MATH 2XX3
Assignment 1
Due January 25, 2012
1. Let R be the region in the plane bounded by x = 0, y = 0, x + y = 1 and x + y = 2.
Calculate the integral R (x + y )1/2 dx dy by using the change of vari
McMaster University
Math 2XX3 (Term II, 2013-2014)
Course Information Sheet
Instructor: M. Wang
Office: HH 321
Extension: 23405
e-mail: [email protected]
Office Hours: M 14:00 - 15:30 ; W 13:00 14:30 o
MATH 2XX3
Assignment 3
Due March 7, 2012
1. Consider the parametrized surface given by:
(u, v ) =
1
u(1
3
1
1
1
3 u2 + v 2 ), 3 v (1 1 v 2 + u2 ), 3 (u2 v 2 ) where 0 u 1, 0 v 1.
3
This is (a portion
Information about Test 2
Date: March 12, 2015
Time: 15:30 16:20
Place: T28
Topics Covered:
Sections 7.1 7.6 in Marsden-Tromba except for
Supplement to 7.1 (p. 355-356)
All practice problems from the a
McMASTER UNIVERSITY FINAL EXAMINATION
MATH 2XX3, DAY CLASS
Dr. M. Wang
DATE: April, 2009.
DURATION OF EXAM: 3 hours
FAMILY NAME: _ FIRST NAME:
STUDENT NUMBER:
This exam paper contains 5 questions with
MATH 2XX3 Assignment 3
Due Date: Before Noon, March 6, 2015
1. Find a parametrization for each of the surfaces below:
(i) the part of the surface z 2 x2 y 2 = 1 that lies below the rectangle
[1, 1] [3
Some Facts about Functions
revised September 9, 2013
1
Basic denitions
Denition 1.1. Suppose X and Y are two sets. Then their Cartesian product X Y is dened as
X Y := cfw_(x, y)| x X, y Y .
Example 1.
MATH 2XX3 (Winter 2014) Practice Problems
Question 1. For parts (a) and (b) below, consider the parametrized surface
given by the formula
(u, ) = (eu + eu ) cos , (eu + eu ) sin , 2u)
r
(a) Find a la
MATH 2XX3 Assignment 2
Due Date: Before 12:30 pm, February 13, 2015
1. Let (t) denote the plane curve
c
(aebt cos t, aebt sin t)
where a, b are two positive constants and t 0.
a. Find the arclength fu
MATH 2XX3 Assignment 1
Due Date: Before 12:30 pm, January 23, 2015
x dxdy where D is the region in the rst quad1. Evaluate the integral
D
rant that lies between the circles x2 + y 2 = 4 and x2 + y 2 =
MATH 2XX3 Assignment 4
Due Date: Before 12:30 pm, April 1, 2015
1. Let D be a region in the plane bounded by a simple closed curve C.
Suppose that the area of D is A. Show using Greens theorem that th
Information about Test 1
Date: February 5, 2015
Time: 15:30 16:20
Place: T28
Topics Covered:
Sections 6.1 6.4, 4.3, 4.4 in Marsden-Tromba except for the material on Fubinis
theorem on pp. 342-344
All
Math 2XX3
Practice Problems # 7
February 27, 2017
Not to be submitted, but should be prepared for tutorial Mar 37.
1. Assume f : Rn ! R is C 3 , ~a is a critical point of f , and the Hessian is strict
Math 2XX3
Practice Problems # 11
March 29, 2017
Not to be submitted, but should be prepared for the Final Exam, Thursday April 13 at
9:00am.
1. (a) Calculate the Fourier Series of f (x) = |x|,
< x <
Math 2XX3
Homework Assignment # 1
January 15, 2017
Due Thursday Jan 26, 4:00 pm. Submit your assignment in the appropriate locker slot
in the basement of Hamilton Hall.
1. For the subset U = cfw_(x1 ,
Math 2XX3
Homework # 3
March 5, 2017
Due by 4:00pm on Wednesday March 15, in the appropriate locker slot in the basement
of Hamilton Hall.
1.
For f (x, y, z) = 3y + x2 + z 2
y 3 + x2 z 2 + z 4 , find
Math 2XX3
Hints for Practice Problems # 10 and 11
Practice Problems # 10
1. For powers and product of sin and cos, you get Fourier Series by trig identity: sin x cos x =
1
2
sin(2x), which is a Fourie
Math 2XX3
Homework # 4
March 21, 2017
Due by 4:00pm on Thursday March 30, in the appropriate locker slot in the basement of
Hamilton Hall.
1.
(a) Find the Fourier Series S(x) of f (x) = cos(x/2),
< x
LAST (Family) NAME:
Test # 2
Math 2XX3
FIRST NAME:
ID # :
March 20, 2017
Instructions: This exam consists of 4 questions in 6 pages. Indicate your answers clearly in the
appropriate places. Unless sta
MATH 2XX3 Assignment 3
Due Date: Before Noon, March 6, 2015
1. Find a parametrization for each of the surfaces below:
(i) the part of the surface z 2 x2 y 2 = 1 that lies below the rectangle
[1, 1] [3
MATH 2XX3 Assignment 1
Due Date: Before 12:30 pm, January 23, 2015
1. Evaluate the integral
x dxdy where D is the region in the rst quadD
rant that lies between the circles x2 + y 2 = 4 and x2 + y 2 =
Test 3 / Answers
1. (a) Review the definition 8.2 in the book.
(b) When x > 0 (from the right), |f (x) f (0)| = | x cos(1/x) 0| x < provided 0 < x <
with = 2 .
(c) f is not continuous at x = 0, since
Physics 1AA3 Lab reports
What is being marked?
Introduction, Hypothesis, Method, Results, Discussion, Conclusion, Presentation, and
graphs/tables
Max 4 pages (not including graphs/tables, title page,
Test 1 / Math 2XX3 / Solutions
1. S = cfw_q Q | 0 < q 3 R.
(a) sup S = 3. S does not have a maximum element since 3 6 Q
(b) First, if x > 0, either 0 < x 3 or x > 3. If
0 < x 3, between
any two real