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Differential Equations

Instructor: Kevin Schnelli

Teaching Assistant: Zhigang Bao

Description

This course provides an introduction to differential equations and dynamical systems. The emphasis is on examples and applications to biology, chemistry and physics. We start with a review of basic notions of calculus. We then discuss theory and applications of first and second order differential as well as difference equations. We further study numerical methods for solving them. Next, we discuss some examples of 1D and 2D dynamical systems.

Lectures: Tuesday and Thursday, 2:00pm-3:15pm, Mondi 3

Recitations: Tuesday, 3:30pm-4:20pm, 3rd floor meeting room in the central building

Office hourse: Thursday, 3:15pm-4:00pm, LBW, 3rd floor, Office 113

Credits: 3 ECTS

Final grade: 30% homework, 70% final written exam (first and fifth homework not graded)

Schedule (subject to change)

Date Topic
10/06/15 Introduction, sequences, series, convergence
10/08/15 Real functions, graphs of functions, inverse functions
10/13/15 Fire drill, power series, exponential function, trigonometric functions, continuity
10/15/15 Derivative, Taylor polynomial, Taylor series
10/20/15 Riemann sums, integral, integration by parts and by substitution. Examples of first order differential equations
10/22/15 First order differential equations: initial value problems, separable equations, linear equations
10/27/15 First order differential equations: solution of linear equations with example, slope fields
11/29/15 Euler and Runge-Kutta methods, introduction to one-dimensional dynamical systems, population dynamics and logistics equation
11/03/15 Bifurcation, introduction to second order linear differential equations
11/05/15 Wronski determinant, variation of constants
11/10/15 Constant coefficient linear second order DE, introduction to two dimensional systems
11/12/15 Solution of two dimensional linear systems, eigenvalue problem
11/17/15 Phase plane analysis
11/19/15 Non-linear systems, Lotka-Volterra model
11/23/15 Exam, Mondi 3, 2pm-4pm (Monday!)

Homework

File
Homework 1
Homework 2
Homework 3
Homework 4
Homework 5
Exam

Additional downloads

File
Course organization
Literature
Notes on Taylor's theorem
Examples of vector fields, linear systems
Examples of vector fields, non-linear systems
Phase space for Lotka-Volterra models