Welcome to MATH 2Z03

Fall 2009

Time & Place - Lectures:
  • Section C01: Tu We Fr 12:30-13:20 in BSB/147
  • Section C02: Mo We Th 13:30-14:20 in BSB/B136
  • Section C03: Mo We Th 17:30-18:30 in JHE/376
    Time & Place - Tutorials:
  • Section T01: Tu 17:30-18:20 in TSH/B128
  • Section T02: Th 10:30-11:20 in TSH/B128
  • Section T03: Tu 10:30-11:20 in JHE/376
  • Section T04: Fr 09:30-10:20 in BSB/117
    Time & Place - Computer Labs:
  • Mo 9:30-11:30 in BSB/244
  • Tu 9:30-11:30 in BSB/244
  • We 12:30-14:30 in BSB/244
  • Th 10:30-12:30 in BSB/244
  • Fr 9:30-11:30 in BSB/244


  • Section C01: Dr. Bartosz Protas (Course Coordinator)
    Email: bprotas_AT_mcmaster_DOT_ca
    Office: HH 326, Ext. 24116
    Office hours: by appointment

  • Section C02: Dr. Zdislav Kovarik
    Email: kovarik_AT_mcmaster_DOT_ca
    Office: HH 425, Ext. 23408
    Office hours: by appointment (Email preferred)

  • Section C03: Dr. Ramesh Yapalparvi
    Email: ramesh_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 403A, Ext. 27364
    Office hours: by appointment

    Teaching Assistants:

  • Mohammad Farazmand (Head TA)
    Email: mfarazmand_AT_gmail_DOT_com
    Office: HH 403, Ext. 24411
    Office hours: by appointment

  • Vladislav Bukshtynov
    Email: bukshtu_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 403, Ext. 24411
    Office hours: N/A

  • Ryan Day
    Email: dayr_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 105, Ext. 24336
    Office hours: by appointment

  • Yang Li
    Email: liy99_AT_math_DOT_mcmaster_DOT_ca
    Office: ITB 116, Ext. 27248
    Office hours: by appointment

  • Xiaohui Peng
    Email: xiaohup_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 105, Ext. 24336
    Office hours: by appointment

  • Maochang Qin
    Email: qinm_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 214, Ext. 23414
    Office hours: by appointment

  • Atefeh Shadpour
    Email: shadpa_AT_mcmaster_DOT_ca
    Office: HH 403, Ext. 24411
    Office hours: by appointment


  • Solutions and results of assignment #6 are already posted.

  • Important information regarding the Final Exam is available here.

  • Review session for the final exam will take place during 13:30 - 15:30 on December 17. Please see the following table for classroom and seating information.


    Student's Last Name (range)





  • If you have questions concerning the mark you obtained for an assignment, please contact the Teaching Assistant who marks you assignments (see the link Submission Instructions for details).

  • The student version of MATLAB can also be purchased on-line (see this link) at a comparable price as at the campus bookstore; you will need the core product only without any additional toolboxes

    Outline of the Course:

    The course provides an overview of ordinary differential equations and covers also some related topics, such as Laplace transforms and elements of linear algebra (eigenvalues and eigenvectors). A number of applications to actual problems will be discussed. Students will also acquire programming skills in MATLAB, and will use them to solve a range of problems introduced during lectures.

    Course Objectives:

    By the end of the course students should be familiar with the basic theory concerning ordinary differential equations, and should be able to apply this theory to solve problems arising in applications. They should also be able to develop MATLAB programs for the solution and visualization of such problems.


    An important element of the course are the tutorials during which the Teaching Assistants will introduce MATLAB programming techniques necessary for the solution of homework assignments. MATLAB files containing the material of the tutorials will be posted in advance on the course website, and should be downloaded and reviewed before attending the tutorial. Students are strongly encouraged to bring their own laptops, so that they can actively follow the presentation.

    Primary Reference:

         1) D. Zill and M. Cullen, Advanced Engineering Mathematics, Jones and Bartlett, 3rd edition, (2006)
             [ISBN-13: 9780763745912, ISBN-10: 076374591X].
         2) M. Grasselli and D. Pelinovsky, Numerical Mathematics, Jones and Bartlett, (2008)
             [ISBN-13: 9780763737672, ISBN-10: 0763737674].

    Remark - both textbooks will be the required references for the follow-up course MATH 2ZZ3 (Engineering Mathematics IV) that will be offered in the Winter Term.


    All homework assignments will have to be completed using MATLAB. This software will also be used for presentations during tutorials. While MATLAB can be used in a number of computer labs on the campus, students are encouraged to purchase The Student Edition of MATLAB to be able to work with MATLAB at home.


    Engineering Mathematics I and II (MATH 1Z04 \& MATH 1ZZ5), or equivalent


    Six homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due by midnight on the dates indicated in the table. Solutions of the assignments should be prepared using the template file available from the course website, and be submitted electronically to the suitable Email address. Please see here for detailed instructions concerning submission of homework assignments. Late submissions will not be accepted under any circumstances. The solutions will be posted on the course website after the due date.

    Homework Post & Due Dates (tentative):


    Post Date

    Due Date

    HW 1

    Monday, September 21

    Monday, September 28

    HW 2

    Monday, October 5

    Tuesday, October 13

    HW 3

    Monday, October 19

    Monday, October 26

    HW 4

    Monday, November 2

    Monday, November 9

    HW 5

    Monday, November 16

    Monday, November 23

    HW 6

    Monday, November 30

    Monday, December 7


    There will be two tests scheduled tentatively on October 6 and November 10 (in lieu of November 17 announced initially). They will last 75 minutes and will take place in the evening (i.e., at or after 7pm) at a location to be announced later. The tests will focus on analytical issues, although may also address elements of MATLAB programming. Only the McMaster standard calculator Casio fx-991 will be allowed during the tests.

    Final Exam:

    The course will be completed by a three-hour final examination. The date and location of the final exam will be announced by the Registrar's office in mid-term.

    Marking Scheme:

    The final mark will be the better one obtained with the following two marking schemes:

         - Final exam (3 hrs) - 50%,
         - Tests (2 x 75 min) - 20%,
         - Five best homework assignments - 30%.

         - Final exam (3 hrs) - 40%,
         - Tests (2 x 75 min) - 20%,
         - Six homework assignments - 40%.

    The instructor reserves the right to alter the grade in justified cases. In such situations, however, the grade can only be increased.

    Excused Absences:

    Exemptions from the assignments or tests for valid reasons are possible, but must be requested through the office of the Associate Dean of the Faculty that you are registered with. In the event of an exemption, no make up test or assignment will be administered, but your course grade will be re-weighted by increasing the weight of the final examination to compensate for the missed test or the weight of the remaining assignments for the missed assignment.

    Academic Integrity:

    You are expected to exhibit honesty and use ethical behaviour in all aspects of the learning process. Academic credentials you earn are rooted in principles of honesty and academic integrity.

    Academic dishonesty is to knowingly act or fail to act in a way that results or could result in unearned academic credit or advantage. This behaviour can result in serious consequences, e.g., the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.

    It is your responsibility to understand what constitutes academic dishonesty. For information on the various types of academic dishonesty please refer to the Academic Integrity Policy,. The following illustrates only three forms of academic dishonesty:
         1) Plagiarism, e.g., the submission of work that is not one's own or for which other credit has been obtained.
         2) Improper collaboration in group work.
         3) Copying or using unauthorized aids in tests and examinations.

    Important Notice:

    The instructor and university reserve the right to modify elements of the course during the term. The university may change the dates and deadlines for any or all courses in extreme circumstances. If either type of modification becomes necessary, reasonable notice and communication with the students will be given with explanation and the opportunity to comment on changes. It is the responsibility of the student to check their McMaster email and course websites weekly during the term and to note any changes.




    Sections from Ref. 1

    Week 1

    September 10-11


    Lecture 1

    Introduction to the Course


    Week 2

    September 14-18


    Lecture 2

    Definitions and Terminology
    Initial-Value Problems


    Lecture 3

    Definitions and Terminology
    Initial-Value Problems


    Lecture 4

    Solution Curves Without a Solution
    Separable Variables


    Week 3

    September 21-25


    Lecture 5

    Separable Variables Cont'd
    Nonlinear Models


    Lecture 6

    Linear Equations


    Lecture 7

    Linear Models
    Preliminary Theory: Linear Equations (skip 3.1.3)


    Week 4

    September 28-October 2


    Lecture 8

    Preliminary Theory: Linear Equations Cont'd (skip 3.1.3)


    Lecture 9

    Preliminary Theory: Linear Equations Cont'd (skip 3.1.3)
    Homogeneous Linear Equations with Constant Coefficients


    Lecture 10

    Homogeneous Linear Equations with Constant Coefficients


    Week 5

    October 2-9 (Test #1 on Tuesday, October 6)


    Lecture 11

    Homogeneous Linear Equations with Constant Coefficients Cont'd
    Nonhomogeneous Equations


    Lecture 12

    Undetermined Coefficients


    Lecture 13

    Undetermined Coefficients Cont'd


    Week 6

    October 12-16 (Holiday on Monday, October 12)


    Lecture 14

    Sections that are not cancelled are to use this as review or catch up


    Lecture 15

    Variation of Parameters


    Lecture 16

    Variation of Parameters Cont'd
    Cauchy-Euler Equations


    Week 7

    October 19-23


    Lecture 17

    Cauchy-Euler Equations Cont'd


    Lecture 18

    Linear Models: Initial-Value Problems


    Lecture 19

    Linear Models: Initial-Value Problems Cont'd


    Week 8

    October 26-30


    Lecture 20

    Linear Models: Boundary-Value Problems


    Lecture 21

    Linear Models: Boundary-Value Problems Cont'd


    Lecture 22

    Review of Linear Algebra


    Week 9

    November 2-6


    Lecture 23

    The Eigenvalue Problem


    Lecture 24

    The Eigenvalue Problem Cont'd
    Powers of Matrices


    Lecture 25

    Orthogonal Matrices


    Week 10

    November 9-13 ([NEW!] Test #2 on Tuesday, November 10)


    Lecture 26

    Diagonalization Cont'd


    Lecture 27

    Preliminary Theory (Systems of Linear Equations)


    Lecture 28

    Homogeneous Linear Systems


    Week 11

    November 16-20


    Lecture 29

    Definition of the Laplace Transform


    Lecture 30

    Definition of the Laplace Transform Cont'd
    The Inverse Transform and Transforms of Derivatives


    Lecture 31

    The Inverse Transform and Transforms of Derivatives Cont'd
    Translation Theorems


    Week 12

    November 23-27


    Lecture 32

    Additional Operational Properties


    Lecture 33

    The Dirac Delta Function


    Lecture 34

    Systems of Linear Differential Equations


    Week 13

    November 30-December 4


    Lecture 35

    Series solutions about Ordinary Points


    Lecture 36

    Series solutions about Singular Points


    Lecture 37

    Review for Exam