Biological Applications Across the Mathematics Curriculum

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Presentation transcript:

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

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)

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

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

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

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.

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

Projection Matrix

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.

Conclusions We’re slowly incorporating Biological examples into numerous courses Resources: www.mathsci.appstate.edu/~ras/course_pages/courses.html www1.appstate.edu/~marland/classes/Math1010/1010h_hw.htm www.mathsci.appstate.edu/~kmp/research/talks.html