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A course in mathematical methods for physicists
Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for th...
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| Lenguaje: | eng |
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CRC Press
2014
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| Acceso en línea: | http://cds.cern.ch/record/1742872 |
| _version_ | 1780942755148595200 |
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| author | Herman, Russell L |
| author_facet | Herman, Russell L |
| author_sort | Herman, Russell L |
| collection | CERN |
| description | Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions |
| id | cern-1742872 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2014 |
| publisher | CRC Press |
| record_format | invenio |
| spelling | cern-17428722021-04-21T20:56:23Zhttp://cds.cern.ch/record/1742872engHerman, Russell LA course in mathematical methods for physicistsMathematical Physics and MathematicsBased on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functionsIntroduction and ReviewWhat Do I Need To Know From Calculus?What I Need From My Intro Physics Class?Technology and TablesAppendix: Dimensional AnalysisProblemsFree Fall and Harmonic OscillatorsFree FallFirst Order Differential EquationsThe Simple Harmonic OscillatorSecond Order Linear Differential EquationsLRC CircuitsDamped OscillationsForced SystemsCauchy-Euler EquationsNumerical Solutions of ODEsNumerical ApplicationsLinear SystemsProblemsLinear AlgebraFinite Dimensional Vector SpacesLinear TransformationsEigenvalue ProblemsMatrix Formulation of Planar SystemsApplicationsAppendix: DiagonaliIntroduction and ReviewWhat Do I Need To Know From Calculus?What I Need From My Intro Physics Class?Technology and TablesAppendix: Dimensional AnalysisProblemsFree Fall and Harmonic OscillatorsFree FallFirst Order Differential EquationsThe Simple Harmonic OscillatorSecond Order Linear Differential EquationsLRC CircuitsDamped OscillationsForced SystemsCauchy-Euler EquationsNumerical Solutions of ODEsNumerical ApplicationsLinear SystemsProblemsLinear AlgebraFinite Dimensional Vector SpacesLinear TransformationsEigenvalue ProblemsMatrix Formulation of Planar SystemsApplicationsAppendix: Diagonalization and Linear SystemsProblemsNonlinear DynamicsIntroductionThe Logistic EquationAutonomous First Order EquationsBifurcations for First Order EquationsNonlinear PendulumThe Stability of Fixed Points in Nonlinear SystemsNonlinear Population ModelsLimit CyclesNonautonomous Nonlinear SystemsExact Solutions Using Elliptic FunctionsProblemsThe Harmonics of Vibrating StringsHarmonics and VibrationsBoundary Value ProblemsPartial Differential EquationsThe 1D Heat EquationThe 1D Wave EquationIntroduction to Fourier SeriesFourier Trigonometric SeriesFourier Series Over Other IntervalsSine and Cosine SeriesSolution of the Heat EquationFinite Length StringsThe Gibbs PhenomenonGreen's Functions for 1D Partial Differential EquationsDerivation of Generic 1D EquationsProblemsNon-sinusoidal Harmonics and Special FunctionsFunction SpacesClassical Orthogonal PolynomialsFourier-Legendre SeriesGamma FunctionFourier-Bessel SeriesSturm-Liouville Eigenvalue ProblemsNonhomogeneous Boundary Value Problems - Green's FunctionsAppendix: The Least Squares ApproximationAppendix: The Fredholm Alternative TheoremProblemsComplex Representations of FunctionsComplex Representations of WavesComplex NumbersComplex Valued FunctionsComplex DifferentiationComplex IntegrationProblemsTransform Techniques in PhysicsIntroductionComplex Exponential Fourier SeriesExponential Fourier TransformThe Dirac Delta FunctionProperties of the Fourier TransformThe Convolution OperationThe Laplace TransformApplications of Laplace TransformsThe Convolution TheoremThe Inverse Laplace TransformTransforms and Partial Differential EquationsProblemsVector Analysis and EM WavesVector AnalysisElectromagnetic WavesCurvilinear CoordinatesTensorsProblemsExtrema and Variational CalculusStationary and Extreme Values of FunctionsThe Calculus of VariationsHamilton's PrincipleGeodesicsProblemsProblems in Higher DimensionsVibrations of Rectangular MembranesVibrations of a Kettle DrumLaplace's Equation in 2DThree Dimensional Cake BakingLaplace's Equation and Spherical SymmetrySchrödinger Equation in Spherical CoordinatesSolution of the 3D Poisson EquationGreen's Functions for Partial Differential EquationsProblemsReview of Sequences and Infinite SeriesSequences of Real NumbersConvergence of SequencesLimit TheoremsInfinite SeriesConvergence TestsSequences of FunctionsInfinite Series of FunctionsSpecial Series ExpansionsThe Order of Sequences and FunctionsProblems.CRC Pressoai:cds.cern.ch:17428722014 |
| spellingShingle | Mathematical Physics and Mathematics Herman, Russell L A course in mathematical methods for physicists |
| title | A course in mathematical methods for physicists |
| title_full | A course in mathematical methods for physicists |
| title_fullStr | A course in mathematical methods for physicists |
| title_full_unstemmed | A course in mathematical methods for physicists |
| title_short | A course in mathematical methods for physicists |
| title_sort | course in mathematical methods for physicists |
| topic | Mathematical Physics and Mathematics |
| url | http://cds.cern.ch/record/1742872 |
| work_keys_str_mv | AT hermanrusselll acourseinmathematicalmethodsforphysicists AT hermanrusselll courseinmathematicalmethodsforphysicists |