MAT 137
Calculus & Modeling II
Davidson College

Instructor

Dr. Laurie Heyer
Chambers 3027
x-2267                                               

Textbooks

  • Calculus for the Life Sciences, Addison Wesley, by Greenwell, Ritchey and Lial
  • Mathematical Models in Biology, Cambridge University Press, by Allman and Rhodes.

Course Description

A continuation of the study of calculus and other mathematical methods for modeling change.   Topics include multivariable calculus, and systems of linear equations, difference equations and differential equations. The last three weeks of the course is devoted to the study of uncertainty, using probability models such as Bayes' rule and random walks. Students will be guided in the discovery and mastery of mathematical techniques in the context of problems in the life sciences.

Announcements:

Bio-Math Connections Fridays 4-5 p.m.

 

Date

Topic

Reading

Homework Assignment

Jan 14

Functions of Several Variables

GRL 9.1

GRL Section 9.1 (p. 484)
# 4, 8, 16, 17, 33
Solutions

Jan 16

Partial Derivatives

GRL 9.2

GRL Section 9.2 (p. 495)
# 16, 18, 26, 36, 52
Solutions

Jan 18

Maxima and Minima

GRL 9.3

GRL Section 9.3 (p. 507)
#22, 24, 26, 32
Solutions

Jan 21

HOLIDAY

Jan 23

Chain Rule for Partial Derivatives

Online notes

Problems

Jan 25

Multiple Integration

GRL 9.5

Solutions

Jan 28

Multiple Integration, cont.

GRL 9.5

Solutions

Jan 30

Multivariable Calculus Models & Recap

Extra double integral problems and solutions

Feb 1

Review I

Feb 4

Systems of Equations

GRL 10.1

GRL Section 10.1 #26, 32, 40, 43, 48, and balance three chemical equations sent by email.
Solutions

Feb 6

Structured Population Models

AR 2.1

AR Section 2.1 (p. 52) #2.1.6
GRL Section 10.3 (p. 569) #22, 46
Solutions

Feb 8

Matrix Algebra and Excel

GRL 10.2-10.3

Solutions

Feb 11

Leslie Matrices
Beluga whales; Aging bacteria
Matrix Inverses

AR 2.2
GRL 10.4

 

Feb 13

Small world networks (PIN1; PIN2; 6 degrees; Kevin Bacon)

GRL 10.4

Solutions

Feb 15

Eigenvalues and Eigenvectors TED

AR 2.3

Solutions

Feb 18

Eigenvalues and Eigenvectors (Geometric interpretation)

GRL 10.5

  

Feb 20

More Linear Algebra Models & Recap

Feb 22

Review II

Feb 25

Fitting Curves to Data (IDH data)

AR 8.1
GRL 1.2

 

Feb 27

Least Squares (Linear Models)

GRL 1.2
AR 8.2

IDH Excel validation
GRL Section 1.2 (p. 27) #7,9
GRL Section 10.1 (p. 549) #52

Feb 29

Least Squares, cont. (Exponential curve-fitting)

AR 8.3

 Two problems in Excel file

Mar 3-7

SPRING BREAK

Mar 10

Predator-Prey Models

AR 3.1

AR Section 3.1 #3, 5

Mar 12

Equilibria

AR 3.2

 N/A

Mar 14

Stability

AR 3.3

 AR Section 3.2 #1, 3; Section 3.3 #7

Mar 17

Competition, Mutualism, and Infection
HIV model

AR 3.4

AR Section 3.4 #3-5

Mar 19

Recap interacting population models

 

 Project #1 assigned

Mar 21

Project work day - no class

 

  

Mar 24

HOLIDAY

Mar 26

Simple Epidemic Models

AR 7.1

  

Mar 28

TBA   Project #1 due at 5:00 p.m. via email

Mar 31

Thresholds and Critical Parameters AR 7.2  

Apr 2

Other Infectious Disease Models

AR 7.3

Apr 4

Review III

Apr 7

Event Trees and Sets

GRL 12.1

 

Apr 9

Basic Probability Rules
RFLP genetic test

GRL 12.2

 

Apr 11

Random Walks in Biology

Powerpoint

  

Apr 14

Basic Probability Rules , cont. GRL 12.2  

Apr 16

Conditional probability and independent events

GRL 12.3

 

Apr 18

Bayes Rule
Reliability of disease testing

GRL 12.3

  

Apr 21

Discrete Random Variables

GRL 12.4

 

Apr 23

Genetics and the Binomial Distribution

AR 6.1-6.2

 

Apr 25

Probability Models & Recap

Apr 28

Review IV

Apr 30

Case Study (CAT scans)

May 2

Final exam preparation

May 5

Project presentations

May 7

Project presentations & Course evaluations

May 9-14

Final Exam period