Courses: MTH290

MTH290 special section
Bio-enriched Differential Equations
Spring 2009
Supported by National Science Foundation∗

Instructor: Dr. C. Chiu (Dr. P. Bates for Fall 09)
Biology consultant: Dr. J. Jackson (Microbiology, MSU)
Graduate teaching assistant: TBA

Prerequisite: MTH132.

Course description: The objective of this course is appreciation and assimilation of the theory and applications of ordinary differential equations (ODEs), especially as a useful tool for modeling and analysis of biological phenomenon. We understand that there is a gap between one semester calculus and differential equations. For example, we need some knowledge of linear algebra, in particular eigenvalues and eigenvectors, in order to present general solutions of systems of linear ODE with constant coefficient. Because of this, other topics (advanced integration techniques and basic knowledge of linear algebra) will be taught as auxiliary tools for solving and analyzing differential equations

List of contents: The following is a tentative list of contents:

• Advanced integration techniques and applications, e.g., integration by parts.
• Elementary linear algebra, e.g., eigenvalues and eigenvectors.
• Functions of several variables.
• Scalar first order differential equations.
• System of ordinary differential equations, including stability analysis.
• Basic numerical techniques and MATLAB

Text Book: Bittinger/Brand/Quintanilla: Calculus for the life sciences.

Computer aided teaching and learning : Lecture notes and other learning materials will be provided through ANGEL on internet.. For this course, we do not plan to do extensive numerical work. However, numerical solutions and computer simulations are crucial for applications of differential equations. In order to visualize the spatial and temporal changes of biological functions, we will have several computer lab sessions and projects using high-end computer software package, MatLab.

The high level software will be able to perform complicate, symbolic calculations and numerical calculations in a short time without much coding work. For this course, we will learn and do the following computational tasks:
• Vector and matrix operations.
• Eigenvalues and eigenvectors.
• Solving systems of linear equations.
• 2-D and 3-D plotting.
• Find analytical solutions to differential equations.
• Find numerical solutions to differential equations.
• Curve fitting and least square methods.

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