Instructor : Peter Bosler, 4823 East Hall, pbosler@umich.edu
Time / Location : Tuesdays and Thursdays, 8AM - 9:30 AM
1123 Lurie Biomedical Engineering Building (LBME)
Textbook : Brian Bradie, A Friendly Introduction to Numerical Analysis. Pearson Prentice Hall, 2006 . ISBN 0-13-013054.
Office Hours : 4823 East Hall; Wednesdays 3-4PM, Fridays 11AM-12PM, and by appointment.
Math 471 is a survey of numerical methods for science and engineering. A numerical method is an algorithm, or sequence of steps, for solving a set of equations. These can be linear equations, nonlinear equations, or differential equations. We will study the accuracy, stability, and efficiency of some of the basic methods.
Scientific problems were traditionally investigated by theory and experiment, but now computer simulations are increasingly relied upon for such problems as airplane design, weather forecasting, modeling the spread of diseases, and improving the efficiency of solar cells, to name just a few examples. Many models are solved by software packages that act as numerical “black boxes,” outputting model solutions for user-supplied input data. In this course we will examine the methods that provide the foundations for those software packages.
Supplementary reading (not required) : Germund Dahlquist and Ake Bjorck, Numerical Methods. Dover, 2003.
Applications
Some homework problems may use applications found in the following texts (not required):
- R. Malek-Madani. Physical Oceanography. CRC Press, 2012.
- J.D. Murray. Mathematical Biology, 3rd edition. Springer, 2002.
- G. Van Brummelin. Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry. Princeton University Press, 2013.
Syllabus
- Floating point arithmetic
- Nonlinear equations and root-finding
- Numerical linear algebra
- Two-point boundary value problems
- Poisson equation
- Eigenvalues
- Polynomial and spline interpolation
- Numerical integration
- Initial value problems and ordinary differential equationsf