Professor Alexandru I. Suciu MATH 2351 · Ordinary Differential Equations Spring 2013

## Course Information

 Course MATH 2351 · Ordinary Differential Equations, Sec 01, Key # 30769 Instructor Alex Suciu Course Web Site www.northeastern.edu/suciu/MATH2351/ode.sp13.html Time and Place Mon, Wed 2:50-4:30 pm, in 409 Robinson Hall Office 435 Lake Hall Phone (617) 373-3899 Email a.suciu@neu.edu Office Hours Mon, Wed 2:00-2:40 and 4:40-5:20, or by appointment Teaching Assistant Floran Kacaku.  Email: kacaku.f@husky.neu.edu Phone: x-5534. Office hours: Mon, Wed, Th 1:00-2:00pm, in 541NI. Textbook Differential Equations, 4th ed., by Paul Blanchard, Robert L. Devaney, and Glen R. Hall, Brooks/Cole, 2011. [Online guide] Grading policy 50% in-class quizzes and exams, 10% homework, 40% final exam

## Homework Assignments

 This course features the use of ordinary differential equations to model and analyze various scientific problems involving population growth and decay, acceleration and velocity, and mechanical vibrations. Various methods to solve differential equations (both qualitative and quantitative) will be studied. Linear algebra techniques will be developed, and applied to systems of differential equations. The Laplace Transform method will also be introduced. Homework assignments will be posted here, as the course progresses. The problems in bold are due the week after being assigned. The problems in parenthesis are suggested as further homework; some of them will be discussed in class after you have a chance to work on them.

 Section Problems Homework due date 1. First-Order Differential Equations 1.1.  Modeling via Differential Equations 4, 11  (1, 2, 5) January 14 1.2.  Separation of Variables 6, 20, 30, 34  (5, 11, 12, 13, 24, 25, 29, 33, 35) 1.5.  Existence and Uniqueness 13, 14  (1, 2, 5, 6) January 23 1.6.  Equilibria and Phase Line 4/16 (3, 11, 12, 15, 23, 24, 29, 30) 1.8.  Linear Differential Equations 4, 20, 22  (3, 9, 10, 19, 21) 1.9.  Integrating Factors (3, 4, 9, 12, 13, 14, 24) 2. First-Order Systems 2.1.  Modeling via Systems 9/10, 20 (21, 22) February 6 2.2.  The Geometry of Systems 10, 12 (7, 9, 11, 13, 16) 2.3.  The Damped Harmonic Oscillator 2(b,c) (5, 6, 7, 8) 2.4.  Analytic Methods for Special Systems 2 (1, 3, 4, 8, 9) 3. Linear Systems 3.1.  Linearity Properties (5, 6, 7, 10, 11, 19, 24, 25, 27, 28) February 27 3.2.  Straight-line Solutions 6, 10 (3, 5, 6, 11, 12, 13, 14, 19, 21) 3.3.  Phase Plane for Real Eigenvalues 4, 8 (1, 2, 3, 4, 9, 13, 19, 20) 3.4.  Complex Eigenvalues 4, 6 (3, 5, 7, 8, 11, 12, 13) 3.5.  Repeated and Zero Eigenvalues 6, 8 (1, 2, 5, 11, 17, 18) March 20 3.6.  Second-order Linear Equations 14, 20 (7, 8, 15, 16, 17, 23, 24, 25) 3.7.  Trace-Determinant Plane 2, 4 (3, 6, 7, 11, 12, 13) 4. Forcing and Resonance 4.1.  Forced Harmonic Oscillators 18 (1, 2, 5, 6, 9, 10, 13) April 3 4.2.  Sinusoidal Forcing 18 (1, 2, 5, 11, 12, 20) 4.3.  Resonance 10 (1, 2, 3, 9, 13, 21) 5. Non-linear Systems 5.1.  Equilibrium Point Analysis 12, 16, 22(a,b) (1, 2, 3, 4, 7, 8, 15, 17, 21, 23) 6. Laplace Transforms 6.1.  Laplace Transforms 14 (11, 13, 15, 17, 19, 21, 23, 25) April 17 6.2.  Discontinuous Functions 12 (5, 7, 9, 10, 11, 13) 6.3.  Second Order Equations 18, 28, 30 (15, 16, 17, 27, 29, 31) 6.4.  Delta Functions and Impulse Forcing 4 (2, 3, 5)

## Class Materials

Some practice quizzes and exams (most with solutions) can be found here.

## Various Policies

• Without prior notice, there will be no makeups of quizzes. In there is a legitimate reason for missing a quiz, you must contact me before the event. On the other hand, I will drop the lowest quiz score, so one missed quiz will not count as a zero.
• You are responsible for information conveyed in class (even if you are absent) or posted on the course web site.
• If you have a concern about the course that cannot be resolved by speaking with me, please see the Undergraduate Math Director.
• All students without legitimate conflicts (approved by the instructor) must take the final exam at the scheduled time. Do not make travel plans that conflict with the final exam.
• It is University policy that no grade, including an Incomplete, can be changed after one year; exceptions must be authorized by the Academic Standing Committee.

 Department of Mathematics Office: 441 Lake Hall Messages: (617) 373-2450 Northeastern University Phone: (617) 373-3899 Fax: (617) 373-5658 Boston, MA, 02115 Email: a.suciu@neu.edu Directions