Welcome to MATH 2ZZ3

Winter 2010

Time & Place - Lectures:
  • Section C01: Tu Th Fr 11:30-12:20 in CNH/104
  • Section C02: Tu We Fr 12:30-13:20 in BSB/147
  • Section C03: Mo We Th 17:30-18:30 in CNH/104
    Time & Place - Tutorials:
  • Section T01: We 11:30-12:20 in HSC/1A1
  • Section T02: Fr 13:30-14:20 in HSC/1A1
  • Section T03: Mo 09:30-10:20 in TSH/B128
    Time & Place - Computer Labs:
  • Mondays 12:30pm - 1:30pm in BSB/241, 1:30 - 2:30pm in BSB/249
  • Tuesdays 9:30am - 11:30am in BSB/249
  • Wednesdays 12:30pm - 2:30pm in BSB/249 (until 2pm on February 10 and 24; moved to BSB/244 for 1:30-2:30 on March 3)
  • Thursdays 12:30pm - 2:30pm in BSB/244
  • Fridays 12:30pm - 2:30pm in BSB/244 (12:30pm-1:30pm and 2:30pm-3:30pm on January 29)


  • Section C01: Dr. Bartosz Protas (Course Coordinator)
    Email: bprotas_AT_mcmaster_DOT_ca
    Office: HH 326, Ext. 24116
    Office hours: Tu Th 1:30-2:30pm

  • Section C02: Dr. Zdislav Kovarik
    Email: kovarik_AT_mcmaster_DOT_ca
    Office: HH 425, Ext. 23408
    Office hours: We 2:30-3:20pm, Th 4:00-6:00pm or by appointment (Email preferred)

  • Section C03: Dr. Agegnheu Atena
    Email: atena_AT_math_DOT_mcmaster_DOT_ca
    Office: HH/327, Ext. 23413
    Office hours: We Th 4:00-5:00pm

    Teaching Assistants:

  • Jonathan Gustafsson (Head TA)
    Email: Jonathan.Gustafsson_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 403, Ext. 24411
    Office hours: Mo 3:30-4:30 pm and Fr 2:30-3:30 pm

  • Nick Rogers (Head TA)
    Email: rogern4_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 403, Ext. 24411
    Office hours: Mo 12:30-1:30pm and We 10:30-11:30am

  • Vladislav Bukshtynov
    Email: bukshtu_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 403, Ext. 24411

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

  • Oumar Mbodji
    Email: oumarms_AT_math_DOT_mcmaster_DOT_ca
    Office: HH 402, Ext. 27103

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

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

  • Zhouwei Zhou
    Email: zhouz3_AT_mcmaster_DOT_ca
    Office: HH 402, Ext. 27103


  • The following adjustments were made in the calculation of the final marks:
    - the results of Test #2 were computed out of 15 points (which was the highest mark obtained) rather than out of 18 points; this corresponds to multiplying the original percentage mark by 1.2,
    - the final marks were curved up with the formula
    new_mark = 100^(2/15) x original_mark^(13/15)
    which changes a mark of 45 into a mark of approx. 50, etc.
    The marks have already been submitted for processing and will be released in due course.

  • Except for some special circumstances, the results of the Final Exam will not be released until officially approved by the University. The mean result was 17.24/33 and the median 17/33.

  • [VERY IMPORTANT!] The topics "Surface Integrals" (lectures 21 & 22) and "Stokes' Theorem" (lecture 23) will be covered based on Chapters 15, 16 and 18 from the textbook "Multivariable Calculus" by G. Cain and J. Herod which is freely available on the web (see also links on the left). These three chapters will be used in lieu of Sections 9.13 and 9.14 from Zill & Cullen. The reason is that Cain & Herod offer a more general treatment of the problem using parametric representation of surfaces, in contrast to explicit representation covered only in Zill & Cullen. Some sample problems from Chapters 15, 16 and 18 of Cain and Herod are available here (courtesy of Dr. J.-P. Gabardo).

  • 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 Fourier series, vector calculus, line and surface integrals together with integral theorems. It also provides an introduction to some elementary partial differential equations. A number of applications to actual problems will be discussed. Students will also further develop their 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 Fourier series, vector calculus, line and surface integrals, as well as partial 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].


    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, II and III (MATH 1Z04, MATH 1ZZ5, & MATH 2Z03), or equivalent


    Five homework assignments will be posted on the course website on the dates indicated in the table below. The assignments will be due one minute past 11:59pm on the dates indicated in the table. Note that while assignments #1, #2, #3 and #4 will be due on Mondays, assignment #5 will be due on Thursday. Solutions of the assignments should be prepared using the current 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, January 25

    Monday, February 1

    HW 2

    Monday, February 8

    Tuesday, February 16

    HW 3

    Monday, February 22

    Monday, March 1

    HW 4

    Monday, March 8

    Monday, March 15

    HW 5

    Thursday, March 25

    Thursday, April 1


    There will be two tests scheduled tentatively on February 4 (Thursday) and March 16 (Tuesday). 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) - 25%,
         - Four best homework assignments - 25%.

         - Final exam (3 hrs) - 40%,
         - Tests (2 x 75 min) - 30%,
         - Five homework assignments - 30%.

    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.

    Course Schedule:



    Sections from Ref. 1

    Week 1

    January 4-8


    Lecture 1

    Introduction to the Course


    Lecture 2

    Orthogonal Functions


    Lecture 3

    Fourier Series


    Week 2

    January 11-15


    Lecture 4

    Fourier Series (cont'd)
    Fourier Cosine and Sine Series


    Lecture 5

    Fourier Cosine and Sine Series (cont'd)
    Complex Fourier Series


    Lecture 6

    Complex Fourier Series (cont'd)


    Week 3

    January 18-22


    Lecture 7

    Vector Functions


    Lecture 8

    Motion on a Curve


    Lecture 9

    Curvature and Components of Acceleration


    Week 4

    January 25-29


    Lecture 10

    Curvature and Components of Acceleration (cont'd)
    Partial Derivatives


    Lecture 11

    Partial Derivatives (cont'd)
    Directional Derivatives


    Lecture 12

    Directional Derivatives (cont'd)


    Week 5

    February 1-5 (Test #1 on Thursday, February 4)


    Lecture 13

    Tangent Planes and Normal Lines


    Lecture 14

    Divergence and Curl


    Lecture 15

    Divergence and Curl (cont'd)
    Lines Integrals


    Week 6

    February 8-12


    Lecture 16

    Lines Integrals (cont'd)
    Independence of Path


    Lecture 17

    Independence of Path (cont'd)
    Double Integrals


    Lecture 18

    Double Integrals (cont'd)


    Week 7

    February 15-19 (Reading Week)


    Week 8

    February 22-26


    Lecture 19

    Double Integrals in Polar Coordinates


    Lecture 20

    Double Integrals in Polar Coordinates (cont'd)
    Green's Theorem


    Lecture 21

    Green's Theorem (cont'd)
    Surface Integrals


    Week 9

    March 1-5


    Lecture 22

    Surface Integrals (cont'd)


    Lecture 23

    Stokes' Theorem
    Triple Integrals


    Lecture 24

    Triple Integrals (cont'd)
    Divergence Theorem


    Week 10

    March 8-12


    Lecture 25

    Divergence Theorem (cont'd)
    Change of Variables in Multiple Integrals


    Lecture 26

    Change of Variables in Multiple Integrals (cont'd)


    Lecture 27

    Separable Partial Differential Equations


    Week 11

    March 15-19 (Test #2 on Tuesday, March 16)


    Lecture 28

    Classical Equations and Boundary-Value Problems


    Lecture 29

    Classical Equations and Boundary-Value Problems (cont'd)


    Lecture 30

    Heat Equation


    Week 12

    March 22-26


    Lecture 31

    Wave Equation


    Lecture 32

    Laplace's Equation


    Lecture 33

    Heat, Wave, Laplace's Equation (cont'd)


    Week 13

    March 29 - April 2 (Holiday on Friday, April 2)


    Lecture 34

    Nonhomogeneous Boundary-Value Problems


    Lecture 35

    Orthogonal Series Expansion


    Lecture 36

    Section that are not cancelled are to use this for review or catch up


    Week 14

    April 5-8


    Lecture 37

    Fourier Series in Two Variables


    Lecture 38

    Review for Exam


    Lecture 39

    Review for Exam