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 won’t 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 don’t 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 won’t 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 curve’. *

*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.