Mathematical methods for physics and engineering / K.F. Riley, M.P. Hobson and S.J. Bence.
Publication details: Cambridge ; New York : Cambridge University Press, c2006.Edition: 3rd editionDescription: xxvii, 1333 p. : ill. ; 26 cmISBN:- 9780521679718
- 515. 22 RIL.
Item type | Current library | Call number | Copy number | Status | Date due | Barcode |
---|---|---|---|---|---|---|
Book Closed Access | Engineering Library | 515. RIL. 1 (Browse shelf(Opens below)) | 1 | Available | BUML23070670 | |
Book Closed Access | Engineering Library | 515. RIL. 2 (Browse shelf(Opens below)) | 2 | Available | BUML23070669 |
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
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