Math 255: Ordinary Differential Equations

This is a sample Math 255 homepage (of Raphaël Ponge), based on Nagle-Saff, 5th Edition.

Useful Links

• Math Counseling Office: http://www.math.ohio-state.edu/counseling .

• Mathematics and Statistics Learning Center: http://www.mslc.math.ohio-state.edu .

Announcements

• Final Exam:
  • The final will take place

  • There will be extra office hours

Handouts

• Review problems for the Final. ( pdf).

• Summary of chapter 7 ( pdf ).

• Review problems on Chap. 7. ( pdf ). Answers ( pdf ).

• Practice problems for Midterm 1 ( pdf ).

• Summary booklet of Chap. 4 (2nd order linear equations) ( pdf ).

• Summary booklet of Chap. 2 (1st order ODE's) ( pdf ).

Homework Assignments

• Assignment #9 due on Thursday, June 5 (complete assignment).
  • Section 8.4: # 9, 13, 15.

  • Pages 87-88: #5, 26, 38.

  • Section 8.5: # 1, 5, 11, 13 (for #13 you also need to use the variation of parameter method from section 4.9).

• Assignment #8 due on Friday, May 30 (complete assignment).
  • Section 8.3: # 1, 5, 9, 11, 14, 15, 16, 25.

  • Section 8.4: # 1, 3. (Note: #13, 15 from 8.4 are dropped.)

• Assignment #7 due on Friday, May 23 (complete assignment).
  • Section 8.2: # 1, 2, 3, 11, 12, 13, 17, 18, 20, 24, 25, 28.

• Assignment #6 due on Thursday, May 15 (complete assignment).
  • Section 7.5: # 3, 9, 11, 17, 21.

  • Section 7.6: # 1, 3, 5, 9, 13, 17, 19, 23, 31, 35.

• Assignment #5 due on Thursday, May 8 (complete assignment).
  • Section 7.4: # 1, 5, 9, 17, 21, 25, 27, 29.

• Assignment #4 due on Friday, May 2 (complete assignment).
  • Section 7.2: # 5, 9, 11, 13, 15, 20, 23, 27.

  • Section 7.3: # 1, 3, 5, 6, 7, 8, 9.

• Assignment #3 due on Thursday, April 24 (complete assignment).
  • Section 4.8: # 3, 5, 8, 13, 21, 27, 35, 37, 39, 41 (in 35, 37 set-up only).

  • Section 4.9: # 1, 5, 6, 7, 17 (hint for #1: look at example 1 pp. 215-216).

• Assignment #2 due on Thursday, April 17 (complete assignment).
  • Section 4.2: 1, 3, 6, 13.

  • Section 4.3: # 1, 3, 7, 9 (no need to compute the Wronskians for #1, 3).

  • Section 4.5: # 3, 7, 14, 15.

  • Section 4.6: # 3, 5, 11, 22.

  • Section 4.7: # 1, 9, 11 (need to use 4.5/4.6).

• Assignment #1 due on Thursday, April 10 (complete assignment).
  • Section 2.3: # 7, 12, 15, 19, 37.

  • Section 2.2: # 7, 9, 14, 24, 31, 34.

  • Section 2.4: # 9, 13, 16, 17, 21.

Prerequisite for the course

Math 254. Not open to students with credit for 415 or 556.

Textbook

Fundamentals of Differential equations (5th edition) by K. Nagle, B. Staff and A. Snider, published by Addison Wesley Longman.

Catalog Description

Basic concepts and methods in solving ordinary differential equations, first and second order linear differential equations, series solutions, numerical methods, Laplace transforms, physical applications.

Aim of the Course

This course is an introduction to the most basic concepts and methods in solving ordinary differential equations. The emphasis of this course is on problem-solving. Upon completion of this course students should know some applications of ordinary differential equations in engineering, physics and some other branches of the sciences.

Syllabus

Introduction
1.1 Background
1.2 Solutions and Initial Value Problems


1st Order Differential Equations
2.3/2.1 Linear Equations-Motion of a Falling Body
2.2 Separable Equations
2.4 Exact Equations


Linear Second Order Equations
4.2/4.3/4.7 Solving a 2nd Linear Differential Equations
4.5/4.6 Homogeneous Linear Equations with Constant Coefficients
4.8 Method of Undetermined Coefficients
4.9 Variation of Parameters
4.1 Mass Spring System

Midterm I

Laplace Transform
7.2/7.3 Definition and Properties of the Laplace Transform
7.4 Inverse Laplace Transform
7.5 Solving Initial Value Problems Using Laplace
7.6 Laplace Transform of Discontinuous and Periodic Functions

Midterm II

Series Solutions of Differential Equations
8.2 Power Series and Analytic Functions
8.3/8.4 Power Series Solutions to Linear Differential Equations
8.5 Cauchy-Euler Equations
8.6 Method of Frobenius - Schroedinger Equation


Reviews

Final Exam

Timetable

Click here to get a tentative timetable.

Homework Assignments

The homework problems are assigned during lectures from Wednesday of the week "n" through Monday of the week "n+1" and are due on Thursday's recitation of week "n+1". The assignments will also be posted on the class website.

Only your 8 best scores will be taken into account, in such way that each of them is worth of 10 points. However, non-turned-in homeworks will not be dropped.

The assignments can also be found in the class website.

Grading Scheme

At the end of the course you will receive a letter grade based on the following categories for a total of 500 points:

• Quizzes (20 points). There will be two quizzes, each of them worth of 10 points. The first one will take place on Thursday, April 10 and the second one on Thursday, May 29.

• Homeworks (80 points). See information above.

• Midterm I (100 points). It will cover the first part of the course: 1st Order Differential Equations (Chap. 2) and Linear 2nd Order Equations (Chap. 4).

• Midterm II (100 points). It will cover the 2nd part of the course: Laplace Transform (Chap. 7).

• Final exam (200 points). On the first two parts for about 30% each of them and on the last part, Series Solutions of Differential Equations (Chap. 8), for about 40%.

Schedule of Exams

• Midterm I: Friday, April 25th at 12:30-1:18 pm in AP 384;

• Midterm II: Friday, May 16th at 12:30-1:18 pm in AP 384;

• Final Exam: Monday, June 9th at 11:30-1:18 pm in AP 384.