MATH 231- DIFFERENTIAL EQUATIONS-U.T.K., SPRING 2011- Dr. Alex Freire

Text: Introduction to Differential Equations, by Nagle-Saff-Snider (7th. Edition, Pearson 2008)

Section 7(20605), MWF 12:20-1:10, Ayres 120

OFFICE HOURS (Ayres 325): by appointment (e-mail to freire@math.utk.edu, or 974-4313): MW 11:00-12:00 and 2:30-3:30

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Ch. 1: Introduction

W 1/12 Solutions and initial-value problems (1.2)

F 1/14 The phase line (Group project D, Chapter 1)

Ch.2: First-order differential equations

W 1/19 Separable equations (2.2)

F 1/21 Linear equations (2.3)

M 1/24 Exact equations (2.4)

W 1/26 Substitutions and transformations (2.6)

Ch. 3: Applications of first-order equations

F 1/28 mixing problems, population models (3.2)

M 1/31 heating and cooling (3.3)

W 2/2 Newtonian mechanics(3.4)

F 2/4 Review/catch-up

M 2/7 EXAM 1 (Chapters 1,2,3)

Ch. 4: Linear second-order equations

W 2/9 homogeneous constant-coefficient equations: real roots (4.2)

F 2/11 complex roots (4.3) (REVIEW COMPLEX NUMBERS PRIOR TO LECTURE)

M 2/14 Non-homogeneous equations (4.4)

W 2/16 Superposition principle (4.5)

F 2/18 Variation of parameters (4.6)

M 2/21 Variable-coefficient equations (4.7)

W 2/23 Free mechanical vibrations (4.9)

F 2/25 Forced mechanical vibrations (4.10)

Ch. 5: Systems

M 2/28 Systems via elimination (5.1,5.2)

W 3/2 Coupled spring-mass systems (5.6)

F 3/ 4 Review/catch-up

M 3/7 EXAM 2 (Chapters 4,5)

Ch. 7: Laplace transforms

W 3/9 Definition, first examples (7.2)

F 3/11 Basic properties (7.3)

3/14 to 3/18: Spring Break

M 3/21 Inverse Laplace transform (7.4)

W 3/23 Solution of initial-value problems (7.5)

F 3/25 Discontinuous and periodic functions (7.6)

M 3/28 Systems via Laplace transforms (7.7)

W 3/30 Review/catch-up

F 4/1 EXAM 3 (Chapter 7)

 

 

 

Ch. 8: Series solutions of differential equations

M 4/4 Power series and analytic functions (8.2)

W 4/6 Power-series solutions of linear second-order equations (8.3)

F 4/8 Equations with analytic coefficients (8.4)

M 4/11 Special functions (8.8)

Ch. 9: Matrix methods for linear systems

W 4/13, F 4/15 Homogeneous linear systems with constant coefficients (9.5)

M 4/18 Complex eigenvalues (9.6)

W 4/20 Non-homogeneous linear systems (9.7)

M 4/25 Generalized eigenvectors (9.8)

W 4/27 The matrix exponential (9.8)

F 4/29 Review, catch-up

FINAL EXAM: Monday, May 9 (Chapters 8,9)

COURSE POLICIES

1. Attendance: students are expected to come to every class. Each lecture will include new material. While I will take attendance daily for control purposes, there is no formal attendance requirement.

2. Course log: This link to the course web page will contain a brief listing of the material covered in each lecture, handouts , announcements and homework problems. It will be updated after every class and should be consulted often. I wonít be using Blackboard.

3. The most important concepts and examples for each topic will be presented in class, but for thorough understanding you are expected to (i) read your textbook and your class notes; (ii) work on the homework problems; (iii) ask questions when there is something you donít understand.

4. The link classroom behavior expectations includes a list of behaviors considered disruptive (math department policy). Please familiarize yourself with it, as this policy will be enforced. This includes: no laptops, cell phones off, no texting allowed during lecture and no reading extraneous material.

5.HOMEWORK- Homework will be collected and graded each week (about 5 to 8 problems/week).Homework problems posted on the course log by Wednesday are due on Friday, at the start of class. Late homework wonít be accepted.

6. EXAMS- There will be three in-class written exams and a final. Of these five grades (including the homework grade), only the highest four will count towards the course total (25% each) .There will be no make-up exams, even in cases of a justifiable absence; if you miss an exam, this will be the grade you will drop.

Expected grading scale: below 50: F; 50-54: D to C-; 55-69: C or C+ 70-84: B or B+; 85-100: A- to A. I do not `grade on a curveí.

Students with disabilities: please contact the Office of Disability Services (2227 Dunford Hall, 974-6087 V/T) if you need special arrangements for this class.