- #1
- 19,546
- 10,280
- Author: Mary L. Boas
- Title: Mathematical Methods in the Physical Sciences
- Amazon Link: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20
- Prerequisities: Calculus
Table of Contents:
Code:
[LIST]
[*] Infinite Series, Power Series
[LIST]
[*] The Geometric Series
[*] Definitions and notation
[*] Applications of Series
[*] Convergent and divergent Series
[*] Testing Series for Convergence; The Preliminary Test
[*] Tests for convergence of series of positive terms; absolute convergence
[*] Alternating series
[*] Conditionally convergent series
[*] Useful facts about series
[*] Power series; interval of convergence
[*] Theorems about power series
[*] Expanding functions in power series
[*] Techniques for obtaining power series expansions
[*] Questions of convergence and accuracy in computations
[*] Some uses of series
[*] Miscellaneous problems
[/LIST]
[*] Complex Numbers
[LIST]
[*] Introduction
[*] Real and imaginary parts of a complex number
[*] The complex plane
[*] Terminology and notation
[*] Complex algebra
[*] Complex infinite series
[*] Complex power series; circle of convergence
[*] Elementary functions of complex numbers
[*] Euler's formula
[*] Powers and roots of complex numbers
[*] The exponential and trigonometric functions
[*] Hyperbolic functions
[*] Logarithms
[*] Complex roots and powers
[*] Inverse trigonometric and hyperbolic functions
[*] Some applications
[*] Miscellaneous problems
[/LIST]
[*] Linear Equations; Vectors, Matrices and Determinants
[LIST]
[*] Intoduction
[*] Set of linear equations, row reduction
[*] Determinants; Cramer's rule
[*] Vectors
[*] Lines and planes
[*] Matrix operations
[*] Linear combinations, linear functions, linear operators
[*] General theory of sets of linear equations
[*] Special matrices
[*] Miscellaneous problems
[/LIST]
[*] Partial Differentiation
[LIST]
[*] Introduction and notation
[*] Power series in two variables
[*] Total differentials
[*] Approximate calculations using differentials
[*] Chain rule or differentiating a function of a function
[*] Implicit differentiation
[*] More chain rule
[*] Application of [URL="https://www.physicsforums.com/insights/partial-differentiation-without-tears/"]partial differentiation[/URL] to maximum and minimum prolems
[*] Maximum and minimum problems with constraints; Lagrange multipliers
[*] Endpoint or boundary point problems
[*] Change of variables
[*] Differentiation of integrals; Leibniz' rule
[*] Miscellaneous problems
[/LIST]
[*] Multiple Integrals; Applications of Integration
[LIST]
[*] Introduction
[*] Double and Triple Integrals
[*] Applications of Integration; Single and Multiple Integrals
[*] Change of Variables in Integrals; Jacobians
[*] Surface Integrals
[*] Miscellaneous Problems
[/LIST]
[*] Vector Analysis
[LIST]
[*] Introduction
[*] applications of vector multiplication
[*] Triple products
[*] Differentiation of vectors
[*] Fields
[*] Directional derivative; gradient
[*] Some other expressions involving [itex]\nabla[/itex]
[*] Line integrals
[*] Green's theorem in the plane
[*] The divergence and the divergence theorem
[*] The curl and Stokes' theorem
[*] Miscellaneous problems
[/LIST]
[*] Fourier Series
[LIST]
[*] Introduction
[*] Simple harmonic motion and wave motion; periodic functions
[*] Applications of Fourier series
[*] Average value of a function
[*] Fourier coefficients
[*] Dirichlet conditions
[*] Complex form of Fourier series
[*] Other intervals
[*] Even and odd functions
[*] An application to sound
[*] Parseval's theorem
[*] Miscellaneous problems
[/LIST]
[*] Ordinary Differential Equations
[LIST]
[*] Introduction
[*] Separable equations
[*] Linear first-order equations
[*] Other methods for first order equations
[*] Second-order linear equations with constant coefficients and zero right-hand side
[*] Second-order linear equations with constant coefficients and right-hand side not zero
[*] Other second-order equations
[*] Miscellaneous problems
[/LIST]
[*] Calculus of Variations
[LIST]
[*] Introduction
[*] The Euler equation
[*] Using the Euler equation
[*] The brachistochrone problem;, cycloids
[*] Several dependent variables; Lagrange's equations
[*] Isoperimetric problems
[*] Variational notation
[*] Miscellaneous problems
[/LIST]
[*] Coordinate Transformations; Tensor Analysis
[LIST]
[*] Introduction
[*] Linear transformations
[*] Orthogonal transformations
[*] Eigenvalues and eigenvectors; diagonalizing matrices
[*] Applications of diagonalization
[*] Curvilinear coordinates
[*] Scale factors and basis vectors for orthogonal systems
[*] General curvilinear coordinates
[*] Vector operators in orthogonal curvilinear coordinates
[*] Tensor analysis - introduction
[*] Cartesian tensors
[*] Uses of tensors; dyadics
[*] General coordinate systems
[*] Vector operations in tensor notation
[*] Miscellaneous problems
[/LIST]
[*] Gamma, Beta, and Error Functions; Asymptotic Series; Stirling's Formula; Elliptic Integrals and Functions
[LIST]
[*] Introduction
[*] The factorial function
[*] Definition of the gamma function; recursion relation
[*] The gamma function of negative numbers
[*] Some important formulas involving gamma functions
[*] Beta functions
[*] The relation between the beta and gamma functions
[*] The simple pendulum
[*] The error function
[*] Asymptotic series
[*] Stirling's formula
[*] Elliptic integrals and functions
[*] Miscellaneous problems
[/LIST]
[*] Series Solutions of Differential Equations; Legendre Polynomials; Bessel Functions; Sets of Orthogonal Functions
[LIST]
[*] Introduction
[*] Legendre's equation
[*] Leibniz' rule for differentiation products
[*] Rodrigues' formula
[*] Generating function for Legendre polynomials
[*] Complete sets of orthogonal functions
[*] Orthogonality of the Legendre polynomials
[*] Normalization of the Legendre polynomials
[*] Legendre series
[*] The associated Legendre functions
[*] Generalized power series or the method of Frobenius
[*] Bessel's equation
[*] The second solution of Bessel's equation
[*] Tables, graphs, and zeros of Bessel functions
[*] Recursion relations
[*] A general differential equation having Bessel functions as solutions
[*] Other kinds of Bessel functions
[*] The lengthening pendulum
[*] Orthogonality of Bessel functions
[*] Approximate formulas for Bessel functions
[*] Some general comments about series solutions
[*] Hermite functions; Laguerre functions; ladder operators
[*] Miscellaneous problems
[/LIST]
[*] Partial Differential Equations
[LIST]
[*] Introduction
[*] Laplace's equation; steady-state temperature in a rectangular plate
[*] The diffusion or heat flow equation; heat flow in a bar or slab
[*] The wave equation; the vibrating string
[*] Steady-state temperature in a cylinder
[*] Vibration of a circular membrane
[*] Steady-state temperature in a sphere
[*] Poisson's equation
[*] Miscellaneous problems
[/LIST]
[*] Functions of a complex variable
[LIST]
[*] Introduction
[*] Analytic functions
[*] Contour integrals
[*] Laurent series
[*] The residue theorem
[*] Methods of finding residues
[*] Evaluation of definite integrals by use of the residue theorem
[*] The point at infinity; residues at infinity
[*] Mapping
[*] Some applications of conformal mapping
[*] Miscellaneous problems
[/LIST]
[*] Integrals Transforms
[LIST]
[*] Introduction
[*] The Laplace transform
[*] Solutions of differential equations by Laplace transforms
[*] Fourier transforms
[*] Convolution; Parseval's theorem
[*] Inverse Laplace transform (Bromwich integral)
[*] The Dirac delta function
[*] Green functions
[*] Integral transform solutions of partial differential equations
[*] Miscellaneous problems
[/LIST]
[*] Probability
[LIST]
[*] Introduction; definition of probability
[*] Sample space
[*] Probability theorems
[*] Sample space
[*] Methods of counting
[*] Random variables
[*] Continuous distributions
[*] Binomial distribution
[*] The normal or Gaussian distribution
[*] The Poisson distribution
[*] Applications to experimental measurements
[*] Miscellaneous problems
[/LIST]
[*] References
[*] Bibliography
[*] Answers to selected problems
[*] Index
[/LIST]
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