Below are some of the major topics
covered in MATH 253.
1. Powerful integrating techniques including
A. By parts
B. Special Powers
C. Trigonometric substitutions
E. Partial fractions
F. Trapezoid rule
G. Simpsons rule
2. Improper Integrals
MATH 253, Fall 2013: Midterm
Answer all of the following questions to the best of your ability. Full credit requires that all
work is shown clearly.
(13) For each of the following statements, determine whether or not it is TRUE or
FALSE, and say
Each problem should be solved without the use of a calculator!
1. Graph and find the area between the curves 2 y = 4 x and 2y = x .
2. Simplify the expression ( )
f( ) n
f n +1 for each function.
a) ( ) 2
f n b) ( ) +1 = n
3. Evaluate ea
HOMEWORK ASSIGNMENT #1, Math 253
1. Sketch the curve r = 1 + cos , 0 2, and nd the area it encloses.
2. Find the dot product a b in the following cases:
(a) a =< 1, 0, 2 >, b =< 2, 0, 1 > . Are these vectors orthogonal?
(b) a =< x2 y3 x3 y2 , x3 y1 x1 y3
HOMEWORK ASSIGNMENT #2, Math 253
1. Find the equation of a sphere if one of its diameters has end points (1, 0, 5) and
(5, 4, 7).
2. Find vector, parametric, and symmetric equations of the following lines.
(a) the line passing through the points (3, 1, 1
The University of British Columbia
10 October 2012
Time: 50 minutes
LAST NAME :
This Examination paper consists of 6 pages (including this one). Make sure you have all 6.
No memory aids allowed. No c
MATH 253 Section 103, Term 1 of 2005-06
Instructor: Denis Sjerve
Office: 107 Math Building. Office Hours: MW 1:00 to 2:30, or by appointment.
Office Phone: (604) 822-2714 Email: firstname.lastname@example.org
Web page: www.math.ubc.ca/~sjer
HOMEWORK ASSIGNMENT 3, Math 253
1. Calculate the following limits, or discuss why they do not exist:
(a) lim 2
(x,y)0 x + y 2
(b) lim 2
[hint: |y 2| |x2 + y 2|]
(x,y)0 x + y 2
2. For each of the following functions, give its domain and calculate
HOMEWORK ASSIGNMENT #4, MATH 253
1. Prove that the following dierential equations are satised by the given functions:
2u 2u 2u
+ 2 + 2 = 0, where u = (x2 + y 2 + z 2 )1/2 .
= 2w, where w = x2 + y 2 + z 2
2. Show that th
Department of Mathematics
MATHS 253: Advancing Mathematics 3
Study Guide: Semester 1, 2013.
Welcome to MATHS 253, which is the standard sequel to MATHS 250, available
in semesters 1 and 2 on the City Campus. It covers topics in linear algebra, multivariab
This document includes three practice questions/examples
for Quiz 3/ midterm (to be held Nov. 8,
of questions for midterm 2 (from Montgomery 8th ed.): 6.1, 6.3, 7.1, 7.21, 8.11, 8.14 (ANOVA