MATH 262: Intermediate Calculus (Fall 2008)
•
Required Textbook: Calculus. Several Variables, by R. Adams, Sixth Edition,
Pearson/Addison-Wesley (2006), ISBN 0-321-30716-X
• Reference: Multivariable Calculus, J. Stewart, 6th Edition
• Prerequisites: MATH 141, MATH 133 or equivalent.
• Topics to be covered:
Chapter 9. Sequences, Series, and Power Series 9.1 Sequences and Convergence. 9.2 Infinite Series. 9.3 Convergence Tests for Positive Series. 9.4 Absolute and
Conditional Convergence. 9.5 Power Series. 9.6 Taylor and Maclaurin Series. 9.7
Applications of Taylor and Maclaurin Series (including Section 17.7 Series solutions of
Differential equations"). 9.8 The Binomial Theorem and Binomial Series.
Chapter 10. Vectors and Coordinate Geometry in 3-Space 10.1 Analytic
Geometry in Three Dimensions. 10.2 Vectors. 10.3 The Cross Product in 3-Space. 10.4
Planes and lines. 10.5 Quadric Surfaces.
Chapter 11. Vector Functions and Curves 11.1 Vector Functions of One Variable. 11.2 Some Applications of Vector Differentiation. 11.3 Curves and
Parametrizations. 11.4 Curvature, Torsion, and the Frenet Frame. 11.5 Curvature and
Torsion for General Parametrizations.
Chapter 12. Partial Differentiation 12.1 Functions of Several Variables. 12.2
Limits and Continuity. 12.3 Partial Derivatives. 12.4 Higher-Order Derivatives. 12.5
The Chain Rule. 12.6 Linear Approximations, Differentiability, and Differentials.
12.7 Gradients and Directional Derivatives. 12.8 Implicit Functions. 12.9 Taylor
Series and Approximations.
Chapter 13. Applications of Partial Derivatives 13.1 Extreme Values. 13.2
Extreme Values of Functions Defined on Restricted Domains. 13.3 Lagrange Multipliers.
Instructors: Prof. N.Sancho BH1130 sancho@math.mcgill.ca, Prof. W Jonsson BH922,
Dr. X. Faber BH1248 xander@math.mcgill.ca
Tutorials (starting September 8th)
Final Grade = 5% Written Assignments + 5% Web work + 90% Final
Help Desk: http://www.math.mcgill.ca/students/helpdesk.php You are strongly
encouraged to make use of this resource.
Academic Integrity: For your success in this course it is essential that the work that
you submit is your own. Copying of any kind will not be tolerated. McGill University
values academic integrity. Therefore all students must understand the meaning and
consequences of cheating, plagiarism
and other academic offenses under the Code of Student Conduct and Disciplinary
Procedures (see www.mcgill.ca/integrity for more information).