Survey of Applicable Mathematics

ISBN-13: 9789401583107 / Angielski / Miękka / 2014 / 1723 str.

K. Rektorys

Opis

This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969.
The thirty-seven chapters cover all the important mathematical fields of use in applications: algebra, geometry, differential and integral calculus, infinite series, orthogonal systems of functions, Fourier series, special functions, ordinary differential equations, partial differential equations, integral equations, functions of one and several complex variables, conformal mapping, integral transforms, functional analysis, numerical methods in algebra and in algebra and in differential boundary value problems, probability, statistics, stochastic processes, calculus of variations, and linear programming. All proofs have been omitted. However, theorems are carefully formulated, and where considered useful, are commented with explanatory remarks. Many practical examples are given by way of illustration. Each of the two volumes contains an extensive bibliography and a comprehensive index.
Together these two volumes represent a survey library of mathematics which is applicable in many fields of science, engineering, economics, etc.
For researchers, students and teachers of mathematics and its applications.

Recenzje

`The book is written for the use of a very wide circle of readers. It seems to me that it is an ideal survey of mathematics needed in colleges for technical professions, in Germany called `Fachhochschule'. I recommend it warmly for this purpose.
H. Koch in Zentralblatt f. Mathematik 805:1, 1995

Spis treści

Volume I Foreword. Prefaces. List of symbols and notation. 1. Arithmetic and Algebra; V. Vilhelm. 2. Trigonometric and Inverse Trigonometric Functions. Hyperbolic and Inverse Hyperbolic Functions; V. Vilhelm. 3. Some Formulae (Areas, Circumferences, Volumes, Surfaces, Centroids, Moments of Inertia); V. Vilhelm. 4. Plane Curves and Constructions; K. Drábek. 5. Plane Analytic Geometry; M. Zelenka. 6. Solid Analytic Geometry; F. Kejla. 7. Vector Calculus; F. Kejla, K. Rektorys. 8. Tensor Calculus; V. Vilhelm. 9. Differential Geometry; B. Kepr. 10. Sequences and Series of Constant Terms. Infinite Products; K. Rektorys. 11. Differential Calculus of Functions of a Real Variable; K. Rektorys. 12. Functions of Two or More Variables; K. Rektorys. 13. Integral Calculus of Functions of One Variable; K. Rektorys. 14. Integral Calculus of Functions of Two and More Variables; k. Rektorys. 15. Sequences and Series with Variable Terms (Sequences and Series of Functions); K. Rektorys. 16. The Space L2. Orthogonal Systems. Fourier Series. Some Special Functions (Bessel Functions, etc.); K. Rektorys. References. Index. Volume II Preface. List of symbols and notations. 17. Ordinary Differential Equations; K. Rektorys. 18. Partial Differential Equations; K. Rektorys. 19. Integral Equations; k. Rektorys. 20. Functions of One andMore Complex Variables; K. Rektorys, J. Fuka. 21. Conformal Mapping; J. Fuka. 22. Fundamentals of the Theory of Sets and Functional Analysis; K. Rektorys. 23. Calculus of Variations; F. Nožička. 24. Variational Methods for Numerical Solution of Boundary-Value Problems for Differential Equations. Finite Element Method. Boundary Element Method; M. Práger. 25. ApproximateSolution of Ordinary Differential Equations; E. Vitásek. 26. Solution of Partial Differential Equations by Infinite Series (by the Fourier Method); K. Rektorys. 27. Solution of Partial Differential Equations by the Finite-Difference Method; E. Vitásek. 28. Integral Transforms (Operational Calculus); J. Nečas. 29. Approximate Solution of Fredholm's Integral Equations; K. Rektorys. 30. Numerical Methods in Linear Algebra; J. Segethová, K. Segeth. 31. Numerical Solution of Algebraic and Transcendental Equations; M. Fiedler. 32. Approximation. Interpolation, Splines; E. Vitásek. 33. Probability Theory; T. Cipra. 34. Mathematical Statistics; T. Cipra. 35. Topics in Statistical Inference; T. Cipra. 36. Stochastic Processes; T. Cipra. 37. Linear Programming; F. Nožička. References. Index.