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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: #15-20
• Integrating factors: pp 32-39 (read and try the examples)
• Try some of: p 39: # 13-20
• 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 1-12 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
Spring-mass 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; 1-5, 24-27 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 17-22 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: 11-15
Sec 3.5: 1-6
Sept 29 lecture
October 4 Nonhomogeneous ODE cont'd
forced vibrations
Sec 3.5, 3.7 Sec 3.5, 13-15 Oct 4 lecture
Soln to in-class 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: 7-8,21-24 Oct 18 lecture
October 20 Properties of Laplace Transform Sec 6.2 Sec 6.2: 1-10, some of 11-20 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 1-12 Oct 27 lecture
November 1 Convolution theorem Sec 6.6 Sec 6.6: 8-11, 12-20
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: 1-6 Nov 15-Review of sys
Nov 15 lecture
November 17 Lin Sys and Phase planes Sec 7.5 Sec 7.5: 1-8 Nov 17 lecture
November 22 Lin Systems: Repeated roots Sec 7.8 Sec 7.8: 1-4, 7-10 Nov 22 lecture
November 24 Lin Systems: Spring-Mass dynamics --- --- Nov 24 lecture
November 29 NxN Lin Systems and Nonhomogeneous problems Sec 7.9 (Undet'd Coeffs) Sec 7.9: 2-4,7 Nov 29 lecture
December 1 Review & practice FinalExam -- -- Dec 1 lecture