Mathematical Tools for Physics - Department of Physics - University

Mathematical Tools for Physics by James Nearing Physics Department University of Miami [email protected] http://www.physics.mia ...

Contents Introduction iii Bibliography v 1 Basic Stuff 1 Trigonometry Parametric Differentiation Gaussian Integrals erf and Gamm ...

Gradient in other Coordinates Maxima, Minima, Saddles Lagrange Multipliers Solid Angle Rainbow 9 Vector Calculus 1 213 Fluid Flo ...

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

I chose this font for the display versions of the text because it appears better on the screen than does the more common Times f ...

Bibliography . Mathematical Methods for Physics and Engineeringby Riley, Hobson, and Bence. Cambridge Uni- versity Press For the ...

good physical insight into what’s going on in some system is far more useful than an unintelligible exact result.” Probability T ...

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

1—Basic Stuff 2 This is the reason that the radian was invented. The radian is the unit designed so that the propor- tionality c ...

1—Basic Stuff 3 The solutions to this areex=y± √ y^2 + 1, and because √ y^2 + 1is always greater than|y|, you must take the posi ...

1—Basic Stuff 4 1.2 Parametric Differentiation The integration techniques that appear in introductory calculus courses include a ...

1—Basic Stuff 5 Ifnis a positive odd integer, these are elementary, n= 1 ∫∞ −∞ dxxne−αx 2 = 0 (nodd) (1.7) To see why this is tr ...

1—Basic Stuff 6 1.4 erf and Gamma What about the same integral, but with other limits? The odd-ncase is easy to do in just the s ...

1—Basic Stuff 7 The same procedure works for other negativex, though it can take several integer steps to get to a positive valu ...

1—Basic Stuff 8 The exact answers are 1 / 4 , 2 / 4 , 1 / 4 , but as two is not all that big a number, the fairly large error sh ...

1—Basic Stuff 9 The prescription is clear, but to remember it you may prefer a mathematical formula. A notation more common in m ...

1—Basic Stuff 10 and for convenience label the endpoints asx 0 andxN. For the sketch ,N= 8. 3. Let∆xk=xk−xk− 1. That is, ∆x 1 =x ...

1—Basic Stuff 11 Fundamental Thm. of Calculus If the function that you’re integrating is complicated or if the function is itsel ...

1—Basic Stuff 12 work in this book, but it is a fairly simple extension of the Riemann integral and I’m introducing it mostly fo ...

1—Basic Stuff 13 An example. A very thin rod of lengthLis placed on thex-axis with one end at the origin. It has a uniform linea ...