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Content from each weekly tutorial is posted on this page, including slides, problems and solutions, Maple code, along with a summary of the material covered. Supplementary problems indicate those not done in tutorial, but which are nevertheless recommended and solved.
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- Date, Time, and Location: Friday, December 1, 2006 at 6:00 P.M. in McConnell 204
- Content: Comprehensive review of the course material with many worked problems of exam-level difficulty.
- Slides: See the slides from each tutorial.
- Problems and Solutions: See the solutions from each tutorial and also previous exams and assignments.

- Date, Time, and Location: Thursday, November 23, 2006 at 11:35 A.M. in Wilson 103
- Content: Fourier sine and cosine series; even and odd extensions of functions. Boundary value problems (BVPs) and how to solve them; solution of the heat diffusion and wave equation BVPs.
- Slides: Tutorial slides
- Problems:
- Problem 3 of MATH 264 Assignment 6, Winter 2006
- Supplementary: Problem 4 of MATH 264 Assignment 6, Winter 2006

- Solutions: Full solutions

- Date, Time, and Location: Thursday, November 16, 2006 at 11:35 A.M. in Wilson 103
- Content: Continuation of Tutorial 10. More examples of Fourier series.
- Slides: See the slides for Tutorial 10.
- Problems:
- Fourier Series of a Real Function (Tutorial Problem)
- Problem 4 (Parts B and D) and Problem 16 (Parts A and D) of Section 17.3 (Greenberg)

- Solutions: Full solutions

- Date, Time, and Location: Thursday, November 9, 2006 at 11:35 A.M. in Wilson 103
- Content: Basics of complex numbers: rectangular and polar forms, converting between forms, Euler's identity, operations on complex numbers. Periodic functions, angular frequency. The Fourier series transformation; the analysis and synthesis equations. Fourier series of real functions. Interpretation of the Fourier series.
- Slides: Tutorial slides
- Problems:
- Problem 4 (Part A) of Section 17.3 (Greenberg)
- Problem 3 (Part B) of MATH 264 Assignment 6, Fall 2006

- Solutions: Full solutions

- Date, Time, and Location: No date
- Content: Continuation of Tutorial 7. More examples of the vector calculus theorems.
- Slides: See the slides for Tutorial 7.
- Problems:
- Supplementary: Problem 3 of Section 16.4 (Adams)
- Supplementary: Problem 7 of Section 16.4 (Adams)
- Supplementary: Problem 11 of Section 16.4 (Adams)
- Supplementary: Problem 13 of Section 16.4 (Adams)

- Solutions: Full solutions

- Date, Time, and Location: Thursday, November 2, 2006 at 11:35 A.M. in Wilson 103
- Content: Continuation of Tutorial 7. More examples of the vector calculus theorems.
- Slides: See the slides for Tutorial 7.
- Problems:
- Problem 3 of Section 16.3 (Adams)
- Supplementary: Problem 5 of Section 16.3 (Adams)
- Problem 1 of Section 16.5 (Adams)
- Supplementary: Problem 3 of Section 16.5 (Adams)
- Problem 5 of Section 16.5 (Adams)
- Supplementary: Problem 7 of Section 16.5 (Adams)

- Solutions: Full solutions

- Date, Time, and Location: Thursday, October 26, 2006 at 11:35 A.M. in Wilson 103
- Content: Orientation of 3D surfaces and the right-hand rule. Fundamental theorems of calculus, including the fundamental theorem for conservative fields, Stokes' and Green's theorems, as well as the divergence theorem (2D and 3D).
- Slides: Tutorial slides
- Problems:
- Problem 7 of Section 15.4 (Adams)
- Problem 11 of Section 15.4 (Adams)
- Problem 1 of Section 16.3 (Adams)

- Solutions: Full solutions

- Date, Time, and Location: Thursday, October 19, 2006 at 11:35 A.M. in Wilson 103
- Content: The field line equation; scalar and vector potential functions. Conservative fields and criteria for existence of the scalar potential.
- Slides: Tutorial slides
- Problems:
- Problems 5 and 7 of Section 15.1 (Adams)
- Example 1 (page 958) of Section 16.2 (Adams)
- Problem 9 of Section 15.2 (Adams)
- Supplementary: Problem 3 of Section 15.2 (Adams)

- Solutions: Full solutions, Maple code

- Date, Time, and Location: Thursday, October 12, 2006 at 11:35 A.M. in Wilson 103
- Content: Evaluating vector and scalar line integrals. Line integral forms; parametrization of 2D and 3D curves. Line integration over unions of curves and closed curves.
- Slides: Tutorial slides
- Problems:
- Problem 3 of Section 15.3 (Adams)
- Problem 7 of Section 15.3 (Adams)
- Problem 1 of Section 15.4 (Adams)
- Problem 5 of Section 15.4 (Adams)
- Problem 17 of Section 15.4 (Adams)

- Solutions: Full solutions, Maple code

- Date, Time, and Location: Thursday, October 5, 2006 at 11:35 A.M. in Wilson 103
- Content: Basics of vector functions and fields. Differential operators: divergence, curl, gradient, and Laplacian. Evaluation of flux integrals and Gauss's law.
- Slides: Tutorial slides
- Problems:
- Problems 5, 7, and 9 of Section 15.5 (Adams)
- Supplementary: Problem 3 of Section 16.2 (Adams)
- Supplementary: Problem 13 of Section 15.6 (Adams)
- Problem 1 of Section 15.6 (Adams)

- Solutions: Full solutions, Maple code

- Date, Time, and Location: Thursday, September 28, 2006 at 11:35 A.M. in Wilson 103
- Content: Evaluation of scalar 3D surface integrals, parametrization of 3D surfaces using two-parameter vector functions.
- Slides: Tutorial slides
- Problems:
- Supplementary: Problem 4 of MATH 264 Assignment 1, Fall 2006
- Problem 8 of Section 15.5 (Adams)
- Problem 9 of Section 15.5 (Adams)
- Supplementary: Problem 15 of Section 15.5 (Adams)

- Solutions: Full solutions, Maple code

- Date, Time, and Location: Thursday, September 21, 2006 at 11:35 A.M. in Wilson 103
- Content: Continuation of Tutorial 1. More examples of multiple integration.
- Slides: See the slides for Tutorial 1.
- Problems:
- Problem 11 of Section 14.2 (Adams)
- Problem 3 of Section 14.5 (Adams)
- Supplementary: Problem 29 of Section 14.6 (Adams)

- Solutions: Full solutions, Maple code

- Date, Time, and Location: Thursday, September 14, 2006 at 11:35 A.M. in Wilson 103
- Content: Basics of multiple integrals. Evaluation by iteration, coordinate transformations, the Jacobian, and the change of variables formula.
- Slides: Tutorial slides
- Problems:
- Problem 9 of Section 14.2 (Adams)
- Supplementary: Problem 9 of Section 14.5 (Adams)
- Problem 19 of Section 14.6 (Adams)

- Solutions: Full solutions, Maple code

Teaching Assistant for MATH 264 (Advanced Calculus), Fall 2006

Email: sacha.nandlall@mail.mcgill.ca

Last updated: December 3, 2006

**Disclaimer:** Great effort has been made to ensure the material presented here is factually correct; however, users of this material are fully responsible for verifying all material (theorems, formulas, solutions, etc.) presented on their own. For errors or questions, please send an email to the address indicated above.

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