Sacha Nandlall's Advanced Calculus Tutorials Webpage - Tutorials  ### [Home][Tutorials][Exams and Assignments][Reference Material]

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.

|| Multiple Integration (1, 2) || 3D Surface and Flux Integrals (3, 4) || Line Integrals (5) ||
|| Vector Fields (4, 6) || Vector Calculus Theorems (7-9) || Fourier Series and BVPs (10-12) || Review ||

#### Final Exam Review Tutorial [top]

• 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.

#### Tutorial #11 (Fourier Series, Part 2) [top]

• 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

#### Tutorial #10 (Fourier Series, Part 1) [top]

• 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:
• Solutions: Full solutions

#### Tutorial #9 (Fundamental Theorems of Calculus, Part 3) [top]

• 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

#### Tutorial #8 (Fundamental Theorems of Calculus, Part 2) [top]

• 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

#### Tutorial #7 (Fundamental Theorems of Calculus, Part 1) [top]

• 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

#### Tutorial #6 (More Vector Fields) [top]

• 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

#### Tutorial #5 (Line Integrals) [top]

• 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

#### Tutorial #4 (Flux Integrals and Vector Fields) [top]

• 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

#### Tutorial #3 (3D Surface Integrals) [top]

• 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

#### Tutorial #2 (More Multiple Integration) [top]

• 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

#### Tutorial #1 (Multiple Integration) [top]

• 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