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Lectures on Applications-Oriented Mathematics [Elektronisk resurs]
- Friedman, Bernard. (författare)
- Twersky, Victor. (författare)
- ISBN 9781118030264
- Publicerad: Hoboken : John Wiley & Sons, 2011
- Engelska 1 online resource (272 p.)
- E-bok
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- Lectures on Applications-Oriented Mathematics; TABLE OF CONTENTS; INTRODUCTION; CHAPTER 1. DISTRIBUTIONS; 1.1 DELTA FUNCTIONS AND DISTRIBUTIONS; Introduction; Symbolic Functions; Change of Variables; Derivatives of Distributions; 1.2 APPLICATIONS OF DISTRIBUTIONS; Integration of Distributions; Limits of Symbolic Functions; Symbolic Functions in More than One Dimension; Illustration from Electrostatics; Equation of Continuity for Electric Charge; 1.3 DISTRIBUTIONS AND TRANSFORMS; An Integral Representation for d(x); The Fourier Integral; Finite Parts of Integrals.
- Operational Methods and Laplace TransformSolution of the Heat Equation; Fourier Series; CHAPTER 2. SPECTRAL THEORY OF OPERATORS; 2.1 LINEAR VECTOR SPACES; Introduction; Examples; Function Spaces; Event Spaces; Inner Product; Schwarz Inequality; Projection; Applications to Probability; 2.2 LINEAR OPERATORS; Adjoint Operator; Quantum Mechanics; Uncertainty Principle; Spectral Representation; Functions of an Operator; Continuous Spectrum; Partial Differential Equations; CHAPTER 3. ASYMPTOTIC METHODS; INTRODUCTION; 3.1 ASYMPTOTIC SERIES; Definition of Asymptotic Expansion.
- Operations with Asymptotic SeriesIntegration by Parts; Improving an Expansion; 3.2 WATSON'S LEMMA; Stirling's Formula; Laplace's Method; 3.3 METHODS OF STEEPEST DESCENT; 3.4 METHOD OF STATIONARY PHASE; Two Dimensions; Finite Limits; 3.5 AIRY INTEGRAL; Contour Integration Procedures; Pole Near Stationary Point; CHAPTER 4. DIFFERENCE EQUATIONS; 4.1 RECURRENCE RELATIONS AND DIFFERENCE EQUATIONS; Introduction; Finite Difference Operators; Connection between Differences and Derivatives; Inverse of a Difference Operator; Simple Recurrence Relations; 4.2 DIFFERENCE EQUATIONS OF ORDER HIGHER THAN ONE.
- Nonhomogeneous Difference Equations4.3 THE METHOD OF THE GENERATING FUNCTION; Linear Difference Equations with Nonconstant Coefficients; Method of Integral Transform; Linear First-Order Equations; 4.4 SUMMATION BY PARTS; Generalization of Summation by Parts; Euler-Maclaurin Formula; 4.5 SPECIAL METHODS; Poisson Process; CHAPTER 5. COMPLEX INTEGRATION; INTRODUCTION; 5.1 ANALYTIC FUNCTIONS; Singularities; Residues; Full-Period Integrals of Trigonometric Functions; Cauchy Principal Value; 5.2 INTEGRALS OF RATIONAL FUNCTIONS; Integrals of Exponentials Multiplied by Rational Functions.
- Evaluation of Infinite Series5.3 INTEGRALS INVOLVING BRANCH POINTS; 5.4 CONTOUR INTEGRAL REPRESENTATIONS OF SOLUTIONS TO THE WAVE EQUATION; CHAPTER 6. SYMBOLIC METHODS; INTRODUCTION; 6.1 DIFFERENTIAL OPERATORS; 6.2 DIFFERENCE OPERATORS; 6.3 LAPLACE TRANSFORMS; 6.4 SYMBOLIC METHODS AND GENERATING FUNCTIONS; 6.5 NONCOMMUTATIVE OPERATORS; CHAPTER 7. PROBABILITY; 7.1 INTRODUCTION; The Algebra of Sets; Finite Sample Space; 7.2 ELEMENTARY PROPERTIES OF PROBABILITY; Method of Assigning Probability; Expected Values; Indicator Functions; Dependent Events; Independent Events; Product Spaces.
- 7.3 INFINITE SAMPLE SPACES.
- Meets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.
Ämnesord
- Mathematics.
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- Electronic books. (LCSH)
Klassifikation
- QA37.2 .F74 (LCC)
- 510 (DDC)
- Ta (kssb/8 (machine generated))
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