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Professor Alexandru I. Suciu
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MTH U345 · Ordinary Differential Equations
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Fall
2008
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 Course Information
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Course
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MTH U345 · Ordinary Differential Equations, Sec 01, Seq B, Key # 24875
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Instructor
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Alex Suciu
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Course Web Site
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www.northeastern.edu/suciu/U345/ode.fa08.html
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Time and Place
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Mon, Wed 2:50-4:30 pm, in 411 Robinson Hall
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Office
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441 Lake Hall
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Phone
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(617) 373-4456
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Email
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a.suciu@neu.edu
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Office Hours
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Mon, Wed 4:40-5:40pm, or by appointment
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Textbook
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Differential Equations, 3rd ed.,
by Paul Blanchard, Robert L. Devaney, and Glen R. Hall, Brooks/Cole, 2006. [Online guide]
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Grade
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50% in-class quizzes and exams, 10% labs and homework, 40% final exam
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Homework Assignments
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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.
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Section
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Problems
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1. First-Order Differential Equations
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1.1. Modeling via Differential Equations
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1, 2, 4, 11, 12
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1.2. Separation of Variables
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1, 5, 11, 13, 20, 24, 25, 29, 30, 33, 35
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1.5. Existence and Uniqueness
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1, 2, 5, 6, 13, 14
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1.6. Equilibria and Phase Line
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3, 4, 11, 12, 15, 16, 23, 24, 29, 30
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1.8. Linear Differential Equations
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3, 4, 9, 10, 19, 20, 21, 22
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1.9. Integrating Factors
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3, 4, 9, 12, 13, 14, 24
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2. First-Order Systems
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2.1. Modeling via Systems
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1-6, 20, 21, 22
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2.2. Geometry of Systems
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7, 9, 10, 11, 13, 16
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2.3. Analytic Methods
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1, 2, 5, 6, 7, 8, 9, 13, 14, 15
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3. Linear Systems
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3.1. Linearity Properties
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5, 6, 7, 10, 11, 19, 27, 28
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3.2. Straight-line Solutions
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3, 5, 6, 11, 12, 17, 19, 21
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3.3. Phase Plane for Real Eigenvalues
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3, 4, 9, 10, 13, 19, 20
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3.4. Complex Eigenvalues
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5, 6, 7, 11, 12, 13, 16, 23
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3.5. Repeated and Zero Eigenvalues
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1, 2, 5, 6, 11, 17, 18
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3.6. Second-order Linear Equations
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7, 8, 15, 16, 17, 23, 24, 25
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3.7. Trace-Determinant Plane
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3, 4, 7
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4. Forcing and Resonance
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4.1. Forced Harmonic Oscillators
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1, 2, 5, 6, 9, 10, 13
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4.2. Sinusoidal Forcing
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1, 2, 5, 11, 12, 20
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4.3. Resonance
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1, 2, 3, 9, 10, 13, 21
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5. Non-linear Systems
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5.1. Equilibrium Point Analysis
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1, 2, 3, 4, 7, 8, 15, 17
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6. Laplace Transforms
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6.1. Laplace Transforms
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11, 13, 15, 17, 19, 21, 23, 25
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6.2. Discontinuous Functions
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5, 7, 9, 10, 11, 12, 13
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6.3. Second Order Equations
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15, 16, 17, 27, 28, 29, 31
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6.4. Delta Functions and Impulse Forcing
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2, 3, 4, 5
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Class Materials
Various Policies
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Without prior notice, there will be no makeups of quizzes or the midterm exam; similarly, computer labs and homework papers will not be accepted late. In either case, you must contact me before the event. On the other hand, I will be dropping the lowest quiz score, so one missed quiz will not count as a zero.
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You are responsible for information conveyed in class (even if you are absent) or posted on the course web site.
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If you have a concern about the course that cannot be resolved by speaking with me, please see the Undergraduate Director of the Math Department, Prof. Alex Martsinkovsky.
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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.
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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.
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