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:
Prerequisites:
Suggested Schedule:
Lecture(s) 
Sections 
Comments/Topics 
12 
10.12 
Functions of two/several variables; Limits, continuity – briefly 
3 
10.3 
Partial derivatives 
4 
10.4 
Tangent planes and linearization; Differentiability (briefly) 
5 
10.5 
Chain rule (include discussion about parameterize curves); Optional: Implicit differentiation 
6 
10.5 
Directional derivatives and gradient vector 
78 
10.6 
Maxima and minima (local and global); Applications 
9 
Optional: Optimization with constraints (10.6.2) and/or Diffusion equation (10.6.3) 

1011 
online notes 
Double integrals and applications 
1215 
11.12 
Linear systems of ODEs: Theory, modeling and examples 
1619 
11.34 + online notes 
Nonlinear systems of ODEs: Theory, modeling and examples 
20 
Optional: Systems of difference equations (10.7) 

2122 
12.1 
Counting: Permutations and combinations; Biological examples. 
23 
12.2 
Basic probability: definitions and examples 
24 
12.3 
Conditional probability; Law of total probability 
25 
12.3 
Independence; Bayes Formula; Applications in biology. 
2627 
Optional: More complicated problems using Bayes formula and conditional probability or distributions of discrete random variables (12.4) 
Additional Notes:
Lectures 9, 20, and 2627 can be used as buffers for the required material or to cover optional material: Optimization with constraints (10.6.2); Diffusion equation (10.6.3); Systems of difference equations (10.7); Distributions of discrete random variables (12.4).
Note: Covering the optional material in 12.4 (mean and variance; binomial, geometric and Poisson distributions) would work best if covered in two lectures.