MAT 140 Multivariable Calculus & ModelingDavidson College

Instructor

Dr. Laurie Heyer
Chambers 3027
x-2267

Course Description

A continuation of the study of calculus and other mathematical methods for modeling change.   Topics include multivariable calculus, and systems of linear, difference, 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.

Math and Science Center

Center for Teaching and Learning (behind circulation desk in Little Library)

How and when will you use math?

Homework Problems Due

Jan 18

Functions of Several Variables

Fetal weight models
Temperature Plots
Topo Maps (self test)
Level Curve Tutorial at Univ. of Minnesota
Functions of two variables in Mathematica

9.1

Jan 20

Plots and Applications, continued

Jan 23

Partial Derivatives

9.2

Section 9.1 (p. 484)
# 4, 8, 10, 15, 16, 33, 42

(note error in book's answer to #15)

Mathematica assignment due by email

Jan 25

Maxima and Minima

Hardy Weinberg Principle

9.3

Section 9.2 (p. 495)
# 16, 18, 20, 26, 36, 42, 48, 52

Jan 27

Multiple Integration

9.5

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

Jan 30

Multiple Integration, cont.
Extra double integral problems

9.5

Section 9.5 #14, 18, 38, 40, 53, 57

Feb 1

Systems of Equations

10.1 9.5 #42, 52, 59, 60, 64

Feb 3

Matrix Algebra

10.2-10.3 Section 10.1 #26, 32, 40, 43, 48 plus balance these chemical equations

Feb 6

Recap and prepare for Review I

Section 10.3 #20, 22, 31, 36, 38, 48

Feb 8

Recap and prepare for Review I

Feb 10
REVIEW I

Feb 13

Leslie Matrices
Matrix Inverses

10.4

Feb 15

Determinants

10.5

Section 10.3 #46 (ignore the hint!)
Section 10.4 #10, 20, 51-55
Worksheet

Feb 17

Eigenvalues and Eigenvectors

TED
Geometric interpretation with Mathematica

10.5 Determinants

Feb 20

Eigenvalues and Eigenvectors, cont.

Linear algebra movies

10.5

Section 10.5 #2, 8, 10

Feb 22

Fitting Curves to Data (duck shape)

1.2

Matrix animation worksheet

Feb 24

Least Squares (Linear and exponential curve-fitting)

1.2

Section 10.5 #15, 16, 21, 22
(ignore plotting instructions, just show 0.98 is an eigenvalue)
plus Curve-fitting worksheet

Feb 27

Small world networks

Dolphin social networks

p. 601

Section 1.2 #7, #9
Two Exponential fits

Feb 29

Recap and Q&A to prepare for Review II   p. 601 #1-4 and this worksheet

Mar 2

REVIEW II

Mar 5 - Mar 9

SPRING BREAK

Mar 12

Predator-Prey Models

Hudson Bay Lynx & Hare
Yellowstone Wolves and Aspen Trees

Predator-Prey dynamics

Mar 14

Interacting Populations in Excel
Predator-Prey dynamics

Mar 16

Equilibria and Stability

Predator-Prey dynamics Questions 2-5, p. 140 of "Predator-Prey dynamics" (short answers, sketch graphs by hand as needed to illustrate points)

Mar 19

Competition and Infection

Interspecific Competition and Competitive Exclusion

Worksheet

Mar 21

Systems of Differential Equations

11.5 Worksheet

Mar 23

Epidemic Models (SIR)

Refined SIR model

Section 11.5 #6, 8, 10
Mar 26

Linear systems of Differential Equations

11.4 Worksheet

Mar 28

Recap and prepare for Review III

Section 11.4 #10, 14

Mar 30

Review III

Apr 2

Event Trees and Sets

12.1

Apr 4

Basic Probability Rules

RFLP genetic test

12.2

Section 12.1 #38, 42, 50, 57, 58
Section 12.2 #14, 18, 24, 36

Apr 6

Conditional probability and independent events

12.3

Section 12.2 #38, 40, 67, 69, 70

Apr 9

HOLIDAY

Apr 11

Bayes Rule

Reliability of disease testing

12.3

Section 12.3 #2, 4, 8, 12, 22, 24, 38, 58

Apr 13

Discrete Random Variables

12.4

Section 12.3 #25, 26, 28, 30, 32, 51, 53, 62, 64, 65, 66

Apr 16

Genetics and the Binomial Distribution

Section 12.4 #2, 4, 8, 18

Apr 18

Binomial Distribution, continued   Worksheet

Apr 20

Continuous Probability Models
Expected Value and Variance
13.1, 13.2 Worksheet

Apr 23

Special Probability Density Functions 13.3 Section 13.1 #14, 24, 28, 29, 30
Section 13.2 #21, 26, 27

Apr 25

Special Probability Density Functions, cont. 13.3 Section 13.3 #6, 10, 12, 14, 30, 42
Apr 27

Recap and prepare for Review IV

Section 13.3 #27, 32, 35, 36, 38

Apr 30

REVIEW IV

May 2

Final exam preparation

Project topic selection (send full citation by email)

May 4

Final exam preparation & course evaluations

May 7

Project presentations

May 9

Project presentations