TY - BOOK AU - Riley,K.F. AU - Hobson,M.P. AU - Bence,S.J. TI - Mathematical methods for physics and engineering SN - 9780521679718 U1 - 515. 22 PY - 2006/// CY - Cambridge, New York PB - Cambridge University Press KW - Mathematical analysis KW - Engineering mathematics KW - Mathematical physics N1 - CONTENT 1 . Preliminary algebra 1.1 Simple functions and equations 1.2 Trigonometric identities 1.3 Coordinate geometry 1.4 Partial fractions 1.5 Binomial expansion 2. Preliminary calculus 2.1 Differentiation 2.2 Integration 2.3 Exercises 2.4 Hints and answers 3. Complex numbers and hyperbolic functions 3.1 The need for complex numbers 3.2 Manuipulation of complex numbers 3.3 Polar representation of complex numbers 3.4 de Moivre's theorem 3.5 Complex logarithms and complex powers etc 4. Serires and Limits 4.1 Series 4.2 Summation of series 4.3 Convergence of infinite series 4.4 Operations with series 4.5 Power series etc 5 Partial differentiation 5.1 Definition of the partial derivative 5.2 The total differential and total derivative 5.3 Exact and inexact differentials 5.4 Useful theorems of partial differentiation 5.5 The chain rule etc 6. Multiple integrals 6.1 Double integrals 6.2 Triple integrals 6.3 Applications of multiple integrals 6.4 Change of variables in multiple integrals 6.5 Exercise etc 7 Vector algebra 7.1 Scalars and vectors 7.2 Addition and subtraction of vectors 7.3 Multiplication by a Scalar 7.4 Basic vector and components 7.5 Magnitude of a vector etc 8 Matrices and vector space 8.1 Vector space 8.2 Linear spaces 8.3 Matrices 8.4 Basic matrix algebra 8.5 Function of matrices etc 9 Normal modes 9.1 Typical oscillatrory systems 9.2 Symmetry and normal modes 9.3 Rayleigh- Ritz method 9.4 Exercises 9.5 Hints and answers 10 Vector calculus 10.1 Differentiation of vectors 10.2 Integration of vectors 10.3 Space curves 10.4 Vector functions of several arguments 10.5 Surfaces etc 11 Line, surface and volume integrals 11.1 Line integrals 11.2 Connectivity of regions 11.3 Green's theorem in a plane 11.4 Conservative fields and potentials 11.5 Surface integrals etc 12 Fourier series 12.1 The dirichlet conditions 12.2 The fourier coefficients 12.3 Symmetry considerations 12.4 Discontinuous functions 12.5 Non-periodic functions etc 13 Integral transforms 13.1 Fourier transforms 13.2 Laplace transforms 13.3 Concluding remarks 13.4 Exercise 13.5 Hints and answers etc 14 First-order ordinary differential equations 14.1 General form of soluton 14.2 First- degree first order eqyations 14.3 Higher -degree first order equations 14.4 Exercises 14.5 Hints and answers 15 Higher-order ordinary differential equations 15.1 Linear equations with constant coefficients 15.2 Linear equations with variable coefficients 15.3 General ordinary differential equations 15.4 Exercises 15.5 Hints and answers 16 Series solutions of ordinary differential equations 16.1 Second- order linear ordinarydifferential equations 16.2 Series solutions about an ordinary point 16.3 Series solutions about a regular singular point 16.4 Obtaining a second solution 16.5 Polynomial solutions etc 17 Eigenfunction methods for differential equations 17.1 Sets of functions 17.2 Adjoint, self-adjoint and hermitian operators 17.3 Properties of hermitian operators 17.4 Sturm- Liouville equations 17.5 Superposition of eigenfunctions:Green's functions etc 18 Special functions 18.1 Legendre functions 18.2 Associated Legendre functions 18.3 Spherical harmonics 18.4 Chebyshev functions 18.5 Bessel functions etc 19 Quantum operators 19.1 Operator formalism 19.2 Physical examples of operators 19.3 Exercise 19.4 Hints and answers 20 Partial differentail equations : general and particular solutions 20.1 Important partial differential equations 20.2 General for of solutions 20.3 General and particular solutions 20.4 The wave equation 20.5 The diffusion equation etc 21 Partial and differential equations : seperation of variables and other methods 21.1 Separation of variables : the general method 21.2 Superposition of separated solutions 21.3 Separation of variables in polar coordinates 21.4 Integral transform methods 21.5 Inhomogeneous problems etc 22 Calculus of variations 22.1 The Euler- Language equation 22.2 Special cases 22.3 Some extentions 22.4 Constrained varation 22.5 Physical variational principles etc 23. Integral equations 23.1 Obtaining an integral equation from a differential equation 23.2 Types of integral equation 23.3 Operator notation and existence of solutions 23.4 Closed-form solution 23.5 Neumann series etc 24 Complex variables 24.1 Function of complex variables 24.2 The cauchy -Riemann relations 24.3 Power series in a complex variable 24.4 Some elementary functions 24.5 Multivalued functions and branch cuts etc 25 Applications of complex variables 25.1 Complex potentials 25.2 Applications of conformal transformations 25.3 Location of Zeros 25.4 Summation of series 25.5 Inverse Lpaplace transform etc 26. Tensors 26.1 Some notation 26.2 Change of basis 26.3 Cartesian tensors 26.4 First - and zero -order Cartesian tensors 26.5 Second - and higher -order Cartesian tensors etc 27 Numerical methods 27.1 Algebraic and transcendental equations 27.2 Convergence of iteration schemes 27.3 Simultaneous linear equations 27.4 Numerical integration 27.5 Finite differences etc 28 Group theory 28.1 Groups 28.2 Finite groups 28.3 Non- Abelian groups 28.4 Permutation groups 28.5 Mappings between groups etc 29 Representation theory 29.1 Dipole moments of molecules 29.2 Choosing an appropriate formalism 29.3 Equivalent representations 29.4 Reducibility of a representation 29.5 The orthogonality theorem for irreducible representations etc 30 Probability 30.1 Venn diagram 30.2 Probability 30.3 Permutations and combinations 30.4 Random variables and distributions 30.5 Properties distribution etc 31 Statistics 31.1 Experiments, samples and populations 31.2 Sample statistics 31.3 Estimators and sampling distribution 31.4 Some basic estimators 31.5 Maximum- likelihood methhod ; Includes index : p.1305 - 1333 ER -