MAT 130 MA & MB
Calculus and Modeling I
Davidson College

Instructor

Dr. Laurie Heyer
Chambers 3027
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Textbooks

Calculus for the Life Sciences
Addison Wesley (2003)
Greenwell, Ritchey and Lial

Mathematical Models in Biology
Cambridge University Press
Allman and Rhodes

Course Description

Life consists of change.   Growth, metabolism, and senescence are examples of changes that occur in every living thing. In humans, change is evident in movement, circulation, learning, and disease. This course investigates mathematical approaches to describing and understanding change. Topics include single variable differential and integral calculus, difference equations and differential equations. Students will be guided in the discovery and mastery of mathematical techniques in the context of problems in the life sciences.

This course is ideal for students who would like to satisfy their math requirement with calculus, and are interested in medicine, biology, chemistry, public health and other life sciences. Successful completion of Calculus and Modeling I prepares students for MAT 135 or MAT 137.

 

Syllabus (pdf file)

Announcements:

Math Center: Sunday 7-11 p.m. and M-Th 9-11 p.m. in Chambers 1046

Summer Research Poster Session, September 3, 7-9 p.m., Chambers Gallery
*** 1 point Extra credit on Review I for paragraphs on two posters, emailed to me by September 10

Bernard Lecture: Sunday, Sept. 6, 8-9 p.m., 900 Room

Bio-Math Connections, Fridays 4-5 pm, Chambers 3146

Please note the following abbreviations in the reading schedule:
GRL = Greenwell, Ritchey and Lial (Calculus for the Life Sciences)
AR = Allman and Rhodes (Mathematical Models in Biology)

Date

Topic

Reading

Homework Assignment
Aug 24

Introduction

 No homework due Wednesday
Aug 26

Populations and Exponential growth

GRL 2.1

Due Friday

GRL 2.1: #20, 24, 28, 32, 37, 38

Aug 28 Logarithmic functions GRL 2.2 GRL 2.2: #12, 20, 36, 40, 50, 56
Aug 31

Additional exponential models; Newton's Law of Cooling

GRL 2.3

GRL 2.2 #68, 72, 82
GRL 2.3 #6, 10, 14, 25, 30

Sept 2 Discrete population models AR 1.1,
Excel tutorial (pp. 1-10) 		 
Sept 4 Discrete population models " "

AR 1.1 #1, 2, 3, 5, 6, 7, 9 and Discrete Models HW
Sept 7 Limits GRL 3.1 GRL 3.1: #12, 26, 28, 30, 46, 50, 52, 81, 83
Sept 9 Continuity GRL 3.2

Worksheet
GRL 3.1 #36, 44, 82
GRL 3.2 #8, 14, 20, 24

Sept 11 Average and Instantaneous Rates of Change GRL 3.3

GRL 3.3 #6, 14, 24, 31, 33

Sept 14 Definition of the Derivative GRL 3.4 GRL 3.4 #8, 18, 20, 34
Sept 16 Graphical Differentiation & Review I Preparation
Recall goals
Everyone can do math! 		GRL 3.5 Optional: GRL 3.5 #7-14
Sept 21

REVIEW I

*Read directions in email before downloading*
Takehome problem, pdf format
Sept 23 Optimization: Blood Vessel Branching
Circulatory system: Why do blood vessels branch the way they do?
Angiogenesis
Chick embryo
  • Relative extrema (section 5.2)
  • Techniques for finding derivatives (section 4.1)
  • Chain rule (section 4.3)
GRL 4.1, 4.2, 4.3, 5.1, 5.2 GRL 4.1 #2, 14, 20
GRL 4.2 #26, 28, 30
GRL 4.3 #8, 12, 24
GRL 5.2 #12, 18, 22
Sept 25 Optimization: Nerve Sheath GRL 4.5, 5.1 GRL 4.2 #33
GRL 4.3 #36, 44, 58
GRL 4.5 #12, 36, 47, 48
GRL 5.1 #14, 22
Sept 28

Optimization: Do Dogs Know Calculus?
Optimal pursuit of frisbees, baseballs, mates and prey

GRL 6.1 GRL 4.2 #22, 38, 40
GRL 5.3 #52, 54, 62
Sept 30 Applications of the Derivative: Biomechanics GRL 4.6 GRL 4.6 #18, 22, 40
GRL 5.2 #26, 38
GRL 5.3 #30, 42, 58
Oct 2

Applications of the Derivative: Enzyme Kinetics

Online GRL 6.1 #20, 24, 44
Oct 5 Absolute Extrema; Related Rates GRL 4.4, 6.2 GRL 6.2 #4, 5, 6
GRL 6.3 #16, 30, 35,
Oct 7 Related Rates, cont.
Strain-gauge plethysmography: method, equipment, application		 GRL 6.3, 6.4

GRL 6.3 #41
GRL 6.4 #20,22

Oct 9 Related Rates, cont.
Asteroid with Spirograph [use settings of 60, -15, 15]
Linear Approximation
GRL 6.5

GRL 6.3 #42
GRL 6.4 #10, 14, 25
GRL 6.5 TBA

Oct 12
FALL BREAK
Oct 14 Prep for Review II    
Oct 16
REVIEW II
Oct 19 Area and Definite Integrals GRL 7.3 GRL 7.3 #4, 14, 16, 18
Oct 21 Integration: Antiderivatives
Project Resources: PLOS, BMC 		GRL 7.1-7.2, 7.5 GRL 7.1 #45, 46, 47, and Worksheet
Oct 23 NO CLASS    
Oct 26 Integration: Pollution and Thermodilution
 GRL 7.1-7.3, 7.5 GRL 7.2 #37, 38
GRL 7.3 #24, 26, 32
Oct 28 Integration: Fundamental Theorem of Calculus GRL 7.4 GRL 7.4 #42, 44, 56, 58, 60
Oct 30 Integration: Volume and Average Value
 GRL 8.3 GRL 8.3 #12, 14, 25, 34, 36
Nov 2 Integration: Numerical Integration GRL 8.1 GRL 8.1 #13-16
GRL 8.4 #24, 26 (calculator)
Nov 4 Differential Equations Models GRL 11.1, 11.6 GRL 11.1 #8, 16, 20, 32
GRL 11.6 #10, 13
Nov 6 Differential Equations Models, cont. GRL 11.2, 11.6 GRL 11.2 #25, 26, 31, 32
GRL 11.6 #11, 12
Nov 9 Differential Equations Models, cont. GRL 11.1, 11.2, 11.6

GRL 11.6 #3, 4, 14, 15, 16
Group Project Topic Due
Nov 11 Qualitative Solutions: Slope Fields
Mathematica practice
N/A Handout
Nov 13 Euler's Method
 		GRL 11.3 GRL 11.3 #8, 18, 20, 31
Nov 16 Discrete Logistic Equation AR 1.2 AR 1.2 #7, 8, 9
Nov 18 Equilibria, Stability and Chaos AR 1.3 AR 1.3 #1, 2, 4; plus problem assigned in class
Send requests for problems to do on Friday
Nov 20 Prepare for Review III  
Nov 23
REVIEW III
Nov 25
THANKSGIVING BREAK
Nov 27
Nov 30 Case Study: Can We Save This Child? Handout Work on poster
Dec 2 Case Study: Can We Save This Child? Handout Work on poster
Dec 4 Group Project Poster Session Poster Due; Presented in class
Dec 6 Reflect and Prepare for Final Exam Formula Sheet
Dec 9 Prepare for Final
Dec 11-17

Final Exams