MATH 360 Section 101
Mathematical Modelling in Science
Session 2021W, Term 1 (Sep - Dec 2021)
Tue Thu 09:30 - 10:50 in LSK 121
Instructor's Web Page
Last update: 2021-09-06
(
preliminaries
)
- Course Canvas page for syllabus, lecture notes, homework and test information, homework submission, etc.
- There is NO course textbook (lecture notes are available on the Canvas page)
- References
- J. Feldman, A. Rechnitzer, E. Yeager, CLP1 Differential Calculus (2019). Sections 3.5, 3.6 (for review).
- J. Feldman, A. Rechnitzer, E. Yeager, CLP2 Integral Calculus (2019). Section 2.4 (for review).
- J. Lebl, Notes on Diffy Qs (2019). Parts of Chapter 1.
- S. Strogatz, Nonlinear Dynamics and Chaos (2016). Parts of Chapters 2, 3, 10.
- S. Slingerland and L. Kump, Mathematical Modeling of Earth's Dynamical Systems: A Primer (2001). Part of Chapter 3.
- L. Edelstein-Keshet, Mathematical Models in Biology (2005). Part of Chapter 7
- M. Laurent and N. Kellershohn, Multistability: a major means of differentiation and evolution in biological systems, Trends in Biochemical Sciences 24 (1999) 418-422.
- R. May and G. Oster, Bifurcations and dynamic complexity in simple ecological models, American Naturalist 110 (1976) 573-599.
- N. Britton, Essential Mathematical Biology (2003). Parts of Chapter 6 and 4
- M. Nowak, Evolutionary Dynamics (2006). Part of Chapter 6
Course Instructor: Wayne Nagata
Office: online
Office Hours: TBA, see course Canvas page for updates
Email: nagata(at)math(dot)ubc(dot)ca
Homework Assignments
Homework is due at 11:59 p.m. on the due date (LEAVE ENOUGH TIME for unexpected submission system delays).
Hand in ON TIME for marks, using the course Canvas page.
Late homework (date/time stamp after due date/time) will not be marked.
See the Canvas page for specific assignments.
Learning Outcomes
In the course, we introduce and analyze mathematical models from biology, earth science, chemistry and physics.
Only basic knowledge (e.g. from high school science courses) from these other subjects is assumed.
We use mathematical methods of optimization, dynamical systems (continuous-time and discrete-time), and probability (including stochastic processes).
By the end of the course, a student should be able to:
- interpret results from a mathematical model in terms of the intended application
- critically assess the applicability and limitations of a mathematical model
- determine, and justify, local or global extrema for a function of one variable that appears in a mathematical model
- draw the graph of a function of one variable that appears in a mathematical model
- rescale variables and rewrite an ODE model in dimensionless form
- determine the explicit solution of an initial value problem for a first-order ODE by the method of separation of variables
- determine the explicit solution of an initial value problem for a nonhomogeneous linear first-order ODE by the method of undetermined coefficients
- for an autonomous first-order ODE: find the equilibria, plot the vector field, use linearized stability analysis, draw the phase portrait, draw graphs of solutions, draw the bifurcation diagram and classify local bifurcations, identify if bistability or hysteresis occurs
- use a box model to help formulate an appropriate first-order ODE for an application
- use the law of mass action to formulate ODEs to model chemical reaction kinetics
- use the quasi-static approximation to reduce a system of two or more coupled ODEs into a single ODE
- rescale variables and rewrite a recursion model in dimensionless form
- determine the explicit solution of an initial value problem for a linear recursion with constant coefficients
- for a recursion: find the fixed points, use linearized stability analysis, draw the staircase/cobweb diagram, draw the phase portrait, draw the bifurcation diagram and classify local bifurcations, determine 2-cycles and their stability using analyical, graphical or numerical methods
- solve mathematical problems involving basic probability concepts: event, frequency, independence, random variable, mean (expected value), conditional probability
- formulate and analyze a model of a large population with different genotypes, with or without selection
- formulate and analyze a stochastic process model of a finite population
Assessment of Learning Outcomes
- 20% - Homework
- 30% - Midterm Test
- 50% - Final Examination