Mathematics 120, Section 101

(Honours) Differential Calculus

Department of Mathematics, Undergraduate Math courses, University of British Columbia

Math 120 is the honours version of Math 100, covering mostly the same topics, but in greater foundational depth and with more emphasis on harder and/or theoretical exercises. Some precise definitions and statements of theorems will be given, but only limited theoretical facility will be expected of students.

Prerequisite: Principles of Mathematics 12 along with a letter of invitation from the Mathematics Department based on performance in the Euclid Contest or a scholarship score of at least 650 on the Provincial Principles of Mathematics exam.

Instructor

Joel Feldman

E-mail	feldman@math.ubc.ca
Office	Math 221
Phone	822-5660
Home page	http://www.math.ubc.ca/~feldman/

Text

Adams, Single Variable Calculus, fourth edition.

I will post all handouts, problem sets, final grades, etc. on the web here.

Topics

Preview and Review: functions, absolute values, inequalities, preview of calculus.
Limits and Rates of Change: limits of sequences and functions, limit laws, continuity, Intermediate Value Theorem. [Chapter 1]
Derivatives: tangents and differentiability, higher derivatives, differentiation formulae (including chain rule), implicit differentiation, Mean Value Theorem and applications (monotonicity, concavity). [Chapter 2]
Elementary Functions: inverse functions and their derivatives, derivatives of trig and inverse trig functions, exponential and logarithmic functions and their derivatives, exponential growth and decay. [Chapter 3]
Applications: curve sketching, maximum and minimum problems, related rate problems, l'Hôpital's Rule. [Chapter 4]
Approximation: linearization (with error estimate), quadratic and higher approximations, Taylor polynomials and Taylor's theorem with Lagrange remainder, Taylor series for exp, sin, cos. [Chapter 4]

Grading

There will be weekly problem sets. Of these, four are to be handed in (due on Tuesdays, Sept 26, Oct 10, Nov 7 and Nov 21). They will account for about 5% of the final mark.
There will be five quizzes (on Tuesdays, Sept 19, Oct 3, Oct 17, Oct 31 and Nov 14). The best four of these will account for about 20% of the final mark.
There will be one midterm (Tuesday, October 24) accounting for about 20% of the final mark.
The final exam will account for about 55% of the final mark. The final exam of Math 100 and Math 120 will have at least 50% in common. This will be used to normalize grades in Math 120.
Grades will probably be scaled.