MATH 105A REAL ANALYSIS UCSC

Jerey Hellrung Monday, April 09, 2007 Physics 105A, Homework 01 a. Problems 1-1, 1-3, 1-4, 1-6, 1-7, 1-8, 1-10. 1-1. Find the transformation matrix that rotates the axis x3 of a rectangular coordinate system 45 toward x1 around the x2 -axis. Solutio

Jerey Hellrung Wednesday, June 06, 2007 Physics 105A, Homework 09 Final Exam, Spring 2006 PART I. For these questions, pretend you are being asked by a fellow student. Try to give an explanation in one or two sentences to each question. 1. (a) What

Jerey Hellrung Monday, May 14, 2007 Physics 105A, Homework 06 1. A truck has to drive across the desert, from a opint that is a miles north of the equator coordinates (0, a) to a point that is b miles south of the equator and c miles further west

Jerey Hellrung Monday, May 07, 2007 Physics 105A, Homework 05 1. (a) We can rewrite the system of 2 second-order scalar ODEs as a system of 4 rst-order scalar ODEs: 0 0 0 1 0 q1 q1 q2 0 d q2 0 0 0 1 + . q1 = 1/L1 C1 0 R/L1 R/L1 q

Math 100 Composition of Functions 1. A Composition Exercise Martin H. Weissman Let A = {a, b, c, d}. Let B = {1, 2, 3}. Define functions f : A B, and g : B A, by the following: f (a) = 1. f (b) = 3. f (c) = 3. f (d) = 2. g(1) = a. g(2) = d. g(

Math 100 Evens and Odds, First Proofs Martin H. Weissman To practice proof-writing, in a paragraph style, we will prove some basic facts about arithmetic. 1. Evens and Odds In order to prove things about even and odd numbers, we begin by recalling

Name: Quiz 4 A Inflectional vs. Derivational Morphemes (30 pts) Please divide each of the following words into their component morphemes. For each affix (i.e., not for the root), please state whether it is inflectional or derivational. 1. mysteriou

Math 100 Three Proofs by Induction Martin H. Weissman 1. Division with Remainder Theorem 1. Suppose that x and y are natural numbers, and y = 0. Then there exist natural numbers q and r such that: x = qy + r. 0 r < y. Proof. We prove the theore

Chapter 1 Linear Equations 1.1 Introduction A linear equation (over the real numbers R) in the variables x1 , x2 , , xn is a mathematical equation of the form (1.1) a1 x1 + a2 x2 + + an xn = c, with c and the coefficients a1 , , an some ar