Due by 12:00 noon, today 05/12/20. : CU{co} → Problem 1. Consider the Möbius transformation CU{o}...
Exercise 2: Möbius Transformations I (a) [10 points] Denote A := {z € C: |z| < 1}. Prove the following statement. Every Möbius transformation g: A → A who maps A onto A can be written as 9(2) = e® (2- 20 Zoz – 1 with 0 eR and |zo| < 1. Conversely, each such function maps A onto A. (b) [6 points] Find a Möbius transformation f with f(i) = i, f (0) = 0 and f(-i) = 0....
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
VOD Ro 1. [Design Problem (1)] N-channel MOSFET (NMOS) operating in "Saturation" region. a. Consider a circuit as shown in Fig 1. b. You will need to design the circuit such that Ip = 1 (mA), VG = 0 [V], and Vp = 5 [V]. (determine values for R1, R2, Rp, and Rs) 1 W ID = 5 unCox (Vgs - Vrh)2 = K (Vgs - VTH)2 c. Use Vpp = 15 [V], Vs = -15 [V], and 2N7000 for...
Question 4 [12 marks] Some applications of mathematics require the use of very large matrices (several thousand rows for example) and this in turn directs attention to efficient ways to manipulate them. This question focuses on the efficiency of matrix multiplication, counting the number of numerical arithmetic operations (addition, subtraction and multiplication) involved. We start with very simplest case of 2x2 matrices. (a) The standard way of multiplying 2x2 matrices uses 8 multiplications and 4 additions. List the 8 products...