Instructor: Hao Wang
Office: CAB 539
11:00AM - 12:30PM
Tuesday & Thursday
or by appointment
MATH 371 Q1
Mathematical Modeling in the Life Sciences
Winter Term, 2018
Classroom: CAB 281
Time: 9:30AM - 10:50AM
Tuesday & Thursday
Jan 8 - Apr 13, 2018
TEXTBOOK: A Course in Mathematical Biology, by G de Vries, T Hillen, M Lewis, J Mueller, B Schoenﬁsch. SIAM Publishing, Philadelphia, 2006.
COURSE DESCRIPTION: Model development, computation, and analysis for problems in the life sciences. Models include discrete-time models and differential equation models. Model evaluation and prediction. Applications are chosen from epidemiology, ecology, population biology, physiology, and medicine.
EXAMINATION: The Midterm exam will be given in class on February 27, Tuesday.
HOMEWORK ASSIGNMENTS: The assignment problems will be posted in class and on my MATH 371 website. Late assignments will not be marked and a grade of zero will be assigned.
GRADING: Assignments and class participation (30%), Midterm (30%), Final presentation (10%), Final project (30%).
An overall course mark of 60% or more guarantees a passing grade of at least D.
Chapter 1. Introduction
Chapter 2. Discrete-Time Models
Chapter 3. Ordinary Differential Equations
Chapter 4. Partial Differential Equations
Chapter 5. Parameter Estimation
Final presentation schedule:
April 5: Group 1, Group 2, Group 3, Group 4
April 10: Group 5, Group 6, Group 7 (30 mins)
April 12: Group 8, Group 9, Group 10
Final presentations are given on April 5, April 10, April 12. Each group gives a 20-min presentation, however, Group 7 with four members will give a 30-min presentation. Please send me your presentation file before 9:00PM in the previous day.
Matlab sessions in NRE 2-125 from 9:30AM to 10:50AM on March 6 and 8
Please think of selecting a topic from Chapter 9 of textbook or any research topic relevant to my publications (see my website) for your final project:
Final report should be in a standard report format. Final report in presentation format (slides) is NOT acceptable.
3 students per group. Each group submits one report, but all group members need to present some parts in the final presentation.
Data fitting guidance:
Matlab sample programs:
The program for a system of two difference equations: TwoDifferenceEquations.m
(please save both files in the same folder and run ThreeDifferentialEquations.m to obtain results. Here,
rigid.m defines the model and ThreeDifferentialEquations.m compute and plot the solution.)
The toolbox program for a system of two differential equations to plot a user-friendly phase plane: pplane10.m
The program for a scalar PDE: SinglePDE.m
The program for a system of two PDEs: TwoPDEs.m
The programs for data fitting using the central difference derivative approximation:
The programs for data fitting using the direct least-square method:
Assignment #1: Ex 1.4.1(a)(b)(c)(d), Ex 2.4.5, Ex 2.4.8, Ex 2.4.10(a)(b), Ex 2.4.15, Ex 2.4.16, Ex 2.4.18, Ex 2.4.19(a)(b), Ex 3.9.3, Ex 3.9.4, Ex 3.9.5 (a), Ex 3.9.6(a)(b)(c)
(Due date: February 15, Thursday)
Assignment #2: Ex 3.9.12, Ex 3.9.7, Ex 3.9.8, Ex 3.9.9, Ex 3.9.10, Ex 3.9.11, Ex 3.9.16, Ex 3.9.17, Ex 4.5.1, Ex 4.5.2, Ex 4.5.5(a)(b)
(Due date: April 5, Thursday)
Final project report is due in class on April 12 (the last lecture).