Mathematical Methods in the Physical Sciences by Mary L. Boas

[Greg Bernhardt]

• 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:

[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]

 

[ZapperZ]

Note that this book has been discussed numerous times in this forum. I have made several strong recommendations for students to get it:

https://www.physicsforums.com/showthread.php?t=76454

https://www.physicsforums.com/showthread.php?t=650842

https://www.physicsforums.com/showthread.php?t=230281

Zz.

 

[fa.arad]

I already have a hard copy of this book and looking for a pdf version. Is there a place where I could purchase the soft version?

 

[sandy.bridge]

I am getting this book and working through it this summer. As of tomorrow, I am finished all the math required for my degree, so this will be for fun.

 

[Greg Bernhardt]

I am getting this book and working through it this summer. As of tomorrow, I am finished all the math required for my degree, so this will be for fun.

Congrats! Let us know what you think when you get the book.

 

[George Jones]

Years ago, I used Boas as the text for a Mathematical Methods course that I taught on vector analysis, differential equations, and special functions. After the course was over, a post-doc told me that he lurked outside the classroom door while I taught, and that he thought that I must have spent a lot of time preparing my lectures. I told him that Boas spent a lot of time preparing, and that I just followed her lead.

 

[ahmadmz]

I just finished my first year of EE. I have 3 months free and plan to go over this book. How much should i expect to cover in 3 months? Should I set a time limit (e.g 1 week) per chapter or take as much time needed to reasonably understand the material?

 

[sandy.bridge]

I, personally, wouldn't recommend setting "deadlines" for chapter completion. This is your time off, and I would exploit this fact via learning at your own pace. Furthermore, I would venture to say that the chapter difficulties are not uniform.

 

[johnqwertyful]

The one complaint about the book is that the publisher messed up the copying pretty badly at places. Difficult to read to sometimes unreadable. Ink blots, cut of pages, etc. All the boxed formulas/theorems are very dark and hard to read.

 

[ZapperZ]

The one complaint about the book is that the publisher messed up the copying pretty badly at places. Difficult to read to sometimes unreadable. Ink blots, cut of pages, etc. All the boxed formulas/theorems are very dark and hard to read.

Are you sure you bought the legit version of the text? It sounds like one of those cheap, pirated, illegal copies. I have the 2nd edition, and I've seen and browsed through the 3rd edition. I have never seen anything resembling what you mentioned.

Zz.

 

[AlephZero]

The one complaint about the book is that the publisher messed up the copying pretty badly at places. Difficult to read to sometimes unreadable. Ink blots, cut of pages, etc. All the boxed formulas/theorems are very dark and hard to read.

Even professional book printers screw up sometimes and few pages get trashed. If you bought it from a reputable bookseller, they should exchange it for a properly printed copy free of charge.

But as ZZ said, it's very unusual for a "whole book" to be badly printed or bound without somebody noticing there was a problem.

 

[johnqwertyful]

Are you sure you bought the legit version of the text? It sounds like one of those cheap, pirated, illegal copies. I have the 2nd edition, and I've seen and browsed through the 3rd edition. I have never seen anything resembling what you mentioned.

Zz.

I bought a physical copy off Amazon. A few other people complained about the same thing

 

[ajayguhan]

Which is better kreyszig or boas ?

 

[Radarithm]

Would Calc 1 be enough for this book? Or do I need to wait till I teach myself Calc 2 & 3?

 

[wakefield]

Would Calc 1 be enough for this book? Or do I need to wait till I teach myself Calc 2 & 3?

You'll need to know various techniques of integration and it would help to be familiar with sequences and series already.

 

[RaulTheUCSCSlug]

Would Calc 1 be enough for this book? Or do I need to wait till I teach myself Calc 2 & 3?

I believe that with the use of Green's theorem and some other integration techniques, you will need to look at techniques from Calc 3 and at least gone through Calc 1 and Calc 2. I know you posted this long time ago, but perhaps a member reading this will have the same question.

Cheers!