# (Honours) Differential Calculus

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

## 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

**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 rules (including chain rule),
implicit differentiation, Mean Value Theorem and applications (monotonicity,
concavity). [Chapter 2]
**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]
**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.
They will account for about 5% of the final mark.
- There will be two midterms (Tuesday, October 2 and Tuesday, November 6)
with each accounting for about 20% of the final mark.
- The final exam will account for about 55% of the final mark.
- Grades
**will** probably **be scaled**.