Advanced mathematical methods in science and engineering. (2014)

• Record Type: Book
• Further Information: Note: S.I. Hayek.
• Authors: Hayek, Sabih I, 1938-
• Contents: Ordinary Differential Equations; DEFINITIONS; LINEAR DIFFERENTIAL EQUATIONS OF FIRST ORDER; LINEAR INDEPENDENCE AND THE WRONSKIAN; LINEAR HOMOGENEOUS DIFFERENTIAL EQUATION OF ORDER N WITH CONSTANT COEFFICIENTS; EULER’S EQUATION; PARTICULAR SOLUTIONS BY METHOD OF UNDETERMINED COEFFICIENTS; PARTICULAR SOLUTIONS BY THE METHOD OF VARIATIONS OF PARAMETERS; ABEL’S FORMULA FOR THE WRONSKIAN; INITIAL VALUE PROBLEMS Series Solutions of Ordinary Differential Equations ; INTRODUCTION; POWER SERIES SOLUTIONS; CLASSIFICATION OF SINGULARITIES; FROBENIUS SOLUTION Special Functions; BESSEL FUNCTIONS; BESSEL FUNCTION OF ORDER ZERO; BESSEL FUNCTION OF AN INTEGER ORDER N; RECURRENCE RELATIONS FOR BESSEL FUNCTIONS; BESSEL FUNCTIONS OF HALF ORDERS; SPHERICAL BESSEL FUNCTIONS; HANKEL FUNCTIONS; MODIFIED BESSEL FUNCTIONS; GENERALIZED EQUATIONS LEADING TO SOLUTIONS IN TERMS OF BESSEL FUNCTIONS; BESSEL COEFFICIENTS; INTEGRAL REPRESENTATION OF BESSEL FUNCTIONS; ASYMPTOTIC APPROXIMATIONS OF BESSEL FUNCTIONS FOR SMALL ARGUMENTS; ASYMPTOTIC APPROXIMATIONS OF BESSEL FUNCTIONS FOR LARGE ARGUMENTS; INTEGRALS OF BESSEL FUNCTIONS; ZEROES OF BESSEL FUNCTIONS; LEGENDRE FUNCTIONS; LEGENDRE COEFFICIENTS; RECURRENCE FORMULAE FOR LEGENDRE POLYNOMIALS; INTEGRAL REPRESENTATION FOR LEGENDRE POLYNOMIALS; INTEGRALS OF LEGENDRE POLYNOMIALS; EXPANSIONS OF FUNCTIONS IN TERMS OF LEGENDRE POLYNOMIALS; LEGENDRE FUNCTION OF THE SECOND KIND QN (X); ASSOCIATED LEGENDRE FUNCTIONS; GENERATING FUNCTION FOR ASSOCIATED LEGENDRE FUNCTIONS; RECURRENCE FORMULAE FOR Pn m ; INTEGRALS OF ASSOCIATED LEGENDRE FUNCTIONS; ASSOCIATED LEGENDRE FUNCTION OF THE SECOND KIND Qn m Boundary Value Problems and Eigenvalue Problems ; INTRODUCTION ; VIBRATION, WAVE PROPAGATION OR WHIRLING OF STRETCHED STRINGS; LONGITUDINAL VIBRATION AND WAVE PROPAGATION IN ELASTIC BARS; VIBRATION, WAVE PROPAGATION AND WHIRLING OF BEAMS; WAVES IN ACOUSTIC HORNS; STABILITY OF COMPRESSED COLUMNS; IDEAL TRANSMISSION LINES (TELEGRAPH EQUATION); TORSIONAL VIBRATION OF CIRCULAR BARS; ORTHOGONALITY AND ORTHOGONAL SETS OF FUNCTIONS; GENERALIZED FOURIER SERIES; ADJOINT SYSTEMS; BOUNDARY VALUE PROBLEMS; EIGENVALUE PROBLEMS; PROPERTIES OF EIGENFUNCTIONS OF SELF-ADJOINT SYSTEMS; STURM-LIOUVILLE SYSTEM; STURM-LIOUVILLE SYSTEM FOR FOURTH-ORDER EQUATIONS; SOLUTION OF NON-HOMOGENEOUS EIGENVALUE PROBLEMS; FOURIER SINE SERIES; FOURIER COSINE SERIES; COMPLETE FOURIER SERIES; FOURIER-BESSEL SERIES; FOURIER–LEGENDRE SERIES Functions of a Complex Variable ; COMPLEX NUMBERS; ANALYTIC FUNCTIONS; ELEMENTARY FUNCTIONS; INTEGRATION IN THE COMPLEX PLANE; CAUCHY’S INTEGRAL THEOREM; CAUCHY’S INTEGRAL FORMULA; INFINITE SERIES; TAYLOR’S EXPANSION THEOREM; LAURENT’S SERIES; CLASSIFICATION OF SINGULARITIES; RESIDUES AND RESIDUE THEOREM; INTEGRALS OF PERIODIC FUNCTIONS; IMPROPER REAL INTEGRALS; IMPROPER REAL INTEGRAL INVOLVING CIRCULAR FUNCTIONS; IMPROPER REAL INTEGRALS OF FUNCTIONS HAVING SINGULARITIES ON THE REAL AXIS; THEOREMS ON LIMITING CONTOURS; INTEGRALS OF EVEN FUNCTIONS INVOLVING LOG X; INTEGRALS OF FUNCTIONS INVOLVING Xa ; INTEGRALS OF ODD OR ASYMMETRIC FUNCTIONS; INTEGRALS OF ODD OR ASYMMETRIC FUNCTIONS INVOLVING LOG X; INVERSE LAPLACE TRANSFORMS Partial Differential Equations of Mathematical Physics; INTRODUCTION; THE DIFFUSION EQUATION; THE VIBRATION EQUATION; THE WAVE EQUATION; HELMHOLTZ EQUATION; POISSON AND LAPLACE EQUATIONS; CLASSIFICATION OF PARTIAL DIFFERENTIAL EQUATIONS; UNIQUENESS OF SOLUTIONS; THE LAPLACE EQUATION; THE POISSON EQUATION; THE HELMHOLTZ EQUATION; THE DIFFUSION EQUATION; THE VIBRATION EQUATION; THE WAVE EQUATION Integral Transforms ; FOURIER INTEGRAL THEOREM; FOURIER COSINE TRANSFORM; FOURIER SINE TRANSFORM; COMPLEX FOURIER TRANSFORM; MULTIPLE FOURIER TRANSFORM; HANKEL TRANSFORM OF ORDER ZERO; HANKEL TRANSFORM OF ORDER ν; GENERAL REMARKS ABOUT TRANSFORMS DERIVED FROM THE FOURIER INTEGRAL THEOREM; GENERALIZED FOURIER TRANSFORM; TWO-SIDED LAPLACE TRANSFORM; ONE-SIDED GENERALIZED FOURIER TRANSFORM; LAPLACE TRANSFORM; MELLIN TRANSFORM; OPERATIONAL CALCULUS WITH LAPLACE TRANSFORMS; SOLUTION OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS BY LAPLACE TRANSFORMS; OPERATIONAL CALCULUS WITH FOURIER COSINE TRANSFORM; OPERATIONAL CALCULUS WITH FOURIER SINE TRANSFORM; OPERATIONAL CALCULUS WITH COMPLEX FOURIER TRANSFORM; OPERATIONAL CALCULUS WITH MULTIPLE FOURIER TRANSFORM; OPERATIONAL CALCULUS WITH HANKEL TRANSFORM Green’s Functions ; INTRODUCTION; GREEN’S FUNCTION FOR ORDINARY DIFFERENTIAL BOUNDARY VALUE PROBLEM; GREEN’S FUNCTION FOR AN ADJOINT SYSTEM; SYMMETRY OF THE GREEN’S FUNCTIONS AND RECIPROCITY; GREEN’S FUNCTION FOR EQUATIONS WITH CONSTANT COEFFICIENTS; GREEN’S FUNCTIONS FOR HIGHER ORDERED SOURCES; GREEN’S FUNCTION FOR EIGENVALUE PROBLEMS; GREEN’S FUNCTION FOR SEMI-INFINITE ONE DIMENSIONAL MEDIA; GREEN’S FUNCTION FOR INFINITE ONE-DIMENSIONAL MEDIA; GREEN’S FUNCTION FOR PARTIAL DIFFERENTIAL EQUATIONS; GREEN’S IDENTITIES FOR THE LAPLACIAN OPERATOR; GREEN’S IDENTITY FOR THE HELMHOLTZ OPERATOR; GREEN’S IDENTITY FOR BI-LAPLACIAN OPERATOR; GREEN’S IDENTITY FOR THE DIFFUSION OPERATOR; GREEN’S IDENTITY FOR THE WAVE OPERATOR; GREEN’S FUNCTION FOR UNBOUNDED MEDIA—FUNDAMENTAL SOLUTION; FUNDAMENTAL SOLUTION FOR THE LAPLACIAN; FUNDAMENTAL SOLUTION FOR THE BI-LAPLACIAN; FUNDAMENTAL SOLUTION FOR THE HELMHOLTZ OPERATOR; FUNDAMENTAL SOLUTION FOR THE OPERATOR, - ∇2 + μ2 ; CAUSAL FUNDAMENTAL SOLUTION FOR THE DIFFUSION OPERATOR; CAUSAL FUNDAMENTAL SOLUTION FOR THE WAVE OPERATOR; FUNDAMENTAL SOLUTIONS FOR THE BI-LAPLACIAN HELMHOLTZ OPERATOR; GREEN’S FUNCTION FOR THE LAPLACIAN OPERATOR FOR BOUNDED MEDIA; CONSTRUCTION OF THE AUXILIARY FUNCTION-METHOD OF IMAGES; GREEN’S FUNCTION FOR THE LAPLACIAN FOR HALF-SPACE; GREEN’S FUNCTION FOR THE LAPLACIAN BY EIGENFUNCTION EXPANSION FOR BOUNDED MEDIA; GREEN’S FUNCTION FOR A CIRCULAR AREA FOR THE LAPLACIAN; GREEN’S FUNCTION FOR SPHERICAL GEOMETRY FOR THE LAPLACIAN; GREEN’S FUNCTION FOR THE HELMHOLTZ OPERATOR FOR BOUNDED MEDIA; GREEN’S FUNCTION FOR THE HELMHOLTZ OPERATOR FOR HALF-SPACE; GREEN’S FUNCTION FOR A HELMHOLTZ OPERATOR IN QUARTER-SPACE; CAUSAL GREEN’S FUNCTION FOR THE WAVE OPERATOR IN BOUNDED MEDIA; CAUSAL GREEN’S FUNCTION FOR THE DIFFUSION OPERATOR FOR BOUNDED MEDIA; METHOD OF SUMMATION OF SERIES SOLUTIONS IN TWO DIMENSIONAL MEDIA Asymptotic Methods ; INTRODUCTION; METHOD OF INTEGRATION BY PARTS; LAPLACE’S INTEGRAL; STEEPEST DESCENT METHOD; DEBYE’S FIRST ORDER APPROXIMATION; ASYMPTOTIC SERIES APPROXIMATION; METHOD OF STATIONARY PHASE; STEEPEST DESCENT METHOD IN TWO DIMENSIONS; MODIFIED SADDLE POINT METHOD: SUBTRACTION OF A SIMPLE POLE; MODIFIED SADDLE POINT METHOD: SUBTRACTION OF POLE OF ORDER N; SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS FOR LARGE ARGUMENTS; CLASSIFICATION OF POINTS AT INFINITY; SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH REGULAR SINGULAR POINTS; ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULAR POINTS OF RANK ONE; THE PHASE INTEGRAL AND WKBJ METHOD FOR AN IRREGULAR SINGULAR POINT OF RANK ONE; ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH IRREGULAR SINGULAR POINTS OF RANK HIGHER THAN ONE; ASYMPTOTIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS WITH LARGE PARAMETERS Numerical Methods; INTRODUCTION; ROOTS OF NON-LINEAR EQUATIONS; ROOTS OF A SYSTEM OF NON-LINEAR EQUATION; FINITE DIFFERENCES; NUMERICAL DIFFERENTIATION; NUMERICAL INTEGRATION; ORDINARY DIFFERENTIAL EQUATIONS: INITIAL VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS: BOUNDARY VALUE PROBLEMS; ORDINARY DIFFERENTIAL EQUATIONS: EIGENVALUE PROBLEMS; PARTIAL DIFFERENTIAL E
• Edition: Second edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 510; Mathematics; Mathematics -- Problems, exercises, etc
• Languages: English
• ISBNs: 9781420081985
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.