# 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:
• J. Brannan and W. Boyce, Differential equations. An introduction to modern methods and applications, 3rd edition, 3rd edition, Wiley, 2015.

Grading:
• The final grade will be determined as follows:

 Homework: 30% Midterm Exam: 30% Final Exam: 40%

• The scores will be averaged as percentage grades with the given weights.
• Homework will be given every week, it is due in class the following Tuesday.
• I reserve the right to substitute in-class Quizzes for part of the homework score.

### 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)