Spring Semester 2018

Applied Differential Equations and Modeling

Syllabus

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Summary:
This course offers an introduction to ordinary differential equations and their applications. Mathematical modeling of continuous-time dynamics has its origins in classical mechanics but is now prevalent in all areas of physical and life sciences. Attempting to solve such problems often leads to a differential equation. Consequently, a variety of analytical and numerical methods have been developed to deal with various classes of equations and initial value problems, the most important of which is the class of linear equations. Other methods (such as Laplace transform) for solving many differential equations of special form will also be discussed. The course underlines the importance of qualitative analysis of differential equations, with a discussion of simple models such as the Lotka-Volterra equation.

Contact Information:
Instructor:Marcel Oliver
Email:m.oliver@jacobs-university.de
Phone:200-3212
Office hours:  Tu 11:00, We 10:00 in Research I, 107
TA:Dzmitry Rumiantsau
Email:d.rumiantsau@jacobs-university.de

Time and Place:
Lectures:  Tu/Th 17:15-18:30 in West Hall 8
Discussion:  Mo 18:45-19:30 in West Hall 8

Textbook/Further Reading:

Grading:

Class Schedule (subject to change!)

Feb. 1., 2018: Introduction, Overview, First example: Newton's law of cooling (Brannan/Boyce, Section 1.1)
Feb. 6., 2018: Newton's law of cooling (ctd.); integrating factors (Brannan/Boyce, Section 1.2)
Feb. 8., 2018: Separable equations (Brannan/Boyce, Section 2.1)
Feb. 13., 2018: Modeling examples (Brannan/Boyce, Section 2.2)
Feb. 15., 2018: Non-uniqueness and blowup for nonlinear problems (Brannan/Boyce, Section 2.3)
Feb. 20., 2018: Population dynamics and logistic growth (Brannan/Boyce, Section 2.4)
Feb. 22., 2018: Exact equations and integrating factors (Brannan/Boyce, Section 2.5)
Feb. 27., 2018: Numerical methods (Brannan/Boyce, Section 2.6)
Mar. 1., 2018: Trapezoidal rule and Runge-Kutta methods (Brannan/Boyce, Section 2.7)
Mar. 6., 2018: Crash course in Linear Algebra I (Brannan/Boyce, Section 3.1)
Mar. 8., 2018: Crash course in Linear Algebra I
Mar. 13., 2018: Systems of two first-order linear equations (Brannan/Boyce, Section 3.2 and 3.3)
Mar. 15., 2018: Systems of two first-order linear equations, complex and repeated eigenvalues (Brannan/Boyce, Section 3.4 and 3.5)
Mar. 20., 2018: Second order linear equations I (selected topics from Brannan/Boyce, Chapter 4)
Mar. 22., 2018: Second order linear equations I (selected topics from Brannan/Boyce, Chapter 4)
Apr. 3., 2018: Midterm review
Apr. 5., 2018: Midterm Exam
Apr. 10., 2018: The Laplace transform (Brannan/Boyce, Section 5.1 and 5.2
Apr. 12., 2018: The inverse Laplace transform, solving differential equations (Brannan/Boyce, Section 5.3 and 5.4
Apr. 17., 2018: Discontinuous and periodic functions, applications to forcing (Brannan/Boyce, Sections 5.5-5.7
Apr. 19., 2018: Linear stability (Brannan/Boyce, Section 7.1
Apr. 24., 2018: Almost linear systems (Brannan/Boyce, Section 7.2
Apr. 26., 2018: Predator-prey systems (Brannan/Boyce, Section 7.3 and 7.4)
May 3, 2018: Periodic solutions and limit cycles (Brannan/Boyce, Section 7.5)
May 8, 2018: Chaos and strange attractors (Brannan/Boyce, Section 7.6)
May 15, 2018: Final exam review
TBA: Final Exam, Room TBA



Last modified: 2018/02/05
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/spring2018/acm262/index.html
Marcel Oliver (m.oliver@jacobs-university.de)