Mathematical Tools for Physics

Mathematical Tools for Physics by James Nearing Physics Department University of Miami mailto:[email protected] Copyright 2003, ...

Contents Introduction................. iv Bibliography................ vi 1 Basic Stuff................. 1 Trigonometry Parametr ...

7 Operators and Matrices.......... 168 The Idea of an Operator Definition of an Operator Examples of Operators Matrix Multiplica ...

Basis Change 13 Vector Calculus 2............. 396 Integrals Line Integrals Gauss’s Theorem Stokes’ Theorem Reynolds’ Transport ...

Introduction I wrote this text for a one semester course at the sophomore-junior level. Our experience with students taking our ...

last couple of chapters were added after the class was over. There is enough here to select from if this is a course text. If yo ...

Bibliography Mathematical Methods for Physics and Engineeringby Riley, Hobson, and Bence. Cambridge University Press For the qua ...

Numerical Recipesby Press et al. Cambridge Press The standard current compendium surveying techniques and theory, with programs ...

Basic Stuff 1.1 Trigonometry The common trigonometric functions are familiar to you, but do you know some of the tricks to remem ...

1—Basic Stuff 2 It results from one figure and the relation between the radius of the circle, the angle drawn, and the length of ...

1—Basic Stuff 3 The other three functions are sechx= 1 coshx , cschx= 1 sinhx , cothx= 1 tanhx Drawing these is left to problem ...

1—Basic Stuff 4 The solutions to this areex=y± √ y^2 + 1, and because √ y^2 + 1is always greater than|y|, you must in this case ...

1—Basic Stuff 5 Similarly the derivative ofcoshxissinhx. Note the plus sign here, not minus. Where do hyperbolic functions occur ...

1—Basic Stuff 6 Now differentiate this integral with respect toα, d dα ∫∞ 0 e−αxdx= d dα 1 α or − ∫∞ 0 xe−αxdx= − 1 α^2 And diff ...

1—Basic Stuff 7 To see why this is true, sketch a graph of the integrand (start with the casen= 1). For the integral over positi ...

1—Basic Stuff 8 Now do the rest of these integrals by parametric differentiation, introducing a parameter with which to carry ou ...

1—Basic Stuff 9 I used t = u^2 and then the result for the Gaussian integral, Eq. ( 9 ). A simple and useful identity is (see pr ...

1—Basic Stuff 10 tabulation. It’s reprinted byDoverPublications (inexpensive and very good quality). There’s also a copy on the ...

1—Basic Stuff 11 There are 8 possibilities here, 23 , so you expect (on average) one run out of 8 to give you 3 heads. Probabili ...

1—Basic Stuff 12 The first quotient in the last equation is, in the limit that∆x→ 0 , the derivative offwith respect to its firs ...