Math 241 Chapter 11 11.1 Cartesian Coordinates in Space
Dr. Justin O. Wyss-Gallifent
1. Preliminaries: How to plot points in 3-space, the coordinate planes, the first octant. Emphasize how perspective can be confusing at first. 2. Distance between points:
MATH 410: Homework 2 Section 1.2
Due in class Friday 2/10/2012
1. For each of the following statements, determine whether it is true or false and informally justify your answer. (a) Z is dense in R. (b) R
>0
* * *
is dense in R.
(c) Q \ Z is dense in R. N
MATH 410: Homework 2 Solutions Section 1.2 1. For each of the following statements, determine whether it is true or false and informally justify your answer. (a) Z is dense in R. Solution: False. For example (0, 1, 0.2) contains no integers. (b) R>0 is de
MATH 410: Homework 3 Section 2.2
Due in class Friday 2/17/2012
1. For each of the following statements determine whether it is true or false and justify informally: (a) Every bounded sequence converges. (b) A convergent sequence of positive numbers has a
MATH 410: Homework 3 Solutions Section 2.2 1. For each of the following statements determine whether it is true or false and justify informally: (a) Every bounded sequence converges. Solution: False. For example cfw_(-1)n .
1 n
(b) A convergent sequence o
MATH 410: Homework 4 Section 2.4
Due in class Friday 2/24/2012
1. For each of the following statements determine whether it is true or false and justify informally: (a) Every sequence in (0, 1) has a convergent subsequence. (b) Every sequence in (0, 1) ha
MATH 410: Homework 5 Section 3.3 1. Prove that there is a solution to the equation
Due in class Friday 3/2/2012
*
1 + x2 - 2x = 0 with x > 0 x + x2 Note: This is book problem 3. 2. Suppose that f : R R is continuous and that f (R) is bounded. Prove that t
MATH 410: Homework 6 Section 3.6
Due in class Friday 3/9/2012
1. Define f : [0, ) R by f (x) = 1 + x2 . First prove that f fits the hypotheses for Theorem 3.29 in the book and then elaborate on what the consequence of this theorem is. Note: This is not a
Math 241 Project 1 What to Submit:
Due in Discussion on Tuesday 2/28/2012
For this project you will need to turn in a printout of what you typed into Matlab and the printouts of the plot windows for those questions asking you to plot. For the eager: If yo
PRESENTATION GUIDE AND RUBRIC FOR PHYSICAL SCIENCE 105
You will be engaged in a learning task that will require you to collaborate with others and use a variety of
strategies to complete a PowerPoint presentation which will be 5 to 7 minutes in length. Ex
Caring &
Communicating
The Art of Nursing
Reflect on:
your own thoughts about the meaning of
caring.
how will your beliefs about caring and
nursing influence your practice.
Blais & Hayes, Professional Nursing Practice Concepts and Perspectives.
3rd custom
Math 241 Exam 2 Spring 2013
Instructions: There are 4 answer sheets. Write your name, section number, and problem number
on each sheet. Do one problem per page, you may use the back if necessary. All work must be
shown to receive full credit. N0 calculato
Math 241 Spring 2013 Final Exam
0 Follow the instructions as to Which problem goes on which answer sheet. You may use the
back of the answer sheets.
0 No calculators are permitted.
0 One page of notes is permitted.
0 Do not evaluate integrals or simplify
Quiz 1 _ I MATH 241, SPRING 2013
92m NAMEzmmu, 6W /
Problem 1.(2 points.) Find an inequality satised by all points that belong to the
closed ball with radius 4 and center (1, 0, 1).
X (\ I \I A}
V = u\ ' A! 3
_ .L A L. A , J "
U - w: * J3 3 Ni K
»
jQQQW/ 6Wtf « OZHV lieu/W-
Math 241 Exam 1 A' . , Spring 2013
Instructions: Ihere are 4 answer sheets. Write your name, section number, and problem number
on each sheet. Do one problem per page, you may use the back if necessary. All work must be
shown to
MATH 410: Homework 1 Solutions Section 1.1 1. For each of the following statements determine whether it is true or false and justify (informally) your answer. (a) The sum of irrational numbers is irrational. Solution: False. For example + (-) = 0. (b) The
MATH 410: Homework 1 Section 1.1
Due in class Friday 2/3/2012
1. For each of the following statements determine whether it is true or false and justify (informally) your answer. (a) The sum of irrational numbers is irrational. (b) The product of irrationa
Math 241 Chapter 12 12.1 Definitions and Examples of Vector Valued Functions
Dr. Justin O. Wyss-Gallifent
1. Definition: For each t, F (t) (or usually, and later, r(t) points from the origin to a point on the curve. 2. Classic examples: Circles, helices,
Math 241 Chapter 13 13.1 Functions of Several Variables 1. Definition: A function like f (x, y), f (x, y, z), g(s, t) etc.
Dr. Justin O. Wyss-Gallifent
2. Definition of the graph of a function of two variables and classic examples like: Plane, paraboloid,
Math 241 Chapter 14 14.1 Double Integrals
Dr. Justin O. Wyss-Gallifent
1. These can be defined via a Riemann Sum method like in Calculus I but the net result is: We can define the double integral of f (x, y) over R, denoted R f (x, y) dA to be the signed
Math 241 Chapter 15 15.1 Vector Fields
Dr. Justin O. Wyss-Gallifent
1. Define a vector field: Assigns a vector to each point in the plane or in 3-space. Can be visualized as loads of arrows. Can represent a force field or fluid flow - both are useful. 2.
Math 241 Chapter 15 Integral Study Guide ^ Important 1: Curves are always parametrized by r(t) = x(t) ^ + y(t) + z(t) k for a t b Note i ^ ^ that some components might be 0 and the k component will definitely be 0 in 2D. ^ Important 2: Surfaces are always
Math 241 Sections 01* Exam 1
Dr. Justin O. Wyss-Gallifent
Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appropriate for the methods taught in this course. Partial credit will be given for any work, words or i
Math 241 Exam 1 Sample 1 Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appropriate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the pr
Math 241 Exam 1 Sample 3 Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appropriate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the pr
Math 241 Exam 1 Sample 3 Solutions ^ 1. (a) We have P = 2 ^ - 2 - 1 k and to make it length 1 we: Q i ^ ^ P Q 2 ^- 2 - 1 k i ^ = 4 + 4 + 1 |P Q|
(b) We need ^ ( ^ - 2 + k) (2 ^ + 5 ) = 0 i ^ i ^ 2 - 10 = 0
=5
(c) We have
a b 2 + 10 ^ (1 ^ + 2 + 3 k) i ^ P
Math 241 Exam 1 Sample 4 Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appropriate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the pr