1. Biological Applications Across the Mathematics Curriculum
Katrina Palmer
René Salinas
Appalachian State University

2. Outline Majors Non-Majors New Life Sciences Concentration
Courses that incorporate Biology
Calculus I
Linear Algebra
Computational Math
Numerical Methods
Non-Majors
Introduction to Math (MAT 1010)

3. Life Science Concentration
Applied Math degree with special 3000-level Math-Bio course (Allman/Rhodes)
Biology minor with specialization option
Molecular biology
Ecology

4. Some Math Courses Math 1010: Introduction to Math*
Math 1110: Calculus 1
Math 2240: Linear Algebra*
Math 3130: Differential Equations
Math 3XXX: Computational Math
Math 4310: Numerical Methods

5. Introduction to Math (1010)
Mathematics
Difference equations
Matrix multiplication
Biology
Exponential/logistic growth
Disease models
Age structured models

6. Excel models Questions for Students
For the SIR model, find the Infection rate and recovery rate that result in the highest infection peak.
For the SID, create a disease that kills the most people. The resulting low death rate is initially counter-intuitive.

7. Linear Algebra Example (Caswell, p
Linear Algebra Example (Caswell, p. 91) Geographically subdivided population

8. Projection Matrix

9. Student Questions
Find the eigenvalues of A and the eigenvalues of the two diagonal blocks.
Which block contains the dominant eigenvalue?
Find the eigenvector corresponding to the dominant eigenvalue.
What does this say biologically?
Change F5 to 1.5 and F6 to 3 and answer the above questions.

10. Conclusions
We’re slowly incorporating Biological examples into numerous courses
Resources:
www1.appstate.edu/~marland/classes/Math1010/1010h_hw.htm