# (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.

Prerequisite: MATH 12. High-school calculus and one of (a) a score of 95% or higher in BC Principles of Mathematics 12 or Pre-calculus 12; or (b) a score of 95% or higher in the BC provincial examination for Principles of Mathematics 12 or Pre-calculus 12; or (c) BC Principles of Mathematics 12 or Pre-calculus 12 with a letter of invitation from the Mathematics Department based on performance in the Euclid Contest; or (d) permission from Mathematics Department Head.

## Instructor

### Joel Feldman

 E-mail feldman@math.ubc.ca Office Math 221 Phone 604-822-5660 Home page http://www.math.ubc.ca/~feldman/ Office hours Mon 1:30-2:30, Tues 11:00-12:00, Thurs 2:00-3:00

## Text

Robert A. Adams and Christopher Essex, Calculus: Single Variable, (or Calculus: A Complete Course) seventh edition or any earlier edition. (The earlier editions have Adams as the sole author.)

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

## Topics

1. Preview and Review: functions, absolute values, inequalities, preview of calculus.
2. Limits and Rates of Change: limits of sequences and functions, limit laws, continuity, Intermediate Value Theorem. [Chapter 1]
3. Derivatives: tangents and differentiability, higher derivatives, differentiation rules (including chain rule), implicit differentiation, Mean Value Theorem and applications (monotonicity, concavity). [Chapter 2]
4. Elementary Functions: inverse functions and their derivatives, exponential and logarithmic functions and their derivatives, exponential growth and decay, derivatives of trig and inverse trig functions. [Chapter 3]
5. Applications: curve sketching, maximum and minimum problems, related rate problems, l'Hôpital's Rule. [Chapter 4]
6. 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]