110262 Applied Differential Equations and Modeling

• Homework and Project sheets
• Other class materials
• Course notes from Fall 2005 introducing to Matlab , older notes from Spring 2003 "Introduction to Octave and Matlab" by J. Nielsen (segmented into 5 pdf handout files and 3 presentations, download here ), and an introduction to Octave by H. Selhofer and M. Oliver (pdf).
• The official Octave homepage.
• The official Matlab website.
• CLAMV primer

The course introduces ordinary differential equations from an application point of view. The course discusses fundamental concepts including the derivation of ODEs as models for continuous-time dynamical behavior, examples of first- and second-order equations, analytical and numerical solution techniques for initial value problems, systems of linear ODEs, Laplace transform techniques. It also provides brief introductions to existence and uniqueness theorems, the qualitative theory of nonlinear systems in two dimensions, and the parameter dependence of solution behavior. A second element of this course is the application of ODEs to understand and predict quantitative phenomena in the natural sciences and engineering. Examples come predominantly from engineering and biology, and include case-study type problems.

All students in the School of Engineering and Science with an interest in the application of Mathematics to real-life problems, and a mathematical background equivalent to either Engineering and Science Mathematics 1B (Multivariable Calculus, ODE) or Analysis I/II should consider taking this course as a home school elective. Students of Applied and Computational Mathematics can take this course as part of their first or second year major requirement. Basic familiarity with Matlab (on the level of NatSciLab Math 110212) or a similar mathematical software package is assumed.

The course serves as an equivalent for the course Mathematics 264: "Differential Equations with Linear Algebra" offered at Lafayette College.

Instructor of Record:	Peter Oswald
Email:	p.oswald@jacobs-university.de,
Phone:	200-3179
Office hours:	Tuesday 3:30-5:00pm (or by appointment) in Research I, 113

TA:	Jan Cannizzo
Email:	j.cannizzo@jacobs-university.de
Tutorial and Contact Hours:	Wednesday afternoon by agreement

Lectures :

Tu 9:45-11:00 and Th 8:15-9:30

• J.R. Brannan, W.E. Boyce, Differential Equations: An Introduction to Modern Methods and Applications, Wiley&Sons, 2007. ISBN-13 978-0-471-65141-3.
• M. Braun, Differential Equations and their Applications: An Introduction to Applied Mathematics, Springer, 1993.

• W.E. Boyce, R.C. DiPrima Elementary Differential Equations and Boundary Value Problems , Wiley&Sons, 2004 (also older editions). ISBN-13 978-0-471-65141-3.
• J.C. Robinson, An Introduction to Ordinary Differential Equations, Springer, 1993.
• E.J.D. Murray: Mathematical Biology I: An Introduction, 3rd edition, Springer, 2002.
• F.C. Hoppenstaedt, C.S. Peskin: Modeling and Simulation in Medicine and the Life Sciences, 2nd edition, Springer, 2002.

Homework is handed out roughly every two weeks. Written solutions need to be turned in on the due date, no late homework will be accepted. There will be one larger modeling exercise (called Project) which will include the discussion, analysis, numerical simulations, and parameter studies of differential equations models. Further details and submission rules will be announced together with the homework and project sheets at a later time, read them carefully! Students should be able to present and explain project and homework solutions on request.

Homework is your individual work. Projects will be collaborative work in groups of two (exceptions can be granted by the instructor under certain circumstances). However, two conditions apply:

• Each member of a group carries individual responsibility for at least 40% of the work done.
• Each member of the group is able to explain the complete project solution without help from others.

You may consult books and internet resources, provided you quote the source in the respective part of the report.

An in-class Midterm Exam will be conducted on Thursday March 26, a Final Exam is scheduled during the Finals Period in May.

• The final grade will be computed from the weighted average of percentages of maximal scores with the weights

  Homework:	20%
  Project:	20%
  Midterm Exam:	20%
  Final Exam:	40%

  
  according to the following table:

  Cutoff score:	95%	90%	85%	80%	75%	70%	65%	60%	55%	50%	45%	40%
  IUB Points:	1.0	1.33	1.67	2.0	2.33	2.67	3.0	3.33	3.67	4.0	4.33	4.67