Department
of Mathematics
Mathematics 31S. Calculus II with Applications to the Life Sciences.
Fall 2016
Course Outline
Time
and Place: MWF
11:00 am - 10:50 am Millikan 2393
Instructor:
Dr. Adolfo J. Rumbos
Office: Andrew
2287.
Phone/e-mail: ext. 18713 /
Office Hours:
MWF 10:05 am - 10: 50 am, TR
10:00 am – 11:00 am,
or by appointment
Courses Website: http://pages.pomona.edu/~ajr04747/
Text: Calculus for the Life Sciences
by Sebastian J. Schreiber, Karl J. Smith,
and Wayne M. Getz
Prerequisites: Math
30 (grade of C- or better)
Course Description.
In this course we study integral and differential calculus in the
context of problems arising in the life sciences. We will be dealing mainly with problems that come
up in population biology concerning the description of the evolution in time of
the size of the population of a given species, as well as the interaction of
several species living in a common environment.
Analysis of this type of problems leads naturally to differential equations. These are expressions involving an unknown
function (which one seeks to find) and its derivatives. We will spend the first
part of the course learning how to analyze the differential equations that come
up in the study of the problems mentioned above. Some of the equations can be solved using
integral calculus, but others cannot be solved easily, and so the best one can
do is to use approximations, in particular, linear approximations, to analyze
them. We will see that sometimes those approximate solutions to the equations
actually tell us a lot about the system we are studying.
The specific topics to be covered are listed in the attached Tentative Schedule of Lectures and Examinations.
Assigned
Grading Policy.
Grades will be based on the homework, two 50-minute examinations, plus a
comprehensive final examination. The
grades will be computed as follows:
homework
20%
Two 50-minute
exams 50%
final examination 30%
Final Examination.
Time: Friday,
December 16 9:00 am
Math
31S Fall 2016
Tentative Schedule of Lectures and
Examinations
Date Topic
W Aug. 31 A conservation principle:
One-compartment dilution
F Sep.
2 Recovering a function from
its rate of change
M Sep. 5 What
is a differential equation?
W Sep. 7 Review of integration: The
Fundamental Theorem of Calculus
F Sep. 9 The
natural logarithm function
M Sep. 12 The
natural logarithm function (continued)
W Sep. 14 The exponential function
F Sep. 16 The exponential function (continued)
M Sep. 19 Solving
first order differential equations
W Sep. 21 Separation of variables
F Sep. 23 Linear first order differential
equations
M Sep. 26 Linear
first order differential equations with constant coefficients
W Sep. 28
Applications of first order
differential equations
F Sep. 30 Qualitative
analysis of a first order equation.
M Oct. 3 Qualitative
analysis (continued)
W Oct.
5 Models of population
growth
F Oct. 7 Models
of population growth (continued)
M Oct. 10 Review
W Oct. 12 Exam 1
F Oct. 14 The logistic model of population
growth
M Oct. 17 Fall
recess: No Classes
W Oct. 19 The logistic model (continued)
F Oct. 21
Solving the logistic model:
Partial fractions
M Oct. 24 Partial
fractions (continued)
W Oct. 26 Linearization
F Oct. 28 Integration by parts
M Oct. 31 Integration
by parts (continued)
W Nov. 2 Principle of linearized stability
F Nov. 4 Systems
of differential equations
Date Topic
M Nov. 7 Solving systems of differential
equations
W Nov. 9 Phase-plane
analysis: nullclines, equilibrium points and stability
F Nov. 11 Phase-plane analysis (continued)
M Nov. 14 Population
models of two interacting species
W Nov. 16 Predator-Prey models: The
Lotka-Volterra equations
F Nov. 18
M Nov. 21 Predator-prey
models continued
W Nov. 23 Competition and cooperation
F Nov. 25 Thanksgiving recess
M Nov. 28 The
principle of competitive exclusion.
W Nov. 30 Review
F Dec. 2 Exam 2
M Dec. 5 Review
W Dec. 7 Review
F Dec. 16 Final Examination