Fundamentals of Mathematical Physics

• Autore: Kraut Edgar A
• Pubblicazione: Newburyport, : Dover Publications, 2013
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (1001 p.)
• Disciplina: 530.15
• Soggetto topico: Mathematical physics; Engineering & Applied Sciences; Applied Physics
• Note generali: Description based upon print version of record.
• Nota di contenuto: Title Page; Copyright Page; preface; errata; Table of Contents; CHAPTER ONE - vector algebra; INTRODUCTION; 1-1 DEFINITIONS; 1-2 EQUALITY OF VECTORS AND NULL VECTORS; 1-3 VECTOR OPERATIONS; 1-4 EXPANSION OF VECTORS; 1-5 VECTOR IDENTITIES; 1-6 PROBLEMS AND APPLICATIONS; CHAPTER TWO - matrix and tensor algebra; 2-1 DEFINITIONS; 2-2 EQUALITY OF MATRICES AND NULL MATRICES; 2-3 MATRIX OPERATIONS; 2-4 DETERMINANTS; 2-5 SPECIAL MATRICES; 2-6 SYSTEMS OF LINEAR EQUATIONS; 2-7 LINEAR OPERATORS; 2-8 EIGENVALUE PROBLEMS; 2-9 DIAGONALIZATION OF MATRICES; 2-10 SPECIAL PROPERTIES OF HERMITIAN MATRICES ; 2-11 TENSOR ALGEBRA2-12 TENSOR OPERATIONS; 2-13 TRANSFORMATION PROPERTIES OF TENSORS; 2-14 SPECIAL TENSORS; 2-15 PROBLEMS AND APPLICATIONS; CHAPTER THREE - vector calculus; 3-1 ORDINARY VECTOR DIFFERENTIATION; 3-2 PARTIAL VECTOR DIFFERENTIATION; 3-3 VECTOR OPERATIONS IN CYLINDRICAL AND SPHERICAL COORDINATE SYSTEMS; 3-4 DIFFERENTIAL VECTOR IDENTITIES; 3-5 VECTOR INTEGRATION OVER A CLOSED SURFACE; 3-6 THE DIVERGENCE THEOREM; 3-7 THE GRADIENT THEOREM; 3-8 THE CURL THEOREM; 3-9 VECTOR INTEGRATION OVER A CLOSED CURVE; 3-10 THE TWO-DIMENSIONAL DIVERGENCE THEOREM ; 3-11 THE TWO-DIMENSIONAL GRADIENT THEOREM3-12 THE TWO-DIMENSIONAL CURL THEOREM; 3-13 MNEMONIC OPERATORS; 3-14 KINEMATICS OF INFINITESIMAL VOLUME, SURFACE, AND LINE ELEMENTS; 3-15 KINEMATICS OF A VOLUME INTEGRAL; 3-16 KINEMATICS OF A SURFACE INTEGRAL; 3-17 KINEMATICS OF A LINE INTEGRAL; 3-18 SOLID ANGLE; 3-19 DECOMPOSITION OF A VECTOR FIELD INTO SOLENOIDAL AND IRROTATIONAL PARTS; 3-20 INTEGRAL THEOREMS FOR DISCONTINUOUS AND UNBOUNDED FUNCTIONS; 3-21 PROBLEMS AND APPLICATIONS; CHAPTER FOUR - functions of a complex variable; 4-1 INTRODUCTION; 4-2 DEFINITIONS; 4-3 COMPLEX ALGEBRA ; 4-4 DOMAIN OF CONVERGENCE4-5 ANALYTIC FUNCTIONS; 4-6 CAUCHY'S APPROACH; 4-7 CAUCHY'S INTEGRAL THEOREM; 4-8 CAUCHY'S INTEGRAL REPRESENTATION OF AN ANALYTIC FUNCTION THEOREM:; 4-9 TAYLOR'S SERIES; 4-10 CAUCHY'S INEQUALITIES; 4-11 ENTIRE FUNCTIONS; 4-12 RIEMANN'S THEORY OF FUNCTIONS OF A COMPLEX VARIABLE; 4-13 PHYSICAL INTERPRETATION; 4-14 FUNCTIONS DEFINED ON CURVED SURFACES; 4-15 LAURENT'S SERIES; 4-16 SINGULARITIES OF AN ANALYTIC FUNCTION; 4-17 MULTIVALUED FUNCTIONS; 4-18 RESIDUES; 4-19 RESIDUE AT INFINITY; 4-20 GENERALIZED RESIDUE THEOREM OF CAUCHY; 4-21 PROBLEMS AND APPLICATIONS ; CHAPTER FIVE - integral transforms5-1 INTRODUCTION; 5-2 ORTHOGONAL FUNCTIONS; 5-3 DIRAC'S NOTATION; 5-4 ANALOGY BETWEEN EXPANSION IN ORTHOGONAL FUNCTIONS AND EXPANSION IN ORTHOGONAL VECTORS; 5-5 LINEAR INDEPENDENCE OF FUNCTIONS; 5-6 MEAN-SQUARE CONVERGENCE OF AN EXPANSION IN ORTHOGONAL FUNCTIONS; 5-7 INTEGRATION AND DIFFERENTIATION OF ORTHOGONAL EXPANSIONS; 5-8 POINTWISE CONVERGENCE OF AN ORTHOGONAL EXPANSION; 5-9 GIBBS'S PHENOMENON; 5-10 THE FINITE SINE TRANSFORM; 5-11 THE FINITE COSINE TRANSFORM; 5-12 PROPERTIES OF FINITE FOURIER TRANSFORMS ; 5-13 CONNECTION WITH CLASSICAL THEORY OF FOURIER SERIES
• Sommario/riassunto: Indispensable for students of modern physics, this text provides the necessary background in mathematics for the study of electromagnetic theory and quantum mechanics. Clear discussions explain the particulars of vector algebra, matrix and tensor algebra, vector calculus, functions of a complex variable, integral transforms, linear differential equations, and partial differential equations. This volume collects under one cover the mathematical ideas formerly available only by taking many separate courses. It offers in-depth treatments, with a minimum of mathematical formalism. Suitable for stu
• Titolo autorizzato: Fundamentals of Mathematical Physics
• ISBN: 0-486-13160-2; 1-62198-611-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9911007077603321
• Lo trovi qui: Univ. Federico II
• Serie: Dover Books on Physics