LEADER 05189nam 22007573u 450 001 9911006640403321 005 20230803040110.0 010 $a1-5231-2509-8 010 $a0-486-16936-7 035 $a(CKB)3710000000317758 035 $a(EBL)1890228 035 $a(SSID)ssj0001117933 035 $a(PQKBManifestationID)12491842 035 $a(PQKBTitleCode)TC0001117933 035 $a(PQKBWorkID)11106164 035 $a(PQKB)10809776 035 $a(MiAaPQ)EBC1890228 035 $a(Au-PeEL)EBL1890228 035 $a(CaONFJC)MIL570337 035 $a(OCoLC)869525090 035 $a(EXLCZ)993710000000317758 100 $a20141222d2013|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Methods in Physics and Engineering 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2013 215 $a1 online resource (722 p.) 225 1 $aDover Books on Physics 300 $aDescription based upon print version of record. 311 08$a0-486-65649-7 327 $aTitle Page; Copyright Page; Preface; Table of Contents; Chapter 1. Linear Algebra; 1.1 Linear Equations. Summation Convention; 1.2 Matrices; 1.3 Determinants; 1.4 Systems of Linear Algebraic Equations. Rank of a Matrix; 1.5 Vector Spaces; 1.6 Scalar Product; 1.7 Orthonormal Basis. Linear Transformations; 1.8 Quadratic Forms. Hermitian Forms; 1.9 Systems of Ordinary Differential Equations. Vibration Problems; 1.10 Linear Programming; Chapter 2. Hilbert Spaces; 2.1 Infinite-dimensional Vector Spaces. Function Spaces; 2.2 Fourier Series; 2.3 Separable Hilbert Spaces; 2.4 The Projection Theorem 327 $a2.5 Linear Functionals2.6 Weak Convergence; 2.7 Linear Operators; 2.8 Completely Continuous Operators; Chapter 3. Calculus of Variations; 3.1 Maxima and Minima of Functions. Lagrange Multipliers; 3.2 Maxima and Minima of Functionals. Euler's Equation; 3.3 Hamilton's Principle. Lagrange's Equations; 3.4 Theory of Small Vibrations; 3.5 The Vibrating String; 3.6 Boundary-value Problems of Mathematical Physics; 3.7 Eigenvalues and Eigenfunctions; 3.8 Eigenfunction Expansions; 3.9 Upper and Lower Bounds for Eigenvalues; Chapter 4. Boundary-value Problems. Separation of Variables 327 $a4.1 Orthogonal Coordinate Systems. Separation of Variables4.2 Sturm-Liouville Problems; 4.3 Series Solutions of Ordinary Differential Equations; 4.4 Series Solutions of Boundary-value Problems; Chapter 5. Boundary-value Problems. Green's Functions; 5.1 Nonhomogeneous Boundary-value Problems; 5.2 One-dimensional Green's Functions; 5.3 Generalized Functions; 5.4 Green's Functions in Higher Dimensions; 5.5 Problems in Unbounded Regions; 5.6 A Problem in Diffraction Theory; Chapter 6. Integral Equations; 6.1 Integral-equation Formulation of Boundary-value Problems; 6.2 Hilbert-Schmidt Theory 327 $a6.4 Integral Equations of the First KindChapter 7. Analytic Function Theory; 7.1 Introduction; 7.2 Analytic Functions; 7.3 Elementary Functions; 7.4 Complex Integration; 7.5 Integral Representations; 7.6 Sequences and Series; 7.7 Series Representations of Analytic Functions; 7.8 Contour Integration; 7.9 Conformal Mapping; 7.10 Potential Theory; Chapter 8. Integral Transform Methods; 8.1 Fourier Transforms; 8.2 Applications of Fourier Transforms. Ordinary Differential Equations; 8.3 Applications of Fourier Transforms. Partial Differential Equations 327 $a8.4 Applications of Fourier Transforms. Integral Equations8.5 Laplace Transforms. Applications; 8.6 Other Transform Techniques; Index; A CATALOG OF SELECTED DOVER BOOKS IN ALL FIELDS OF INTEREST 330 $a Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For t 410 0$aDover Books on Physics 606 $aEngineering -- Mathematics 606 $aEngineering mathematics 606 $aMathematics 606 $aMathematics 606 $aEngineering 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aMathematics - General$2HILCC 615 4$aEngineering -- Mathematics. 615 4$aEngineering mathematics. 615 4$aMathematics. 615 0$aMathematics. 615 0$aEngineering. 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aMathematics - General 676 $a510 700 $aDettman$b John W$040770 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006640403321 996 $aMathematical Methods in Physics and Engineering$9344595 997 $aUNINA