Math 331-6: Spring 2014

 

 Instructor : Hongkun Zhang
 Office :  1340  LGRT
 Phone :  545-2871
 E-Mail :   hongkun <at> math.umass.edu
 Homepage:   http://www.math.umass.edu/~hongkun/teach-331-14.html

            It will be updated regularly. Check it often for information about quizzes, homework and exams!  


Class Meeting : TuTh  11:15 AM - 12:30 PM LGRT 121

 

Office Hours

Thursday. 1-2 pm

 

Teaching Assistants:

   They will be holding office hours and recitations that are open to students in all sections, their office hours will be updated soon. This will occur in the late afternoons on most days of the week at times and location TBA. Students can obtain assistance with coursework during scheduled hours. An appointment is not needed. The course TA's will also be scheduling review sessions prior to each exam.

 

(1)  Monday,        3:30-5:00pm, LGRC A301 -- Haitian;  Monday,  5-6:30, LGRT 121-- Kostis ;
(2)  Tuesday,       5-6:30pm, LGRC 171 -- Joy;
(3)  Wednesday,  4-5:30pm, LGRC A301  --Joy;

(4) Thursday,       5-6:30pm, LGRT A203 -- Haitian;
(5)  Friday,           3-4:30, LGRC A301 -- Kostis.

 

Prerequisites for this course:

Calculus I,II. That is, a thorough knowledge and understanding of differential and integral calculus in one variable; some acquaintance with the basic notions of physical science, for the purposes of motivating and applying differential equations; Calculus III (multi-variable) and Linear Algebra are helpful, but not required.

 

Topics covered in this course:

Chapter 1: 1.1-1.5

Chapter 2: All sections except 2.3 and 2.5.

Chapter 4: 4.0-4.4. Sections 4.5 and 4.6 are optional

Chapter 6: All sections in 6.1-6.4.

 

Spring 2014

 

Last Class: Apr 30

Week

Lecture

Events

Jan 20

1.1   Basic Concepts 1.2 Direction Fields

1.3 Separable ODEs

First lecture Tues

Jan 27

1.3 Separable ODEs (mixing problems),

1.4 Exact ODEs

  

Feb 3

1.5 Linear 1st order ODEs: Integrating Factors

2.1 Homogeneous 2nd order ODEs

Last drop day: Mon Feb 3

Feb 10 

2.1 Homogeneous 2nd order ODEs

2.2 Hom. 2nd Order ODEs with Constant Coeff

     

Feb 17

2.2 Hom. 2nd Order ODEs with Constant Coeff

Holiday: Monday; Tue=Mon

Feb 24

2.4 Modeling of free oscillation of a Mass-spring system

2.6 Existence and Uniqueness of solutions
Mid term Exam

 

Mid-Term Feb 27 in class

Mar 3

2.7 Nonhomogeneous ODEs
2.8 Modeling: Forced Oscillation.

Last day for W: Mar 6

Mar 10

4.0 Matrix and Vector Basics; 4.1 ODE systems

Mar 17

 

Spring Recess

Mar 24

4.3 Phase Plane

    

Mar 31

4.4 Stability
Review

 

Apr 7

6.1 Laplace Transform

    

Apr 14

6.2 ODEs with Laplace
6.3 ODEs with a unit step function

Apr 21

6.3 ODEs with a unit step function
6.4 ODEs with a delta function

Holiday Mon;Wed=Mon

Apr 28

Review

 

May 2-5

Final Exam

 

May 13

Final grade due by midnight

 

 

 

Text : Advanced Engineering Mathematics, 10th Edition by Erwin Kreyszig, ISBN 978-0-470-45836-5, August 2011,  2011 Hardcover, 1280 pages, US $244.95

(required)

 

Grading : There is a final exam worth 3/8 of the grade and one midterm exam worth 2/8 of the grade. 

                 Homework will be assigned weekly, see below. Although they will not be collected weekly for grading correctness, but you need to turn in all of your homework on the day of the midterm exam and before final exam. You will get a score for each of these two collection of homework. Complete homework will count 1/8 of the grade!

                 Online homework on Webwork will also be assigned weekly and will be graded online. Quizzes will be given occasionally without advanced notice;  the problems in the quiz are very similar to those in assigned homework. The grades for the homework on Webwork and the quizzes will count 2/8 of the total grade.

                It is VERY important to do homework.

 

Webwork: You can login your account on Webwork from here

                   Your user name is the words in your Umass email address before @,

                   Your password is your student ID number. Please make sure you change your password once you login your account.

 

 

 

Scales for letter grades:     A : 93     A-: 90     B+: 85     B : 83     B-: 80     C+: 75     C : 73     C-: 70    D+: 65    D : 63     F : <60 

 

 

 

Exam schedule : There will one midterm exam and one final exam. The material covered in the first midterm will be announced in time. The final exam will cover mostly the material of the second half of the semester. 

 

 Other policies:
Makeup exams: you must notify me sufficiently in advance if you have a conflict with an evening exam or the final with another exam or if you're unable to take an exam due to illness or due to an emergency. I may require that you provide documentation for the absence.

LDSS accommodations: If you require extended time on exams due to a disability, it is your responsibility to contact your LDSS liason to make arrangements.

 

Weekly Schedule: Homework 

 You need to turn in all of your homework on the day of the midterm exam and before final exam. You will get a score for each of these two collections of homework.  Complete homework will count 1/8 of the grade!

(1)  When you do these homework, make sure that you write problems on each section using exactly one single page (you can use the back of the page if it is not enough).

(2)  But you can NOT write the homework from two sections on one page, if so then they will only be counted for one section.

(3)  Label clearly on the top right of each page the section of the problems, and label the problems that you have done.

(4)  Remember these two collections of HW problem sets will count 1/8 of your total grades. Late homework will NOT be graded and counted into your grades.

 

               Homework PART I.

               Section 1.1:  3, 4, 9;

               Section 1.2: 3, 5, 7;

               Section 1.3: 2, 3, 5, 15, 12;

               Section 1.4: 1, 2, 3, 5, 12;

               Section 1.5: 3, 4, 12;

Additional homework for Chapter 1. Write a summary for Chapter 1, by answering the following questions: (1) What you have learned in this chapter? (2) What kind of ODE can you solve using methods learned in this Chapter? List at least 3. (Hint: You can look at the summary page on page 44-45).

Remark: Make sure you understand completely the example 5,6,7 in Section 1.3, at least one of them are likely to be in the mid-term exam( with slightly changes)!

              

         Section 2.1 : 3, 4

         Section 2.2 : 1, 2, 7, 11, 16, 21, 23, 25,
  

 

Remark: You need to turn in above HWs on the day of midterm exam!

 

PART II Due on the day of final exam (bring it with you):
   Section 2.4 : 2, 4,
   Section 2.6 : 5, 9, 13

                  Section 2.7 : 1, 3, 5, 11, 12
                  Section 2.8 : 3, 16

 

Additional homework for Chapter 2. Write a summary for Chapter 2, by answering the following questions: (1) What you have learned in this chapter? (2) What kind of ODEs can you solve using methods learned in this Chapter? List them all. (Hint: You can look at the summary page on page 103-104).

 

         Section 4.1 : 1, 2, 10, 11, 13
   Section 4.3 : 1, 3, 6, 11, 13, 15, 18

         Section 4.4 : 1, 3, 5, 11

 

Additional homework for Chapter 4. Write a summary for Chapter 4, by answering the following questions: (1) What you have learned in this chapter? (2) What kind of systems can you solve using methods learned in this Chapter? List all 5 types of critical points, how do you identify them? Draw the trajectories near these critical points. Make sure you understand completely the example 1-6 in Section 4.3, at least two of them are likely to be in the final exam ( with slightly changes)!

 

 

               Section 6.1 : 1, 3, 4, 7, 25, 31, 33
      Section 6.2 : 1, 3, 5, 7, 23, 25

               Section 6.3 : 3,12,18     

Remember you need to turn in the second part of the above problems on the day of final exam (you need to bring them to your exam).