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An edition of Mathematical Methods in the Physical Sciences (1966)

Mathematical Methods in the Physical Sciences

by Mary L. Boas and Mary Layne Boas

★★★ 3.0 (3 ratings)
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★★★ 3.0 (3 ratings)
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An edition of Mathematical Methods in the Physical Sciences (1966)

Mathematical Methods in the Physical Sciences

by Mary L. Boas and Mary Layne Boas

★★★ 3.0 (3 ratings)
57 Want to read
5 Currently reading
4 Have read

Updates the original, comprehensive introduction to the areas of mathematical physics encountered in advanced courses in the physical sciences. Intuition and computational abilities are stressed. Original material on DE and multiple integrals has been expanded.

Publish Date

1983

Publisher

John Wiley & Sons

Language

English

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Previews available in: English

Edition	Availability
01 Mathematical methods in the physical sciences 2006, Wiley in English - 3rd ed. 0471198269 9780471198260	zzzz Locate
02 Mathematical Methods in the Physical Sciences July 22, 2005, Wiley in English 0471198269 9780471198260	zzzz Locate
03 Mathematical methods in the physical sciences 2004, Wiley in English - 3rd ed. 0471198269 9780471198260	zzzz Locate
04 Mathematical methods in the physical sciences 1983, Wiley in English - 2nd ed. 0471044091 9780471044093	zzzz Locate
05 Mathematical Methods in the Physical Sciences 1983, John Wiley & Sons in English	aaaa Preview Only
06 Mathematical methods in the physical sciences 1983, Wiley in English - 2nd ed. 0471099600 9780471099604	zzzz Locate
07 Mathematical methods in the physical sciences. 1966, Wiley in English	zzzz Locate
08 Mathematical methods in the physical sciences 1966, Wiley in English	zzzz Locate
09 Mathematical methods in the physical sciences 1966, Wiley	zzzz Locate
10 Mathematical methods in the physical sciences, by Mary L. Boas Publish date unknown, Wiley & Sons in English - 2nd ed. 0471044091 9780471044093	zzzz Locate

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Book Details

Table of Contents

1. Infinite Series, Power Series

1. The geometric series

2. Definitions and notation

3. Applications of series

4. Convergent and divergent series

5. Testing series for convergence; the preliminary test

6. Tests for convergence of series of positive terms; absolute convergence

7. Alternating series

8. Conditionally convergent series

9. Useful facts about series

10. Power series; interval of convergence

11. Theorems about power series

12. Expanding functions in power series

13. Techniques for obtaining power series expansions

14. Questions of convergence and accuracy in computation

15. Some uses of series

16. Miscellaneous problems

2. Complex Numbers

1. Introduction

2. Real and imaginary parts of a complex number

3. The complex plane

4. Terminology and notation

5. Complex algebra

6. Complex infinite series

7. Complex power series; circle of convergence

8. Elementary functions of complex numbers

9. Euler's formula

10. Powers and roots of complex numbers

11. The exponential and trigonometric functions

12. Hyperbolic functions

14. Complex roots and powers

15. Inverse trigonometric and hyperbolic functions

16. Some applications

17. Miscellaneous problems

3. Linear Equations; Vectors, Matrices, and Determinants

1. Introduction

2. Sets of linear equations, row reduction

3. Determinants; Cramer's rule

5. Lines and planes

6. Matrix operations

7. Linear combinations, linear functions, linear operators

8. General theory of sets of linear equations

9. Special matrices

10. Miscellaneous problems

4. Partial Differentiation

1. Introduction and notation

2. Power series in two variables

3. Total differentials

4. Approximate calculations using differentials

5. Chain rule or differentiating a function of a function

6. Implicit differentiation

7. More chain rule

8. Application of partial differentiation to maximum and minimum problems

9. Maximum and minimum problems with constraints; Lagrange multipliers

10. Endpoint or boundary point problems

11. Change of variables

12. Differentiation of integrals; Leibniz' rule

13. Miscellaneous problems

5. Multiple Integrals; Applications of Integration

1. Introduction

2. Double and triple integrals

3. Applications of integration ; single and multiple integrals

4. Change of variables in integralS; Jacobians

5. Surface integrals

6. Miscellaneous problems

6. Vector Analysis

1. Introduction

2. Applications of vector multiplication

3. Triple products

4. Differentiation of vectors

6. Directional derivative; gradient

7. Some other expressions involving V

8. Line integrals

9. Green's theorem in the plane

10. The divergence and the divergence theorem

11. The curl and Stokes' theorem

12. Miscellaneous problems

7. Fourier Series

1. Introduction

2. Simple harmonic motion and wave motion; periodic functions

3. Applications of Fourier series

4. Average value of a function

5. Fourier coefficients

6. Dirichlet conditions

7. Complex form of Fourier series

8. Other intervals

9. Even and odd functions

10. An application to sound

11. Parseval's theorem

12. Miscellaneous problems

8. Ordinary Differential Equations

1. Introduction

2. Separable equations

3. Linear first-order equations

4. Other methods for first order equations

5. Second-order linear equations with constant coefficients and zero right-hand side

6. Second-order linear equations with constant coefficients and right-hand side not zero

7. Other second-order equations

8. Miscellaneous problems

9. Calculus of Variations

1. Introduction

2. The Euler equation

3. Using the Euler equation

4. The brachistochrone problem; cycloids

5. Several dependent variables; Lagrange's equations

6. Isoperimetric problems

7. Variational notation

8. Miscellaneous problems

10. Coordinate Transformations; Tensor Analysis

1. Introduction

2. Linear transformations

3. Orthogonal transformations

4. Eigenvalues and eigenvectors; diagonalizing matrices

5. Applications of diagonalization

6. Curvilinear coordinates

7. Scale factors and basis vectors for orthogonal systems

8. General curvilinear coordinates

9. Vector operators in orthogonal curvilinear coordinates

10. Tensor analysis—introduction

11. Cartesian tensors

12. Uses of tensors; dyadics

13. General coordinate systems

14. Vector operations in tensor notation

15. Miscellaneous problems

11. Gamma, Beta, and Error Functions; Asymptotic Series; Stirling's Formula; Elliptic Integrals and Functions

1. Introduction

2. The factorial function

3. Definition of the gamma function; recursion relation

4. The gamma function of negative numbers

5. Some important formulas involving gamma functions

6. Beta functions

7. The relation between the beta and gamma functions

8. The simple pendulum

9. The error function

10. Asymptotic series

11. Stirling's formula

12. Elliptic integrals and functions

13. Miscellaneous problems

12. Series Solutions of Differential Equations; Legendre Polynomials; Bessel Functions; Sets of Orthogonal Functions

1. Introduction

2. Legendre's equation

3. Leibniz' rule for differentiating products

4. Rodrigues' formula

5. Generating function for Legendre polynomials

6. Complete sets of orthogonal functions

7. Orthogonality of the Legendre polynomials

8. Normalization of the Legendre polynomials

9. Legendre series

10. The associated Legendre functions

11. Generalized power series or the method of Frobenius

12. Bessel's equation

13. The second solution of Bessel's equation

14. Tables, graphs, and zeros of Bessel functions

15. Recursion relations

16. A general differential equation having Bessel functions as solutions

17. Other kinds of Bessel functions

18. The lengthening pendulum

19. Orthogonality of Bessel functions

20. Approximate formulas for Bessel functions

21. Some general comments about series solutions

22. Hermite functions; Laguerre functions; ladder operators

23. Miscellaneous problems

13. Partial Differential Equations

1. Introduction

2. Laplace's equation ; steady-state temperature in a rectangular plate

3. The diffusion or heat flow equation; heat flow in a bar or slab

4. The wave equation; the vibrating string

5. Steady-state temperature in a cylinder

6. Vibration of a circular membrane

7. Steady-state temperature in a sphere

8. Poisson's equation

9. Miscellaneous problems

14. Functions of a Complex Variable

1. Introduction

2. Analytic functions

3. Contour integrals

4. Laurent series

5. The residue theorem

6. Methods of finding residues

7. Evaluation of definite integrals by use of the residue theorem

8. The point at infinity; residues at infinity

10. Some applications of conformal mapping

11. Miscellaneous problems

15. Integral Transforms

1. Introduction

2. The Laplace transform

3. Solution of differential equations by Laplace transforms

4. Fourier transforms

5. Convolution; Parseval's theorem

6. Inverse Laplace transform (Bromwich integral)

7. The Dirac delta function

8. Green functions

9. Integral transform solutions of partial differential equations

10. Miscellaneous problems

16. Probability

1. Introduction; definition of probability

2. Sample space

3. Probability theorems

4. Methods of counting

5. Random variables

6. Continuous distributions

7. Binomial distribution

8. The normal or Gaussian distribution

9. The Poisson distribution

10. Applications to experimental measurements

11. Miscellaneous problems

Answers to Selected Problems

Edition Identifiers

Open Library: OL49644693M

Work Identifiers

Work ID: OL5588653W

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