Math 2C03
Differential Equations

WINTER 2011 Homepage

Instructor: Gail S. K. Wolkowicz
Lecture Room: HH/302 Mon. & Thurs. 12:30-13:20 & Tues. 13:20-14:20 (as of Mon. Jan. 10.)
Office: Hamilton Hall, Room 318
Office Hours: By appointment.
Telephone: (905) 525-9140, Extension 24808
Email:

wolkowic@mcmaster.ca
Homepage:

http://www.math.mcmaster.ca/wolkowic/wolkowic.html
Tutorial Leader: Anton Sakovich
Tutorials: Thursdays, 15:30-16:20 JHE/264 (beginning Jan. 13)
Tutorial Leader's Office Hours: Wednesdays 12:30-13:30 and Fridays 2:30-3:30pm in the Math Cafe

|Handouts|Assignments|Suggested Homework|Term Tests|Grades| Announcements|Software|

Handouts

  • Course Information Sheet
  • Orthogonal Trajectories
  • Three proofs of the determinant of the Vandermonde matrix.
  • Proof of a Uniqueness Theorem for first order IVPs.
  • Chart for Method of Undetermined Coefficients
  • Notes on the Spring Mass System
  • Table of Laplace Transforms

    • Assignments

    There will be regular assignments due each Tuesday near midnight. Most will be WeBWorKs on-line assignments. There may also be up to 4 hard copy hand-in (more traditional) assignments, with problems that are not easily assigned using WeBWorKs.

  • WebWorks

  • Questions will be available regularly online, at webwork.math.mcmaster.ca/webwork2/Math2C03-Winter2011
  • Your accounts are set up. Your login is your MacID and your password is your student number. You can then easily change your password if you prefer. If you cannot login please send me e-mail.
  • The first on-line task is an Orientation, explaining how to use WeBWorK. To obtain credit, it must be completed by Monday, January 17, 2011. You can start any time.
  • You can find more documentation for students at http://webwork.maa.org/wiki/Category:Students with links to "Available Functions" and "Mathematical notation recognized."
  • The first on-line Assignment will be available January 3, and is due Tuesday, January 18, 2011.
  • It will be up to you to check your WeBWorK account regularly for subsequent assignments and their due dates.

  • Traditional Hand-in Assignments

  • The questions and due dates will be posted here.
  • Traditional assignments will be submitted to the appropriately marked lockers in the basement of Hamilton Hall:
    • Locker C72 (A - F)
    • Locker C73 (G - PE)
    • Locker C74 (PI - Z)

    • Suggested Homework

    Suggested homework problems from your text book, Elementary Differential Equations and Boundary Valuer Problems, 8th edition, will be given here. It is highly recommmended that you work through these problems, but they will not be submitted. You will be able to find the solutions in the Students Solutions Manual.
  • Suggested Homework, last updated April 6, 2011.

    Term Tests

    There will be two term tests, to be held during your regularly scheduled class. The dates and locations are:

  • Term Test 1: Tuesday, Feb. 8, 2011, 1:30-2:30pm. The room assignments depend on the first letter of your last name.
    • "A - M" T28
    • "N - Z" T29/101
    • Practice Test 1 This test does NOT cover all possible topics to be tested.
    • Topics to be tested will be selected from all the material covered in the class lectures, suggested homeworks, and WeBWorK assignments related to the following sections of the text book:
    • Chapter 1: Sections 1.2-1.3 inclusive (including the method of isoclines for determining the direction field)
    • Chapter 2: Sections 2.1-2.8 inclusive (omit 2.9)
    • Chapter 3: Sections 3.1-3.4 inclusive, and 3.5 the repeated roots case as done in class, but not using the method of reduction of order. Reduction of order may be tested on test 2.
    • Chapter 4: Sections 4.1-4.2 inclusive
    • Solutions to Term Test 1
  • Term Test 2: Tuesday, March 15, 2011, 1:30-2:30pm. The room assignments are the same as for the first test and depend on the first letter of your last name.
    • "A - M" T28
    • "N - Z" T29/101
    • Practice Test 2 This test does NOT cover all possible topics to be tested.
    • Topics to be tested will be selected from all the material covered in the class lectures, suggested homeworks, and WeBWorK assignments. The emphasis will be on the material in the following sections of the text book:
    • The Method of Undetermined Coefficients: (see the chart under the Handouts section above). This is related to Chapter 3, section 3.6 and Chapter 4, section 4.3.
    • Variation of Parameters, Chapter 3, section 3.7.
    • Reduction of Order, (as done in class) for both homogeneous and non-homogenous problems. See also Chapter 3, section 3.5 (page 171).
    • Cauchy-Euler: Chapter 5, section 5.5.
    • Applications: Chapter 3, sections 3.8 and 3.9.
    • Higher order linear ODES: Chapter 4, sections 4.1, 4.2, 4.3.
    • LaPlace Transforms: Sections 6.1 and 6.2. Partial fraction decomposition. Theorem 6.3.2 (shift) on page 329.
    • Solutions to Term Test 2
  • Final Examination: Monday, April 25, 2011 at 9:00am. Please re-check the official notification for time and location in case of any last minute changes. Make sure to bring your ID card to the final examination or you will not be permitted to enter. Tentatively,
    • "ABRA - GNAN" IWC 1 (4)
    • "GOOD - POPE" IWC 1 (5)
    • "PULL -ZHU" IWC 1 (6)
    • Practice Final Examination with solutions - see page 2 for the correct answers to the multiple choice questions and detailed solutions to the long answer questions. This test may NOT cover all possible topics to be tested.
    • Detailed solutions to the Multiple Choice questions.
    • Instructions for filling out the OMR scantron cards for the Multiple Choice solutions. Be sure to bring an HB pencil to the examination in order to record your solutions to the multiple choice questions.
      • The final examination will cover the entire course. Topics to be tested will be selected from all the material covered in the class lectures, suggested homeworks, and WeBWorK assignments related to the sections of the text book listed above under Test 1 and Test 2 as well as in:
      • LaPlace Transforms: Chapter 6: Sections 6.3-6.6, inclusive.
      • Series Solutons: Chapter 5: Sections 5.1-5.7, inclusive.
      • From Chapter 5.3 you need to know when you can expect a power series solution and how to find a minimum bound on the radius of convergence. See Theorem 5.3.1. These are well illustrated in the examples in that section: Examples 1 - 5.

        You can try pg 265: #6 and 9(a), (f) and (h). Solutions are in the solutions manual. They use rho for R, the radius of convergence.

      • For Chapter 5.7, you are expected to know the form of the soltuion to expect in the 3 different cases for regular singular points given in Theorem 5.7.1. However you only need to be able to find two linearly independent soltutions in the case when the roots of the indicial equation do not differ by an integer. In the other two cases you only need to be able to find the solution corresponding to the larger root. You can try pg. 292 # 1, 3, 9, and 17 (a), (b) and (c) (in (c) you need only be able to find y_1(x), the solution for the larger root of the indicial equation, and the form of y_2(x) given on the 4th line of page 107 of the student solution manual. You do not need to be able to actually find the coefficients for y_2(x).

    • Grades

    Class marks will be posted here by student number (last 5 digits) at the end of term. Once they are posted, please bring any discrepancy to your instructors attention as soon as possible and certainly before you write the final examination.

    Announcements

  • April 24, 2011. Because a couple of students have asked for clarification and more practice problems, I have been more specific about what you are expected to know in Sections 5.3 and 5.7. See the Tests section above under Final Examination.
  • April 20, 2011. I have posted your class marks for Test 1, Test 2, and WeBWork above in the Grades section. Please check and bring any discrepancy to me by Tuesday, April 26 at noon.
  • April 13, 2011. I have posted a practice final examination in the tests section above and information relevant to the final examination. You will have some multiple choice questions marked by computer. Be sure to bring an HB pencil to the examination to record your solutions to the multiple choice questions. Instructions for filling out the scantron cards is also given above. If you have already used these cards in some other examination, then be sure to read these over. Also, please do not forget to pring your student ID card to the final examination. Otherwise, you will not be admitted. Good Luck!

    Our TA, Anton, will hold office hours on Thursday morning, April 21 from 10:00am-noon in the Math Cafe.

    See the notice below (April 6) for the times and places of the extra tutorial sessions that I will be holding on April 20 and 21.

  • April 6, 2011. The extra session that I will be leading on Wednesday, April 20, 11:00am-1:00pm and Thursday, April 21, 6:00pm-8:00pm will be held in HH/302 (our usual lecture hall).
  • April 6, 2011. I have added a new Homework set to the list of suggested problems. There are only 2 more problems in this set.

    Due to popular demand, I will leave the last WeBWorK Assignment open for an additional wee, i.e., until Sunday, April 17, 2011.

    I now have all of the term tests in my office. Please drop by to pick them up or you can get them back during the extra tutorial sessions that I will be holding on Wednesday, April 20, 11:00am-1:00pm and Thursday, April 21, 6:00pm-8:00pm. I will post the location of the extra sessions once the rooms have been assigned.

    Our TA, Anton, will hold office hours on Thursday morning from 10:00am-noon in the Math Cafe.

  • March 23, 2011. The grades for term tests 1 and 2 are now posted above in the "Grades" section. Please report any discrepancies to me as soon as possible and certainly, before the final examinaation. The term tests will be returned in the tutorial this week. Otherwise, you can get your term tests during the TAs office hours after that.
  • March 15, 2011. The solutions to term test 2 are posted above in the Tests Section.
  • March 14, 2011. The solution to problem 2 in the practice test is:

    Find c_1 and c_2 so that y(x)=c_1 x+c_2 x^2, and so L[y(x)]=L[c_1 x+c_2 x^2]=c_1(3+2xsin(x))+c_2(6x+2x^2sin(x)) =9+12x+6xsin(x)+4x^2sin(x)) Therefore, c_1=3 and c_2=2 and so y(x)=3x+2x^2 and y(2)=14. We are using linearity and superposition.

  • March 11, 2011. I have added a new Homework set to the set of suggested problems.
  • March 7, 2011. I have posted a practice test and the information relevant to the term test 2 to be held next week in the Term Tests section above.
  • March 2, 2011. I have posted the 7th set of suggested problems in the Homework section above.
  • Feb. 16, 2011. I have posted the marks for your first Term Test in the Grades Section above. Once you get pick up your test, please make sure that your grade has been recorded correctly.
  • Feb. 15, 2011. I have posted the solutions to Term Test 1 in the Tests Section above. You can get your graded test back in the tutorial or during the TAs office hours.
  • Feb. 10, 2011. The deadline for application to the Science Cooperative Education Program is Feb. 28, 2011. If you want to learn more about want to find out how to apply click here.

    If you have not already noticed, the WeBWorK Assignment 4 has been opened.

  • Jan. 29, 2011. I have posted a "Practice Test 1" in the Term Tests section above. This is only one example of a possible test, and does not cover all topics to be tested. I have also indicated in that section above, the topics that might be tested in the test on Feb. 8, 2011.

    The first term test will be held on Tuesday, Feb. 8, 2011 from 1:30-2:30pm (i.e., during your regulary scheduled class time). However, you will be writing in a different location. To ensure that there is enough seating, and avoid being accused of cheating, please make sure to go to the correct location. The room assignments depend on the first letter of your last name.

    • "A - M" T28
    • "N - Z" T29/101
  • Jan. 28, 2011. Note that because you are having your first term test on Tuesday, Feb. 8, I have extended the deadline of your WeBWorK assignment 3 until Friday, Feb. 4, 2011 at 11:59pm WeBWorK time. Once posted, the next WeBWorK assignment will be due Tuesday, Feb. 15, 2011, as usual. I have updated the suggested homework problems in the Homework section above (see Set 4).
  • Jan. 26, 2011. I have posted 3 proofs of how to determine the determinant of the Vandermonde matrix in the Handouts section above.
  • Jan. 24, 2011. I have posted a handout on "Orthogonal Trajectories" above in the Handouts section that may help for Assignment 3. I will also ask the TA to go over this application of DEs in the tutorial on Thursday.
  • Jan. 20, 2011. I have posted the 3rd set of suggested problems in the Homework section above.
  • Jan. 12, 2011. I have posted the 2nd set of suggested homework problems in the Homework section above. Your first tutorial meets tomorrow. Assignment 2 is now accessible in WeBWork and is due Tuesday, Jan. 25, 2011.
  • Jan. 7, 2011. Our classroom has been moved to HH/302 beginning on Monday, Jan. 10, 2011.
  • Jan. 5, 2011. I have posted the first set of suggested homework problems in the Homework section above.
  • Jan.4, 2011.
  • Tutorials will begin next week, i.e. on Thursday, Jan. 13, 2011 in JHE/264, (not 246).
  • I will be holding regular office hours on Mondays and Tuesdays from 3:00-4:00pm in my office, HH/318.
  • Our TA, Anton Sakovich, will also be holding office hours beginning next week on Wednesdays 12:30-1:30pm and on Fridays 2:30-3:30pm, in the Math Cafe.
  • Jan. 3, 2011. Tutorials will be on Thursdays in JHE/264 (not Tuesdays in JHE 246 as indicated on the course information sheet). I will inform you in class and here in an announcement once I know when they will begin.
  • Dec. 17, 2010.
    • The first lecture will be held on Monday, January 3, 2011, from 12:30-1:20pm in ITB/AB102.
    • Tutorials will most likely start during the week of Jan. 10, and hence the first tutorial is likely to be on Thursday, January 13, 2011, from 3:30-4:20pm, in JHE 264. The actual start date of the tutorials will be announced in class.

    • Software

    WinPP, XPPAUT, Matlab, and Maple are of particular interest.

    Software for downloading (optional)

    Useful Links

    Instructor's Home Page | Department of Mathematics & Statistics | McMaster University

    maintained by Gail Wolkowicz