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AMATH 351 A: Introduction To Differential Equations And Applications

Meeting Time: 
MWF 10:30am - 11:20am
CMU 120
Jakob J. Kotas

Syllabus Description:

AMATH 351, Spring 2016

University of Washington


Office hours

Jakob Kotas, Instructor ( - Wednesdays 3-5PM, Lewis 115 129

Jeremy Upsal, TA ( - Thursdays 12:30-2:30PM, Lewis 129


Topics covered

First order equations: method of integrating factors, separable equations, exact equations, homogeneous equations. Second order linear equations: homogeneous equations, linear dependence and the Wronskian, methods of undetermined coefficients and variation of parameters for nonhomogeneous equations. Series solutions and second order equations: power series, Euler equations and Frobenius method. The Laplace Transform. Systems of linear equations: eigenvalues and eigenvectors of matrices. Systems of nonlinear equations: perturbation theory. Emphasis on formulation, solution, and interpretation of results. Examples from the physical sciences and engineering.



Proficiency in manipulation of algebraic equations and methods of differentiation and integration at the level of MATH 124 & 125 are assumed.



W.E. Boyce & R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems. The text is not required to pass the course, but obtaining some edition of it is to use as a reference is recommended. Note: this is not the same textbook as the one used by MATH 307, which is a special edition of the original text for use at UW with some chapters removed.



Homework: 30%. Due weekly on Fridays, in-class (paper copy).

Exam 1: 17.5%. Tentatively Mon 4/25. In-class.

Exam 2: 17.5%. Tentatively Mon 5/09. In-class.

Final exam: 35%. Mon 6/06, 8:30-10:20AM.

Extra credit: There will be no extra credit offered.

Regrades: Regrade requests must be accompanied by a written statement explaining the reason for the request. Requests must be received within one week of the return of graded work; requests after this time will be denied.


Homework policy

Collaboration: Collaboration is encouraged, but every student must submit their own assignment consisting of their own work. Late assignments: No late assignments will be accepted for any reason. In the rare event of an emergency, with sufficient documentation, a homework will be dropped and other homeworks re-weighted.

Scoring: Homework problems are graded on a fixed-point scale, with points being awarded for work and completion toward the correct answer.

Dropped scores: The lowest homework score is not dropped.


Exam policy

You are allowed one handwritten, double-sided reminder sheet (8.5”x11” max.) No calculators, computers, or collaboration allowed. The lowest exam score is not dropped.


Attendance policy

Attendance is not recorded nor taken into consideration in grades. However, it is highly recommend that students attend lecture to keep up with the material.


Computing policy

Some Matlab will be used in the course and a basic understanding of Matlab will be beneficial. However, computing is not a main focus of this course. Those interested in learning more about numerical methods should consider taking AMATH 301, Beginning Scientific Computing.


Honor code

Students shall abide by the University of Washington Academic Honesty policies, which are outlined at


Coverage of lectures

Mon 3/28: Introduction & syllabus

Wed 3/30: Ch. 2.1: Linear equations

Fri 4/1: Ch 2.2, 2.5: Separable equations, autonomous equations

Mon 4/4: Ch. 2.5: Autonomous equations, population dynamics

Wed 4/6: Ch. 2.6: Exact equations, first-order homogeneous equations

Fri 4/8: Ch. 3.1: Constant-coefficient, homogeneous equations with real roots

Mon 4/11: Ch. 3.2: The Wronskian

Wed 4/13: Ch. 3.3-3.4: Complex & repeated roots of the characteristic equation

Fri 4/15: Ch. 3.5: Undetermined coefficients

Mon 4/18: Ch. 3.6: Variation of parameters

Wed 4/20: Ch. 3.7-3.8: Vibrations

Fri 4/22: Exam 1 review & Ch. 5.1: Review of Taylor/power series

Mon 4/25: Exam 1

Wed 4/27: Ch. 5.2-5.3: Series solutions near an ordinary point

Fri 4/29: Ch. 6.1: Definition of the Laplace Transform

Mon 5/02: Ch. 6.2: Solving IVP using Laplace Transform

Wed 5/04: Ch. 6.3-6.4: Step functions and differential equations with discontinuous forcing functions

Fri 5/06: Exam 2 review & Ch. 7.1-7.2: Intro to matrices

Mon 5/09: Exam 2

Wed 5/11: Ch. 7.3: Eigenvalues/vectors and systems of algebraic equations

Fri 5/13: Ch. 7.4-5: Constant coefficient, homogeneous systems of equations with real eigenvalues (Jeremy guest lecture)

Mon 5/16: Ch. 7.5: Constant coefficient, homogeneous systems of equations with real eigenvalues

Wed 5/18: Ch. 7.6: Constant coefficient, homogeneous systems of equations with complex eigenvalues

Fri 5/20: Ch. 7.8: Constant coefficient, homogeneous systems of equations with repeated eigenvalues

Mon 5/23: Ch. 9.2-9.3: Nonlinear systems of equations, pendulum example

Wed 5/25: Ch. 9.4-9.5: Competing species & Predator-prey model

Fri 5/27: Ch. 8: Numerical methods

Wed 6/01: Final exam review

Fri 6/03: No class, reading day

Catalog Description: 
Introductory survey of ordinary differential equations; linear and nonlinear equations; Taylor series; and. Laplace transforms. Emphasizes on formulation, solution, and interpretation of results. Examples drawn from physical and biological sciences and engineering. Prerequisite: MATH 125 or MATH 135. Offered: AWSpS.
GE Requirements: 
Natural World (NW)
Last updated: 
January 10, 2018 - 9:20pm