# krainaksiazek the integration theory of linear ordinary differential equations 20045695

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### The Turning Point Problem In The Asymptotic Integration Of Ordinary Linear Differential Equations (Classic Reprint)

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>CalculusKsiążki Obcojęzyczne>Angi...**

Sklep: Gigant.pl

### Ordinary Differential Equations

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Calculus of variationsKsiążki Obcoję...**

Develops The Theory Of Initial-, Boundary-, And Eigen Value Problems, Real And Complex Linear Systems, Asymptotic Behavior And Stability. This Book Emphasizes Differential Inequalities And Treats More Advanced Topics Such As Caratheodory Theory, Nonlinear Boundary Value Problems And Radially Symmetric Elliptic Problems.

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### Ordinary Differential Equations Universal Publishers

**Książki / Literatura obcojęzyczna**

This introductory course in ordinary differential equations, intended for junior undergraduate students in applied mathematics, science and engineering, focuses on methods of solution and applications rather than theoretical analyses. Applications drawn mainly from dynamics, population biology and electric circuit theory are used to show how ordinary differential equations appear in the formulation of problems in science and engineering. The calculus required to comprehend this course is rather elementary, involving differentiation, integration and power series representation of only real functions of one variable. A basic knowledge of complex numbers and their arithmetic is also assumed, so that elementary complex functions which can be used for working out easily the general solutions of certain ordinary differential equations can be introduced. The pre-requisites just mentioned aside, the course is mainly self-contained. To promote the use of this course for self-study, suggested solutions are not only given to all set exercises, but they are also by and large complete with details.

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### Introduction to Linear Algebra and Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Preface 1. Complex Numbers 1.1 Introduction 1.2 The Algebra of Complex Numbers 1.3 The Geometry of Complex Numbers 1.4 Two-dimensional Vectors 1.5 Functions of a Complex Variable 1.6 Exponential Function 1.7 Power Series 2. Linear Algebraic Equations 2.1 Introduction 2.2 Matrices 2.3 Elimination Method 2.4 Determinants 2.5 Inverse of a Matrix 2.6 Existence and Uniqueness Theorems 3. Vector Spaces 3.1 Introduction 3.2 Three-dimensional Vectors 3.3 Axioms of a Vector Space 3.4 Dependence and Independence of Vectors 3.5 Basis and Dimension 3.6 Scalar Product 3.7 Orthonormal Bases 3.8 Infinite-dimensional Vector Spaces 4. Linear Transformations 4.1 Introduction 4.2 Definitions and Examples 4.3 Matrix Representations 4.4 Changes of Bases 4.5 Characteristic Values and Characteristic Vectors 4.6 Symmetric and Hermitian Matrices 4.7 Jordan Forms 5. First Order Differential Equations 5.1 Introduction 5.2 An Example 5.3 Basic Definitions 5.4 First Order Linear Equations 5.5 First Order Nonlinear Equations 5.6 Applications of First Order Equations 5.7 Numerical Methods 5.8 Existence and Uniqueness 6. Linear Differential Equations 6.1 Introduction 6.2 General Theorems 6.3 Variation of Parameters 6.4 Equations with Constant Coefficients 6.5 Method of Undetermined Coefficients 6.6 Applications 6.7 Green's Functions 7. Laplace Transforms 7.1 Introduction 7.2 Existence of the Transform 7.3 Transforms of Certain Functions 7.4 Inversion of the Transform 7.5 Solution of Differential Equations 7.6 Applications 7.7 Uniqueness of the Transform 8. Power-Series Methods 8.1 Introduction 8.2 Solution near Ordinary Points 8.3 Solution near Regular Singular Points 8.4 Bessel Functions 8.5 Boundary-value Problems 8.6 Convergence Theorems 9. Systems of Differential Equations 9.1 Introduction 9.2 First Order Systems 9.3 Linear First Order Systems 9.4 Linear First Order Systems with Constant Coefficients 9.5 Higher Order Linear Systems 9.6 Existence and Uniqueness Theorem Answers and Hints for Selected Exercises; Index

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### Introduction to Partial Differential Equations Dover Publications

**Książki / Literatura obcojęzyczna**

Chapter 1. Fourier series 1.1 Basic concepts 1.2 Fourier series and Fourier coefficients 1.3 A mimimizing property of the Fourier coefficients. The Riemann-Lebesgue theorem 1.4 Convergence of Fourier series 1.5 The Parseval formula 1.6 Determination of the sum of certain trigonemetric series Chapter 2. Orthogonal systems 2.1 Integration of complex-valued functions of a real variable 2.2 Orthogonal systems 2.3 Complete orthogonal systems 2.4 Integration of Fourier series 2.5 The Gram-Schmidt orthogonalization process 2.6 Sturm-Liouville problems Chapter 3. Orthogonal polynomials 3.1 The Legendre polynomials 3.2 Legendre series 3.3 The Legendre differential equation. The generating function of the Legendre polynomials 3.4 The Tchebycheff polynomials 3.5 Tchebycheff series 3.6 The Hermite polynomials. The Laguerre polynomials Chapter 4. Fourier transforms 4.1 Infinite interval of integration 4.2 The Fourier integral formula: a heuristic introduction 4.3 Auxiliary theorems 4.4 Proof of the Fourier integral formula. Fourier transforms 4.5 The convention theorem. The Parseval formula Chapter 5. Laplace transforms 5.1 Definition of the Laplace transform. Domain. Analyticity 5.2 Inversion formula 5.3 Further properties of Laplace transforms. The convolution theorem 5.4 Applications to ordinary differential equations Chapter 6. Bessel functions 6.1 The gamma function 6.2 The Bessel differential equation. Bessel functions 6.3 Some particular Bessel functions 6.4 Recursion formulas for the Bessel functions 6.5 Estimation of Bessel functions for large values of x. The zeros of the Bessel functions 6.6 Bessel series 6.7 The generating function of the Bessel functions of integral order 6.8 Neumann functions Chapter 7. Partial differential equations of first order 7.1 Introduction 7.2 The differential equation of a family of surfaces 7.3 Homogeneous differential equations 7.4 Linear and quasilinear differential equations Chapter 8. Partial differential equations of second order 8.1 Problems in physics leading to partial differential equations 8.2 Definitions 8.3 The wave equation 8.4 The heat equation 8.5 The Laplace equation Answers to exercises; Bibliography; Conventions; Symbols; Index

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### A First Course in Partial Differential Equations with Complex Variables and Transform Methods Dover Publications

**Książki / Literatura obcojęzyczna**

I. The one-dimensional wave equation 1. A physical problem and its mathematical models: the vibrating string 2. The one-dimensional wave equation 3. Discussion of the solution: characteristics 4. Reflection and the free boundary problem 5. The nonhomogeneous wave equation II. Linear second-order partial differential equations in two variables 6. Linearity and superposition 7. Uniqueness for the vibrating string problem 8. Classification of second-order equations with constant coefficients 9. Classification of general second-order operators III. Some properties of elliptic and parabolic equations 10. Laplace's equation 11. Green's theorem and uniqueness for the Laplace's equation 12. The maximum principle 13. The heat equation IV. Separation of variables and Fourier series 14. The method of separation of variables 15. Orthogonality and least square approximation 16. Completeness and the Parseval equation 17. The Riemann-Lebesgue lemma 18. Convergence of the trigonometric Fourier series 19. "Uniform convergence, Schwarz's inequality, and completeness" 20. Sine and cosine series 21. Change of scale 22. The heat equation 23. Laplace's equation in a rectangle 24. Laplace's equation in a circle 25. An extension of the validity of these solutions 26. The damped wave equation V. Nonhomogeneous problems 27. Initial value problems for ordinary differential equations 28. Boundary value problems and Green's function for ordinary differential equations 29. Nonhomogeneous problems and the finite Fourier transform 30. Green's function VI. Problems in higher dimensions and multiple Fourier series 31. Multiple Fourier series 32. Laplace's equation in a cube 33. Laplace's equation in a cylinder 34. The three-dimensional wave equation in a cube 35. Poisson's equation in a cube VII. Sturm-Liouville theory and general Fourier expansions 36. Eigenfunction expansions for regular second-order ordinary differential equations 37. Vibration of a variable string 38. Some properties of eigenvalues and eigenfunctions 39. Equations with singular endpoints 40. Some properties of Bessel functions 41. Vibration of a circular membrane 42. Forced vibration of a circular membrane: natural frequencies and resonance 43. The Legendre polynomials and associated Legendre functions 44. Laplace's equation in the sphere 45. Poisson's equation and Green's function for the sphere VIII. Analytic functions of a complex variable 46. Complex numbers 47. Complex power series and harmonic functions 48. Analytic functions 49. Contour integrals and Cauchy's theorem 50. Composition of analytic functions 51. Taylor series of composite functions 52. Conformal mapping and Laplace's equation 53. The bilinear transformation 54. Laplace's equation on unbounded domains 55. Some special conformal mappings 56. The Cauchy integral representation and Liouville's theorem IX. Evaluation of integrals by complex variable methods 57. Singularities of analytic functions 58. The calculus of residues 59. Laurent series 60. Infinite integrals 61. Infinite series of residues 62. Integrals along branch cuts X. The Fourier transform 63. The Fourier transform 64. Jordan's lemma 65. Schwarz's inequality and the triangle inequality for infinite integrals 66. Fourier transforms of square integrable functions: the Parseval equation 67. Fourier inversion theorems 68. Sine and cosine transforms 69. Some operational formulas 70. The convolution product 71. Multiple Fourier transforms: the heat equation in three dimensions 72. The three-dimensional wave equation 73. The Fourier transform with complex argument XI. The Laplace transform 74. The Laplace transform 75. Initial value problems for ordinary differential equations 76. Initial value problems for the one-dimensional heat equation 77. A diffraction problem 78. The Stokes rule and Duhamel's principle XII. Approximation methods 79. "Exact" and approximate solutions" 80. The method of finite differences for initial-boundary value problems 81. The finite difference method for Laplace's equation 82. The method of successive approximations 83. The Raleigh-Ritz method SOLUTIONS TO THE EXERCISES INDEX

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### Differential Equations and Dynamical Systems Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book contains a systems study of autonomous systems of ordinary differential equations and dynamical systems. The main purpose of the book is to introduce students to the qualitative and geometric theory of ordinary differential equations. However it is also useful as a reference book for mathematicians doing research on dynamical systems. This second edition has been substantially updated. §This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.§Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.§In addition to minor corrections and updates throughout, this new edition contains materials on higher order Melnikov functions and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

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### Linear algebra Politechnika Gdańska

**MATEMATYKA**

Podręcznik dla studentów Politechniki Gdańskiej, którzy zamierzają pogłębić wiedzie z zakresu algebry liniowej w języku angielskim. Spis treści: 1. BEATRICES 1.1 Introduction 1.2 Some types of matrices 1.3. Equal matrices 1.4. Matrix addition 1.5. Scalar multiplication 1.6. Transpose of a matrix 1.7. Symmetric and skew-symmetric matrices 1.8. Matrix multiplication 1.9. The trace of a square matrix 1.10. Exercises 1.11. Answers 2. DETERMINANTS 2.1. Introduction 2.2. Properties of determinants 2.3. Exercises 2.4. Answers 3. INVERTIBLE MATRICES 3.1. Introduction 3.2. A method of obtaining the inverse of a square matrix 3.3. Exercises 3.4. Answers 4. SYSTEMS OF LINEAR EQUATIONS 4.1. Introduction 4.2. Cramer's theorem 4.3. Method of matrix inversion 4.4. Method of Gaussian elimination 4.5. The rank of a matrix 4.6. Fundamental theorem for systems of linear equations 4.7. Application of Gaussian elimination to find the inverse of a matrix 4.8. Exercises 4.9. Answers 5. EIGENVALUES AND EIGENVECTORS 5.1. Introduction 5.2. Eigenvalues and eigenvectors 5.3. Symmetric and skew-symmetric matrices 5.4. Useful properties 5.5. Application to ordinary differential equations 5.6. Case of repeated roots 5.7. Nonhomogeneous equation. Variation of parameters 5.8. Undetermined coefficients 5.9. Exercises 5.10. Answers REFERENCES

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### Stochastic Integration with Jumps Cambridge University Press

**Książki / Literatura obcojęzyczna**

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of c

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### The Mathematics of Classical and Quantum Physics Dover Publications

**Książki / Literatura obcojęzyczna**

VOLUME ONE 1 Vectors in Classical Physics Introduction 1.1 Geometric and Algebraic Definitions of a Vector 1.2 The Resolution of a Vector into Components 1.3 The Scalar Product 1.4 Rotation of the Coordinate System: Orthogonal Transformations 1.5 The Vector Product 1.6 A Vector Treatment of Classical Orbit Theory 1.7 Differential Operations on Scalar and Vector Fields *1.8 Cartesian-Tensors 2 Calculus of Variations Introduction 2.1 Some Famous Problems 2.2 The Euler-Lagrange Equation 2.3 Some Famous Solutions 2.4 Isoperimetric Problems - Constraints 2.5 Application to Classical Mechanics 2.6 Extremization of Multiple Integrals 2.7 Invariance Principles and Noether's Theorem 3 Vectors and Matrics Introduction 3.1 "Groups, Fields, and Vector Spaces" 3.2 Linear Independence 3.3 Bases and Dimensionality 3.4 Ismorphisms 3.5 Linear Transformations 3.6 The Inverse of a Linear Transformation 3.7 Matrices 3.8 Determinants 3.9 Similarity Transformations 3.10 Eigenvalues and Eigenvectors *3.11 The Kronecker Product 4. Vector Spaces in Physics Introduction 4.1 The Inner Product 4.2 Orthogonality and Completeness 4.3 Complete Ortonormal Sets 4.4 Self-Adjoint (Hermitian and Symmetric) Transformations 4.5 Isometries-Unitary and Orthogonal Transformations 4.6 The Eigenvalues and Eigenvectors of Self-Adjoint and Isometric Transformations 4.7 Diagonalization 4.8 On The Solvability of Linear Equations 4.9 Minimum Principles 4.10 Normal Modes 4.11 Peturbation Theory-Nondegenerate Case 4.12 Peturbation Theory-Degenerate Case 5. Hilbert Space-Complete Orthonormal Sets of Functions Introduction 5.1 Function Space and Hilbert Space 5.2 Complete Orthonormal Sets of Functions 5.3 The Dirac d-Function 5.4 Weirstrass's Theorem: Approximation by Polynomials 5.5 Legendre Polynomials 5.6 Fourier Series 5.7 Fourier Integrals 5.8 Sphereical Harmonics and Associated Legendre Functions 5.9 Hermite Polynomials 5.10 Sturm-Liouville Systems-Orthogaonal Polynomials 5.11 A Mathematical Formulation of Quantum Mechanics VOLUME TWO 6 Elements and Applications of the Theory of Analytic Functions Introduction 6.1 Analytic Functions-The Cauchy-Riemann Conditions 6.2 Some Basic Analytic Functions 6.3 Complex Integration-The Cauchy-Goursat Theorem 6.4 Consequences of Cauchy's Theorem 6.5 Hilbert Transforms and the Cauchy Principal Value 6.6 An Introduction to Dispersion Relations 6.7 The Expansion of an Analytic Function in a Power Series 6.8 Residue Theory-Evaluation of Real Definite Integrals and Summation of Series 6.9 Applications to Special Functions and Integral Representations 7 Green's Function Introduction 7.1 A New Way to Solve Differential Equations 7.2 Green's Functions and Delta Functions 7.3 Green's Functions in One Dimension 7.4 Green's Functions in Three Dimensions 7.5 Radial Green's Functions 7.6 An Application to the Theory of Diffraction 7.7 Time-dependent Green's Functions: First Order 7.8 The Wave Equation 8 Introduction to Integral Equations Introduction 8.1 Iterative Techniques-Linear Integral Operators 8.2 Norms of Operators 8.3 Iterative Techniques in a Banach Space 8.4 Iterative Techniques for Nonlinear Equations 8.5 Separable Kernels 8.6 General Kernels of Finite Rank 8.7 Completely Continuous Operators 9 Integral Equations in Hilbert Space Introduction 9.1 Completely Continuous Hermitian Operators 9.2 Linear Equations and Peturbation Theory 9.3 Finite-Rank Techniques for Eigenvalue Problems 9.4 the Fredholm Alternative for Completely Continuous Operators 9.5 The Numerical Solutions of Linear Equations 9.6 Unitary Transformations 10 Introduction to Group Theory Introduction 10.1 An Inductive Approach 10.2 The Symmetric Groups 10.3 "Cosets, Classes, and Invariant Subgroups" 10.4 Symmetry and Group Representations 10.5 Irreducible Representations 10.6 "Unitary Representations, Schur's Lemmas, and Orthogonality Relations" 10.7 The Determination of Group Representations 10.8 Group Theory in Physical Problems General Bibliography Index to Volume One Index to Volume Two

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### Mathematical Analysis Birkhäuser

**Książki / Literatura obcojęzyczna**

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables.§The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis.§Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.§Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis.

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### Applied Probability Springer, Berlin

**Książki / Literatura obcojęzyczna**

This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences. Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory. Kenneth Lange is Professor of Biomathematics and Human Genetics and Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics.This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary probability theory. Given these prerequisites, Applied Probability presents a unique blend of theory and applications, with special emphasis on mathematical modeling, computational techniques, and examples from the biological sciences.§Chapter 1 reviews elementary probability and provides a brief survey of relevant results from measure theory. Chapter 2 is an extended essay on calculating expectations. Chapter 3 deals with probabilistic applications of convexity, inequalities, and optimization theory. Chapters 4 and 5 touch on combinatorics and combinatorial optimization. Chapters 6 through 11 present core material on stochastic processes. If supplemented with appropriate sections from Chapters 1 and 2, there is sufficient material here for a traditional semester-long course in stochastic processes covering the basics of Poisson processes, Markov chains, branching processes, martingales, and diffusion processes. Finally, Chapters 12 and 13 develop the Chen-Stein method of Poisson approximation and connections between probability and number theory.§Kenneth Lange is Professor of Biomathematics and Human Genetics and§Chair of the Department of Human Genetics at the UCLA School of Medicine. He has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics,§and applied stochastic processes. Springer-Verlag published his books§Numerical Analysis for Statisticians and Mathematical and Statistical Methods for Genetic Analysis Second Edition, in 1999 and 2002, respectively.

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### Representation and Control of Infinite Dimensional Systems Birkhäuser

**Książki / Literatura obcojęzyczna**

The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability. This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter systems. In the first place, the difficulty stems from the essential unboundedness of the system operator. Secondly, when control and observation are exercised through the boundary of the domain, the operator representing the sensor and actuator are also often unbounded. §The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form.§The book should be useful for mathematicians and theoretical engineers interested in the field of control.§

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### A First Course in Applied Mathematics Wiley & Sons

**Książki / Literatura obcojęzyczna**

This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Due to the broad range of applications, mathematical concepts and techniques and reviewed throughout, especially those in linear algebra, matrix analysis, and differential equations. Some classical definitions and results from analysis are also discussed and used. Some applications (postscript fonts, information retrieval, etc.) are presented at the end of a chapter as an immediate application of the theory just covered, while those applications that are discussed in more detail (ranking web pages, compression, etc.) are presented in dedicated chapters. Acollection of mathematical models of a slightly different nature, such as basic discrete mathematics and optimization, is also provided. Clear proofs of the main theorems ultimately help to make the statements of the theorems more understandable, and a multitude of examples follow important theorems and concepts. In addition, the author builds material from scratch and thoroughly covers the theory needed to explain the applications in full detail, while not overwhelming readers with unneccessary topics or discussions. In terms of exercises, the author continuously refers to the real numbers and results in calculus when introducing a new topic so readers can grasp the concept of the otherwise intimidating expressions. By doing this, the author is able to focus on the concepts rather than the rigor. The quality, quantity, and varying level of difficulty of the exercises provides instructors more classroom flexibility. Topical coverage includes linear algebra; ranking web pages; matrix factorizations; least squares; image compression; ordinary differential equations; dynamical systems; and mathematical models.

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### Special Functions Oxford University Press

**Książki / Literatura obcojęzyczna**

The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painleve equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a valuable text and reference work.

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t1=0.083, t2=0, t3=0, t4=0.024, t=0.083