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Nov 21, 2024
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MA 3710 - Mathematical Biology3 lecture hours 0 lab hours 3 credits
Course Description
This course is an overview of several techniques used in the development and analysis of mathematical models that illustrate various biological processes. The topics covered involve applications of ordinary and partial differential equations, dynamical systems and statistical analysis. Applications include population models, infectious disease and epidemic models, genetics, tumor growth and DNA sequencing. (prereq: MA 235 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
• interpret biological assumptions in terms of mathematical equations
• construct mathematical models to illustrate a biological processes
• write computer simulations for a biological model
• analyze a model numerically and graphically
• find equilibria of system of equations
• perform local stability analysis
• solve counting problems involving the addition and multiplication rules, permutations, and combinations
• compute probability of discrete events
Prerequisites by Topic
• Know the techniques of limits, differentiation, and integration
• Be able to determine the solution of first-order differential equations by the method of separation of variables
• Be able to determine appropriate integrating factors for first-order linear differential equations
• Be able to apply and solve first-order differential equations of selected applications
Course Topics
• Introduction to Mathematical Biology (1 class)
• Constructing a model (2 classes)
• Exponential and Logistic Growth (2 classes)
• Population-genetic models (2 classes)
• Models of interaction among species (1 class)
• Epidemiological models of disease spread ( 1 class)
• Matlab Review (1 class)
• Numerical and graphical techniques (2 classes)
• Finding equilibrium (1 class)
• Performing local stability analysis: one variable model (2 classes)
• Finding an approximate equilibrium ( 1 class)
• Matrices, Eigenvalues, Eigenvectors ( 1 class)
• Performing local stability analysis: Non-linear models with multiple variables (2 classes)
• Counting principles: Addition and Multiplication Rules (1 class)
• Permutations (1 class)
• Combinations (1 class)
• Arrangements with repetitions (1 class)
• Probability ( 1 class)
• Conditional probability and independence of events ( 1 class)
• Exams (3 classes)
• Review ( 2 classes)
Coordinator
Kseniya Fuhrman
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