Mathematical Tools for Physics - Department of Physics - University

2—Infinite Series 34 The original function is a maximum when this denominator is a minimum. When the numbersNand kare big, you c ...

2—Infinite Series 35 2.7 Useful Tricks There are a variety of ways to manipulate series, and while some of them are simple they ...

2—Infinite Series 36 2.8 Diffraction When light passes through a very small opening it will be diffracted so that it will spread ...

2—Infinite Series 37 Use this and the light amplitude is 2 A −ksinθ sin ( − ka 2 sinθ ) cos ( k(r 0 − a 2 sinθ)−ωt ) (2.29) Thew ...

2—Infinite Series 38 When you use the binomial expansion, put the binomial in the standard form,(1 +x)as in the second line of t ...

2—Infinite Series 39 mistake; go back and find it. You can do this sort of analysis everywhere, and it is one technique that pro ...

2—Infinite Series 40 vy(t) =v 0 −gt, y(t) =v 0 t− 1 2 gt^2 (2.32) Should you expect this? Not if you remember that there’s air r ...

2—Infinite Series 41 at the preceding two sets of equations and letvt−→ ∞. The result is precisely the equations (2.32), just as ...

2—Infinite Series 42 The electric field on the axis of a ring is something that you can compute easily. The only component of th ...

2—Infinite Series 43 smallc, and the key is to realize that the only place the integrand gets big is in the neighborhood of θ= 0 ...

2—Infinite Series 44 Exercises 1 Evaluate by handcos 0. 1 to four places. 2 In the same way, evaluatetan 0. 1 to four places. 3 ...

2—Infinite Series 45 Problems 2.1 (a) If you borrow $200,000 to buy a house and will pay it back in monthly installments over 30 ...

2—Infinite Series 46 2.12 What is the series expansion forcscx= 1/sinx? As in the previous problem, use your knowledge of the si ...

2—Infinite Series 47 2.22 Use a pocket calculator that can handle 100! and find the ratio of Stirling’s approximation to the exa ...

2—Infinite Series 48 Write the next couple of lines of the triangle and then prove that this algorithm works, that is that the m ...

2—Infinite Series 49 is one of the following answers. Examine them to determine if any is plausible. That is, examine each and s ...

2—Infinite Series 50 and you can repeat the process. For comparison take the exact solution and do a power series expansion on i ...

2—Infinite Series 51 2.49 In problem2.18you found the power series expansion for the error function — good for small arguments. ...

Complex Algebra . When the idea of negative numbers was broached a couple of thousand years ago, they were considered suspect, i ...

3—Complex Algebra 53 z 1 =x 1 +iy 1 z 2 =x 2 +iy 2 y 1 +y 2 z 1 +z 2 x 1 +x 2 The graphical interpretation of complex numbers is ...