Mathematical methods for physics and engineering /
K.F. Riley, M.P. Hobson and S.J. Bence.
- 3rd edition.
- Cambridge ; New York : Cambridge University Press, c2006.
- xxvii, 1333 p. : ill. ; 26 cm.
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
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
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