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Math222


COURSE INFORMATION


Semester: Summer 2012

Instructor: Nicolas Fraiman

Email: fraiman@math.mcgill.ca


Office: Burnside Hall, room 1008

Office hours: Tue, Thu 4:00PM - 5:30PM


Classroom: Rutherford Physics Building 112

Class hours: MTWR 1:35 PM - 3:55 PM



LINKS


MCGILL


NEWS


  • 28 May: A review session is booked in ARTS W-120 on Wednesday 30.
  • 26 May: A study guide to review for the final exam has been posted.
  • 25 May: Course evaluations are available to students from May 23-30.
  • 23 May: The final exam will take place on Thursday 31 at 9:00am.
  • 18 May: Midterm grades have been posted on the MyCourses website.
  • 8 May: The midterm will take place on Monday 14 in Leacock room 219.


SYLLABUS


  1. Infinite series: Infinite sequences and series. Testing convergence and divergence of series. Power series and their use for representing functions. Taylor polynomials and Taylor series.

  2. Vector functions: Review of parametric equations and polar coordinates. Review of vector geometry. Derivatives and integrals of vector functions; arc length and curvature of space curves; motion in space: velocity and acceleration.

  3. Partial derivatives: Functions of several variables and their partial derivatives. Tangent planes. The chain rule. Directional derivatives and gradient vectors. Maximal and minimal values; Lagrange multipliers.

  4. Multiple integrals.



COURSE MATERIALS


Textbook: J. Stewart, Multivariable Calculus: Early Transcendentals.
Any edition will do. Any calculus book covering the material should be a satisfactory substitute.


Classroom attendance and taking notes in class are important. The lectures will not follow exactly the textbook. Your classroom notes will be of essential help for the preparation of the midterm and final examinations.


Review study guide.


Previous exams:



ASSIGNMENTS AND EVALUATION


Your evaluation for this course will be based on WeBWorK assignments, a midterm, and an examination.

  • WeBWorK assignments: There will be four assignments. You can attempt each problem an unlimited number of trials.

  • Class midterm test: There will be an in-class midterm on Monday 14.

  • Final examination: The examination will take place on Thursday 31.


Your final mark will consist of 

60% E + 30% M + 10% W    or    90% E + 10% W,
whichever is greater. Your final grade will be a letter grade based on your final mark.



WEBWORK INFORMATION


  • Website: http://msr02.math.mcgill.ca/webwork2/MATH222_MAY2012/
  • Deadlines:
    • Assignment 1 opens on Wednesday 2 and is due on Wednesday 9.
    • Assignment 2 opens on Wednesday 9 and is due on Monday 14.
    • Assignment 3 opens on Wednesday 16 and is due on Thursday 24.
    • Assignment 4 opens on Thursday 2 and is due on Wednesday 30.


RECOMMENDED EXERCISES

References are to the class textbook. You should feel comfortable solving some from the list below.

7th edition6th edition
Chapter 11
§1: 23-56
§2: 27-42, 43-48
§3: 3-8, 29-32
§4: 3-32
§5: 2-20
§6: 2-30
§8: 3-28
§9: 3-10, 15-20
§10: 5-12, 13-20
§11: 13-22
 Chapter 11
§1: 17-46
§2: 21-34, 35-40
§3: 3-8, 27-30
§4: 3-32
§5: 2-20
§6: 2-28
§8: 3-28
§9: 3-10, 15-18
§10: 5-12, 13-20
§11: 13-22
Chapter 12
§3: 15-20, 39-44
§4: 1-7, 9-12
§5: 6-12, 23-40, 69-74
 Chapter 12
§3: 15-20, 35-40
§4: 1-7, 9-12
§5: 6-12, 23-38, 67-72
Chapter 13
§1: 3-6, 7-14, 40-44
§2: 9-20, 23-26, 35-40
§3: 1-6, 17-20, 21-23
§4: 3-14, 15-18, 37-42
 Chapter 13
§1: 3-6, 7-14, 36-38
§2: 9-20, 23-26, 33-38
§3: 1-6, 17-20, 21-23
§4: 3-14, 15-18, 33-38
Chapter 14
§1: 59-64, 69-70
§2: 5-22, 29-38
§3: 15-40, 53-58, 63-70
§4: 1-6, 11-16, 25-30
§5: 1-12, 21-34, 45-48
§6: 7-17, 21-26, 41-46
§7: 5-18, 29-36
§8: 3-18, 19-21
 Chapter 14
§1: 55-60, 65-66
§2: 5-22, 29-38
§3: 15-38, 51-56, 61-68
§4: 1-6, 11-16, 25-30
§5: 1-12, 21-34, 45-48
§6: 7-17, 21-26, 39-44
§7: 5-18, 29-36
§8: 3-17, 18-19
Chapter 15
§2: 1-14, 15-22
§3: 1-10, 17-32, 43-54
§4: 5-14, 19-27, 29-32
§5: 3-10
§6: 1-12
§7: 3-18, 19-22, 39-42
§8: 17-28
§9: 21-34
 Chapter 15
§2: 1-14, 15-22
§3: 1-18, 19-28, 39-50
§4: 5-14, 19-27, 29-32
§5: 3-10
§16.6: 37-47
§7: 3-18, 19-22, 37-40
§8: 17-26
§9: 21-34


SCHEDULE PLAN

This is an approximate timetable for the course (all dates are subject to change)


INFINITE SERIES

Tue 1 Introduction: Sequences and series (Sections §11.1 and §11.2)
Wed 2 Convergence Tests: Comparison tests, integral test, absolute convergence, ratio and root tests (Sections §11.3, §11.4, §11.5, §11.6 and §11.7)
Thu 3 Power Series: Representation of functions as power series (Sections §11.8 and §11.9)
Mon 7 Taylor Series: Taylor and McLaurin series, applications (Sections §11.10 and §11.11)

VECTOR FUNCTIONS

Tue 8 Review of vector geometry: Coordinate system, dot and cross product (Sections §12.1, §12.2, §12.3 and §12.4)
Wed 9 Vector functions: Space curves, derivatives and integrals (Sections §13.1 and §13.2)
Thu 10 Motion in space: Length, curvature, velocity and acceleration (Sections §13.3 and §13.4)
Mon 14 Midterm test

PARTIAL DERIVATIVES

Tue 15 Functions of several variables: Limits and continuity (Sections §14.1 and §14.2)
Wed 16 Partial differentiation: Partial derivatives, tangent planes and linear approximations (Sections §14.3 and §14.4)
Thu 17 Directional derivatives: Chain rule, gradient vector (Sections §14.5 and §14.6)
Mon 21 National Patriots' Day / Victoria Day
Tue 22 Extrema of functions: Maximum and minimum values, Lagrange multipliers (Sections §14.7, §14.8)

MULTIPLE INTEGRALS

Wed 23 Double Integrals: Integrals over rectangles and regions, iterated integrals (Sections §15.1, §15.2 and §15.3)
Thu 24 Double Integrals: Polar coordinates, applications (Sections §10.3, §15.4 and §15.5)
Mon 28 Triple Integrals: Triple integrals, cylindrical coordinates (Sections §15.7 and §15.8)
Tue 29 Triple Integrals: Spherical coordinates, change of variables (Sections §15.9 and §15.10)
Wed 30 Review
Thu 31 Final exam