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.

MAT 17A: Calculus for Biology and Medicine
Approved: 2010-09-17, Tim Lewis

ATTENTION:

This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

This course requires the Math Placement Exam. Read More.

Units/Lecture:

4

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Neuhauser’s “Calculus for biology and Medicine” 3rd Edition
Search by ISBN on Amazon: 9780321644688

Prerequisites:

Math Placement Exam

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:

This course covers Chapters 1 – 5: Limits and derivatives; Applications of differentiation in biology; Linear finite difference equations.