
Announcements for UBC Math 265 Sections 101, 103; Fall 2010
Announcements for UBC Math 265 Sections 101, 103; Fall 2010
Study Aids
 The Math Dept website has a collection of past final exams for Math 265. They are good practice. (NOTE: some exams occasionally have questions on material we did not cover this year. Ask me if you are unsure.)
 Here is a site that can help you review by working through problems in Boyce and Diprima. This site supplies step by step solutions. You can use the book problems for extra review and check your solution against these.
Solution site .
Thanks to Joaquin Miralles for pointing this out.
 In the final exam, the following table of Laplace transforms will be provided for you: Lapl.Tr Table
Homework assignments:
The homework assigned each week is posted here.
 Here is the final version of Homework 1, due Sept 22 in class.
For extra practice (BUT NOT TO HAND IN), you may want to try out the following
problems from Boyce and Diprima (9th Ed):
 Direction fields: p 8: #1520
 Models and ODEs: p 2324 (read, think about)
 Integrating factors: pp 3239 (read and try the examples)
 Try some of: p 39: # 1320
 Here is the final version of Homework 2, due Sept 29 in class.
 Here is Homework 3. This homework will not be collected. It is meant to help you prepare for the Midterm test. I may add more problems and the solutions will be posted on the weekend of Oct 2.
For extra practice (BUT NOT TO HAND IN), you may want to try out
problems from Boyce and Diprima (9th Ed) listed in the table below. Solutions will not be provided, but there are answers to most of these in the book.
 Here is the final version of Homework 4. Note that Problem 1 is slightly expanded, and I added Problem 4.
It will be due in class on Oct 20. Part of the homework ("Problem 5")
is to find out how to
do any question that you could not get on the midterm. See copy of midterm here.

Here is a copy of Midterm 1 (Oct 6) Version 1 and Version 2. Be sure and work on all questions that you did not get on the test.
 Here is Homework 5, due in class on Oct 27.
Slightly modified copy was posted here Oct 20 at 10:00AM.
 Here is Homework 6, due in class on NEW!! The HW6 due date has been pushed to Monday Nov 8 to allow people more time in view of tests and other work this week.
 Here is a copy of Midterm 2 (Nov 10)
Section 101,
Section 103 Version A and Section 103 Version B. Be sure and work on all questions that you did not get on the test.
 Here is most of Homework 7. Part of the HW is to redo any midterm problem that you were unsure of during the test. (see link directly above this entry for copies of the test).
Unsure about how to redo the problems on the midterm test? Consult these Hints for some help and resources to check out.
 Homework 8: Download a copy of this past from Dec 2009, Your homework 8 is to hand in this exam with all questions worked out. You will get credit towards your homework score as well as a good chance to do some early review for your Math 265 exam.
Note: there are other versions of past exams on this UBC math dept link.
DEC 1 NOTE: The HW has been extended to Friday morning Dec 3 by 9:00AM. Submit (stapled, with your section number) in MX 1111 (slip under my door).
Solutions
I will post solutions to homework assignments here from time to time. Once
the homework is collected, these solutions will be visible.
What are we learning in class?
You can find the topics covered and the class notes in the table below. Sections refer to the 9th edition of Boyce and Diprima.
Dates 
Topics 
Reference 
Problems to try 
Class Notes
and examples 
September 8 
Introduction: What is a differential equation?
Example: LRC circuit;
Initial Value Problem (IVP)
First order ODEs
Direction Fields

Chapter 1, Sec 2.1 
p 39 some of 112 
Sept 8 lecture
Examples 
September 13 
First order ODEs cont'd
Stirred tank reactor example
Integrating factor method
and examples

Sec 2.1, Sec 2.3 p 52 Example 1 
Sec 2.1: 21, 30, 33 
Sept 13 lecture
Examples 
September 15 
More applications
Separable ODEs
Derivation of Torricelli's Law
Other examples (Newton's law of cooling,
falling under gravity with drag) 
Sec 2.2 
Sec 2.2: 21, 23, 25, 27
Sec 2.3: 3, 13, 16, 17, 23, 27 
Sept 15 lecture
Rocket example 
September 20 
Second order ODEs
Springmass system, LRC circuit
Linear 2nd order ODE with constant
coeffs
characteristic eqn
Superposition principle

Sec 3.1 
Sec 3.1: 15, 21, 23, 25 
Sept 20 lecture
Example 
September 22 
Linear 2nd order ODE cont'd
classifying roots of char. eqn
Existence, uniqueness of solutions
Wronskian, fundamental set of solns

Sec 3.2 (briefly) 
Sec 3.2; 15, 2427 
Sept 22 lecture 
September 27 
Fundamental set of solns, Cont'd
Wronskian cont'd
Complex roots of char eqn
Oscillatory solns with/without decay 
Sec 3.3 
Sec 3.3 1722 
Sept 27 lecture
Examples
exp(iwt)

September 29 
Repeated roots of char. eqn
Intro to nonhomog ODE
Method of Undetermined coeff's 
Sec 3.4, Sec 3.5 
Sec 3.4: 1115 Sec 3.5: 16 
Sept 29 lecture 
October 4 
Nonhomogeneous ODE cont'd
forced vibrations 
Sec 3.5, 3.7 
Sec 3.5, 1315 
Oct 4 lecture
Soln to inclass work
Hard example

October 6 
Review 
Various 
Various 
Oct 6 lecture
Some Examples

October 13 
Mechanical Vibrations 
Sec 3.7 
TBA 
Oct 13 lecture
Some Useful Trig

October 18 
Intro to Laplace Transform 
Sec 6.1 
Sec 6.1: 78,2124 
Oct 18 lecture

October 20 
Properties of Laplace Transform 
Sec 6.2 
Sec 6.2: 110, some of 1120 
Oct 20 lecture

October 25 
Laplace Transform of step functions and shifts 
Sec 6.3, 6.4 
Sec 6.3: 1,3,5, 19,21,23
Sec 6.4: Some of 1 13 
Oct 25 lecture
Some useful facts
Lapl.Tr Table

October 27 
Laplace Transform of impulses 
Sec 6.5 
Sec 6.5: Some of 112 
Oct 27 lecture

November 1 
Convolution theorem 
Sec 6.6 
Sec 6.6: 811, 1220
Extra problems
Solutions 
Nov 1 lecture
interpreting convolutions
Miscellaneous: IC's at t not= 0

November 3 and 8 
Systems of first order Linear ODEs 
Chap 7 
TBA 
Nov 3 and Nov 8 lectures

November 8 
Systems of 1st order Lin ODEs Contd 
Chap 7 
Sample Problems
Solutions

More Nov 8 lecture

November 15 
Lin Sys and Complex roots 
Sec 7.6 
Sec 7.6: 16

Nov 15Review of sys
Nov 15 lecture

November 17 
Lin Sys and Phase planes 
Sec 7.5 
Sec 7.5: 18

Nov 17 lecture

November 22 
Lin Systems: Repeated roots 
Sec 7.8 
Sec 7.8: 14, 710

Nov 22 lecture

November 24 
Lin Systems: SpringMass dynamics 
 


Nov 24 lecture

November 29 
NxN Lin Systems and Nonhomogeneous problems 
Sec 7.9 (Undet'd Coeffs) 
Sec 7.9: 24,7

Nov 29 lecture

December 1 
Review & practice FinalExam 
 


Dec 1 lecture

