 1 ± xn -- 2.15 Forms containing pairs of binomials: a+bx and α+βx -- 2.16 Forms containing the trinomial a+bxk+c x2k -- 2.17 Forms containing the quadratic trinomial a+bx+cx2 and powers of x. , 2.18 Forms containing the quadratic trinomial a+bx+cx2 and the binomial α+βx -- 2.2 Algebraic functions -- 2.20 Introduction -- 2.21 Forms containing the binomial a+bxk and √x -- 2.22-2.23 Forms containing n(a + bx)k -- The square root -- Cube root -- 2.24 Forms containing a+bx and the binomial α+βx -- 2.25 Forms containing a+bx+cx2 -- Integration techniques -- 2.26 Forms containing a+bx+cx2 and integral powers of x -- 2.2712 Forms containing a+c x2 and integral powers of x -- 2.28 Forms containing a+bx+c x2 and first-and second-degree polynomials -- 2.29 Integrals that can be reduced to elliptic or pseudo-elliptic integrals -- 2.3 The Exponential Function -- 2.31 Forms containing eax -- 2.32 The exponential combined with rational functions of x -- 2.4 Hyperbolic Functions -- 2.41-2.43 Powers of sinh x, cosh x, tanh x, and coth x -- Powers of hyperbolic functions and hyperbolic functions of linear functions of the argument -- 2.44-2.45 Rational functions of hyperbolic functions -- 2.46 Algebraic functions of hyperbolic functions -- 2.47 Combinations of hyperbolic functions and powers -- 2.48 Combinations of hyperbolic functions, exponentials, and powers -- 2.5-2.6 Trigonometric Functions -- 2.50 Introduction -- 2.51-2.52 Powers of trigonometric functions -- 2.53-2.54 Sines and cosines of multiple angles and of linear and more complicated functions of the argument -- 2.55-2.56 Rational functions of the sine and cosine -- 2.57 Integrals containing a ± b sin x or a ± b cos x -- 2.58-2.62 Integrals reducible to elliptic and pseudo-elliptic integrals -- 2.63-2.65 Products of trigonometric functions and powers -- 2.66 Combinations of trigonometric functions and exponentials -- 2.67 Combinations of trigonometric and hyperbolic functions -- 2.7 Logarithms and Inverse-Hyperbolic Functions -- 2.71 The logarithm. , 2.72-2.73 Combinations of logarithms and algebraic functions -- 2.74 Inverse hyperbolic functions -- 2.75 Logarithms and exponential functions -- 2.8 Inverse Trigonometric Functions -- 2.81 Arcsines and arccosines -- 2.82 The arcsecant, the arccosecant, the arctangent and the arccotangent -- 2.83 Combinations of arcsine or arccosine and algebraic functions -- 2.84 Combinations of the arcsecant and arccosecant with powers of x -- 2.85 Combinations of the arctangent and arccotangent with algebraic functions -- 3-4 Definite Integrals of Elementary Functions -- 3.0 Introduction -- 3.01 Theorems of a general nature -- 3.02 Change of variable in a definite integral -- 3.03 General formulas -- 3.04 Improper integrals -- 3.05 The principal values of improper integrals -- 3.1-3.2 Power and Algebraic Functions -- 3.11 Rational functions -- 3.12 Products of rational functions and expressions that can be reduced to square roots of first-and second-degree polynomials -- 3.13-3.17 Expressions that can be reduced to square roots of third-and fourth-degree polynomials and their products with ration -- 3.18 Expressions that can be reduced to fourth roots of second-degree polynomials and their products with rational functions -- 3.19-3.23 Combinations of powers of x and powers of binomials of the form (α+βx) -- 3.24-3.27 Powers of x, of binomials of the form α+βxp and of polynomials in x -- 3.3-3.4 Exponential Functions -- 3.31 Exponential functions -- 3.32-3.34 Exponentials of more complicated arguments -- 3.35 Combinations of exponentials and rational functions -- 3.36-3.37 Combinations of exponentials and algebraic functions -- 3.38-3.39 Combinations of exponentials and arbitrary powers -- 3.41-3.44 Combinations of rational functions of powers and exponentials -- 3.45 Combinations of powers and algebraic functions of exponentials. , 3.46-3.48 Combinations of exponentials of more complicated arguments and powers -- 3.5 Hyperbolic Functions -- 3.51 Hyperbolic functions -- 3.52-3.53 Combinations of hyperbolic functions and algebraic functions -- 3.54 Combinations of hyperbolic functions and exponentials -- 3.55-3.56 Combinations of hyperbolic functions, exponentials, and powers -- 3.6-4.1 Trigonometric Functions -- 3.61 Rational functions of sines and cosines and trigonometric functions of multiple angles -- 3.62 Powers of trigonometric functions -- 3.63 Powers of trigonometric functions and trigonometric functions of linear functions -- 3.64-3.65 Powers and rational functions of trigonometric functions -- 3.66 Forms containing powers of linear functions of trigonometric functions -- 3.67 Square roots of expressions containing trigonometric functions -- 3.68 Various forms of powers of trigonometric functions -- 3.69-3.71 Trigonometric functions of more complicated arguments -- 3.72-3.74 Combinations of trigonometric and rational functions -- 3.75 Combinations of trigonometric and algebraic functions -- 3.76-3.77 Combinations of trigonometric functions and powers -- 3.78-3.81 Rational functions of x and of trigonometric functions -- 3.82-3.83 Powers of trigonometric functions combined with other powers -- 3.84 Integrals containing 1 − k2 sin2 x, 1 − k2 cos2 x, and similar expressions -- 3.85-3.88 Trigonometric functions of more complicated arguments combined with powers -- 3.89-3.91 Trigonometric functions and exponentials -- 3.92 Trigonometric functions of more complicated arguments combined with exponentials -- 3.93 Trigonometric and exponential functions of trigonometric functions -- 3.94-3.97 Combinations involving trigonometric functions, exponentials, and powers -- 3.98-3.99 Combinations of trigonometric and hyperbolic functions. , 4.11-4.12 Combinations involving trigonometric and hyperbolic functions and powers. , Translated from the Russian.

Additional Edition: ISBN 0-12-384933-0

Language: English

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Format: 1 online resource (1220 p.)

Edition: 7th ed.

ISBN: 0-12-373862-8 , 0-12-384934-9 , 1-280-96276-3 , 9786610962761 , 0-08-047111-0

Content: The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with

Note: "Translated from Russian by Scripta Technica, Inc." , Table of Integrals, Series, and Products; Copyright Page; Table of Contents; Preface to the Seventh Edition; Acknowledgments; The Order of Presentation of the Formulas; Use of the Tables; Index of Special Functions; Notation; Note on the Bibliographic References; Chapter 0. Introduction; 0.1 Finite Sums; 0.2 Numerical Series and Infinite Products; 0.3 Functional Series; 0.4 Certain Formulas from Differential Calculus; Chapter 1. Elementary Functions; 1.1 Power of Binomials; 1.2 The Exponential Function; 1.3-1.4 Trigonometric and Hyperbolic Functions; 1.5 The Logarithm , 1.6 The Inverse Trigonometric and Hyperbolic FunctionsChapter 2. Indefinite Integrals of Elementary Functions; 2.0 Introduction; 2.1 Rational Functions; 2.2 Algebraic Functions; 2.3 The Exponential Function; 2.4 Hyperbolic Functions; 2.5-2.6 Trigonometric Functions; 2.7 Logarithms and Inverse-Hyperbolic Functions; 2.8 Inverse Trigonometric Functions; Chapter 3-4. Definite Integrals of Elementary Functions; 3.0 Introduction; 3.1-3.2 Power and Algebraic Functions; 3.3-3.4 Exponential Functions; 3.5 Hyperbolic Functions; 3.6-4.1 Trigonometric Functions; 4.2-4.4 Logarithmic Functions , 4.5 Inverse Trigonometric Functions4.6 Multiple Integrals; Chapter 5. Indefinite Integrals of Special Functions; 5.1 Elliptic Integrals and Functions; 5.2 The Exponential Integral Function; 5.3 The Sine Integral and the Cosine Integral; 5.4 The Probability Integral and Fresnel Integrals; 5.5 Bessel Functions; Chapter 6-7. Definite Integrals of Special Functions; 6.1 Elliptic Integrals and Functions; 6.2-6.3 The Exponential Integral Function and Functions Generated by It; 6.4 The Gamma Function and Functions Generated by It; 6.5-6.7 Bessel Functions; 6.8 Functions Generated by Bessel Functions , 6.9 Mathieu Functions7.1-7.2 Associated Legendre Functions; 7.3-7.4 Orthogonal Polynomials; 7.5 Hypergeometric Functions; 7.6 Confluent Hypergeometric Functions; 7.7 Parabolic Cylinder Functions; 7.8 Meijer's and MacRobert's Functions (G and E); Chapter 8-9. Special Functions; 8.1 Elliptic Integrals and Functions; 8.2 The Exponential Integral Function and Functions Generated by It; 8.3 Euler's Integrals of the First and Second Kinds; 8.4-8.5 Bessel Functions and Functions Associated with Them; 8.6 Mathieu Functions; 8.7-8.8 Associated Legendre Functions; 8.9 Orthogonal Polynomials , 9.1 Hypergeometric Functions9.2 Confluent Hypergeometric Functions; 9.3 Meijer's G-Function; 9.4 MacRobert's E-Function; 9.5 Riemann's Zeta Functions zeta(z,q) and zeta(z), and the Functions Phi(z,s,v) and xi(s); 9.6 Bernoulli Numbers and Polynomials, Euler Numbers; 9.7 Constants; Chapter 10. Vector Field Theory; 10.1-10.8 Vectors, Vector Operators, and Integral Theorems; Chapter 11 Algebraic Inequalities; 11.1-11.3 General Algebraic Inequalities; Chapter 12. Integral Inequalities; 12.11 Mean Value Theorems; 12.21 Differentiation of Definite Integral Containing a Parameter , 12.31 Integral Inequalities , English

Additional Edition: ISBN 1-322-15846-0

Additional Edition: ISBN 0-12-373637-4

Language: English

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Format: 1 online resource

Edition: Thirty-third edition.

ISBN: 9781498777810 , 1498777813 , 9781351641494 , 1351641492

Series Statement: Advances in Applied Mathematics

Content: "Containing more than 6,000 entries, CRC Standard Mathematical Tables and Formulas, 33rd Edition continues to provide essential formulas, tables, figures and detailed descriptions. The newest edition of this popular series also features many diagrams, group tables, and integrals that are not available online. This edition also incorporates important topics such as max plus algebra, financial options, pseudospectra, and proof methods. Newly updated topics reflecting new results include coupled analogues, general relativity, radar, and significant equations of mathematics."--Provided by publisher.

Note: Chapter 1 Numbers and Elementary Mathematics -- chapter 2 Algebra -- chapter 3 Discrete Mathematics -- chapter 4 Geometry -- chapter 5 Analysis -- chapter 6 Special Functions -- chapter 7 Probability and Statistics -- chapter 8 Scientific Computing -- chapter 9 Mathematical Formulas from the Sciences -- chapter 10 Miscellaneous.

Additional Edition: Print version: ISBN 9781498777803

Language: English

Keywords: Mathematical formulae

DOI: 10.1201/9781315154978

URL: https://www.taylorfrancis.com/books/9781315154978