Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
ATTENTION:
Units/Lecture:
Prerequisites:
Suggested Schedule:
Lecture(s) |
Sections |
Comments/Topics |
1-3 |
1.1-1.3 |
Preliminaries: Elementary functions/Graphing. Include one full lecture on ‘scaling’, log transforms, and log-log/semi-log plots |
4 |
2.1 |
Discrete models of exponential growth and decay |
5 |
2.2 |
Sequences |
6 |
2.3 |
Biological examples of discrete models (e.g. Logistic map).Basic ideas of fixed points/steady states, stability, periodic solutions and chaos). |
7 |
3.1 |
Limits - only informal definition of a limit |
8 |
3.2, 3.5 |
Continuity of functions (very briefly); Intermediate value theorem and the bisection method |
9 |
3.3, 3.4 |
Limits; Limits at infinity; Trig limits (briefly, without detailed proofs); Sandwich Theorem, |
10-11 |
4.1 |
Definition of derivative and geometric meaning; Derivative as the rate of change; Differentiability |
12 |
4.2 |
Power rule and basic rules of differentiation - no detailed proof of the power rule, but discuss idea of the proof using a simple (quadratic) example |
13 |
4.3 |
Product and quotient rules |
14-15 |
4.4 |
Chain rule; Implicit differentiation; Related rates; Higher derivatives |
16 |
4.5, 4.6 |
Derivatives of exponential and trigonometric functions |
17 |
4.7 |
Derivatives of inverse and logarithmic functions |
18 |
4.8 |
Linear approximation |
19 |
5.1 |
Extrema;(Optional: Mean value theorem) |
20 |
5.2 |
Monotonicity and concavity |
21 |
5.3 |
Graphing-examples including sigmoidal curves |
22 |
5.3, 5.4 |
Graphing; Optimization |
23 |
5.4 |
Optimization |
24 |
5.5 |
L’Hospital’s Rule |
25 |
5.6 |
Stability of fixed points in difference equations |
26-27 |
Use remaining lectures as buffer for material above and/or to cover optional material in 5.7 (Numerical method for root finding - Newton-Raphson Method) |
Additional Notes: