Math53

Math 53

Ordinary Differential Equations with Linear Algebra

Winter, 2007

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Instructor:

Name: Ralph L. Cohen

Office: 383-X (3rd floor, Building 380)

Phone: 723-1862

e-mail: ralph@math.stanford.edu

Office Hours: Mon, Wed: 1:00 pm - 2:15 pm or by appointment.

Lectures: Every MWF at either 10:00 - 10:50 or 2:15 - 3:05 in 380Y.

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Teaching Assistants

Name Office email Office hours

Nathan Brown 380-T nbrown@math.stanford.edu T and W, 4:30 - 6:00 pm

Kaiyuan Zhang 380-G kzhang@math.stanford.edu T, 4:00-4:50, Th, 4:00 - 4:50,

and 7:00 - 7:50 pm

Baosen Wu 380-R bwu@math.stanford.edu M, 4:00-4:50, T, 3:10-4:50,

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Sections

Besides registering in Axess for a lecture section, you must also register in CourseWork

for one of the following six sections :

Section 3 meets in 550-553R at 11:00 am, TA: Zhang

Section 4 meets in 90-92Q at 10:00 am, TA: Brown

Section 5 meets in 260-244 at 2:15 pm, TA: Wu

Section 6 meets in MitchB67 at 1:15 pm, TA: Zhang

Section 7 meets in Meyer147 at 11:00 am, TA: Wu

Section 8 meets in 200-013 at 1:15 pm, TA: Brown

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Textbook and Syllabus

The textbook for the course is "Differential Equations, with Boundary Value Problems ", 2nd edition, by Polking, Boggess, and Arnold.

Here is a link to the course Syllabus

Here is a revised syllabus for the last two weeks of the quarter: revised syllabus

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Course Description and Prerequisites

This is an introductory course in ordinary differential equations (ODEs). The primary focus will be on techniques for finding explicit solutions to ODEs. We will also study some nonlinear equations, elementary numerical methods, and ways of qualitatively describing solutions of ODEs without solving them explicitly. Math 51 or equivalent is required for this course. In particular, you should be familiar with one-variable differentiation and integration, two-variable differentiation, vectors, matrices, systems of linear equations, determinants, and inverses, though some of this material is covered in Chapter 7 of the text and will be briefly reviewed in the course.

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Grading Policy

Homework: 10%.

Midterms: 50%.

Final Exam: 40%.

Letter grades are assigned based on relative standing within the class.

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Homework Policy

Assignments will consist of a reading assignment and exercises for each class. They will be posted on the web every Thursday and due in section the following Thursday. They will be graded and returned in section the following Thursday.

You are encouraged to discuss any aspect of this class, including the material covered in lectures, the readings, and the problem sets, with anyone, including other students in the class and the SUMO tutors. You can also consult any source that may help you with the class in general and the problem sets in particular. However, you must write your own solutions to the problem sets. As the best way to learn the techniques covered in this class is to practice using them, you are encouraged to work through as many of the odd-numbered exercises in the textbook as possible. You will find answers and solutions to these problems in the textbook and in the student solution manual, respectively.

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Exam Schedule

Midterm #1:

Thursday, February 1, 7:00 pm-8:30 pm., Braun Auditorium.

Alternate exam given Thursday, February 1, 4:30 pm - 6:00 pm in room 380-D in the Math Bldg. If you have an academic conflict and need to take this exam, make sure you let your TA know by Thursday, January 25.

The midterm will cover sections 1.1 - 1.3, 2.1 - 2.8, and 4.1 - 4.4 You should also be familiar with the applications described in sections 3.1 - 3.4.

REMEMBER: You are responsible for the proofs in section 4.1

Practice Exams. The practice exams are old midterms (from previous quarters). Remember that those exams may have covered slightly more or less material than our exam.

Here is the midterm from last spring: mid1spring06

Here is an old midterm with solutions: Old_Midterm1.pdf

Here are the solutions to the first midterm: solutions

Midterm #1 statistics: Mean: 66.5, Median: 67, Std. deviation: 18.3

Here is a histogram of the scores. stats

Midterm #2:

Thursday, March 1, 7:00 pm-8:30 pm., Braun Auditorium.

Alternate exam given Thursday, March 1, 4:30 pm - 6:00 pm in room 380-F in the Math Bldg. If you have an academic conflict and need to take this exam, make sure you let your TA know by Thursday, February 22.

The midterm will cover sections 4.5 - 4.7, 5.1 - 5.8, 8.1, 9.1-9.2, 9.5

REMEMBER: Review the linear algebra in chapter 7! You will need to be able to use it!

Here is a table of LaPlace transforms. laplace.pdf You will be given a table of LaPlace transforms on the exam.

Here is a practice exam (the exam given last year) mid206.pdf

Here are the solutions: solutions

Here are the solutions to the second midterm: solutions

Midterm #2 statistics: Mean: 65, Median: 65, Std. deviation: 16.7

Here is a histogram of the scores. stats

Final Exam::

Monday, March 19, 7-10 pm. Annenberg Auditorium

There will be no make-up time for the final exam.

Here is a practice exam practicefinal

Here are the solutions: solutions

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Calculators

No calculators will be allowed during the exams.

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Tutoring Help

The Stanford University Mathematics Organization (SUMO) holds homework/tutoring help session for all students in the Math 50 series, i.e. 51, 52, 53. These tutoring sessions will be every Monday and Wednesday evening, from 6:00 pm until 10:00 pm, in room 381-T in the Math building. This is a great way to get extra help on your homework!

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CourseWork

CourseWork is a web-based program that will be used in Math 53 to allow students to check grades online, and the instructor to email important Math 53 information to the entire class. It is a secure program, so your grades will be available through CourseWork only to you. YOU MUST SIGN UP FOR A SECTION THROUGH COURSEWORK!!!

Here is a link to CourseWork.

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Homework

Homework 1. Due Thursday, January 18, in class.

Section 2.4 p. 55-56 #4, 6, 18

2.5 p. 61-62 #4

2.2 p. 35-37 #4, 10, 18, 34

2.3 p. 44-46 #4, 11

3.3 p. 126-127 #6, 7, 11, 12a,b

3.4 p. 131-132 #14

Here is a solution set to the first HW assignment: solution1

Homework 2. Due Thursday, January 25, in class.

Section 2.6 #10, 14, 26

   2.7: #4, 10, 26
        2.8: #16
        2.9: #8, 9, 20, 28
        3.1: #2, 12, 18
        4.1: #4, 12, 14

Here is a solution set to the second HW assignment: solution2

Homework 3. Due Thursday, February 8, in class.

Section 4.5:#2, 4, 8, 12, 18, 20, 26

4.6: #2, 6, 14

4.7: #10a, 12, 13

Here is a solution set to the third HW assignment: solution3

Homework 4. Due Thursday, February 15, in class.

Section 5.1 #6, 10

5.2 #6, 10

5.3 #4, 6, 16, 26, 30

5.4 #2, 6, 10, 20, 27

5.5 #2, 6

5.6 #4, 8,

Here is a solution set to the fourth HW assignment: solution4

Homework 5. Due Thursday, February 22, in class.

Section 5.7 #6, 12, 18, 22

8.1 #2, 8

9.1 #2, 53, 54

Here is a solution set to the fifth HW assignment: solution5

Homework 6. Due Thursday, March 8, in class.

Section 9.3 #11, 13, 14

9.6 #2, 4, 5, 6, 8, 14, 18, 26, 36

Here is a solution set to the sixth HW assignment: solution6

Homework 7. Due Thursday, March 15, in class.

Section 9.8 #2, 6, 12, 18

9.7 #3, 4, 9

9.9 #3, 4

6.1 #11

Here is a solution set to the seventh HW assignment: solution7