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Math 20D: Introduction to Differential Equations-Spring 2008-updated June 6, 2008

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Professor: Audrey Terras   email: aterras at ucsd.edu  

Audrey’s Final Exam Week Office Hours: Mon. 12-2, Wed. 1-3  in  7408 AP&M (& by appointment)

Steve’s Final Exam Week Office Hours: Monday 2-4   and    Tuesday 10-12  in APM 6436

Chris’s Final Exam Week Office Hours: Tuesday 1-3 PM  in  APM 6436

Asif’s Final Exam Week Office Hours: Tue 2-4 pm in APM 6434

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Corrected Takehome Final Exam Long Version:  ma20dtakehome.pdf

Final Exam: due before Thursday,  June 12, 2008  2:30 pm  in the homework drop box for your TA.

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meaning of midterm 2 grades:  A   83-100;  B   65-82; C   35-64;  D   30-34;   F    20-29

Practice Midterm2:  practice exam 2

Solutions to practice exam 2   practice exam 2 solutions

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Lecture on power series & odes (5.2) :    power series and odes.pdf

Lecture on Nonhomogeneous equations:    Nonhomogeneous Systems.pdf

Lecture on Fundamental Matrices:   fundamental matrices.pdf.

Lecture on Eigenvalues & ODEs:  eigenvalues & odes.pdf.

Lecture on Separable ODES:   separable odes.pdf.

Lecture on Autonomous & Exact ODEs: auto and exact odes.pdf.

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Lecture: MWF 1:00p - 1:50p CENTR 119

Discussion Sections are on Tuesday:  (no section the first Tuesday, April Fool’s Day)

622294 DI C01 Tu 10:00a - 10:50a YORK 3000A; 622295 DI C02 Tu 11:00a - 11:50a YORK 3000A 

622296 DI C03 Tu 12:00p - 12:50p YORK 3000A; 622297 DI C04 Tu 1:00p - 1:50p YORK 3000A   

622298 DI C05 Tu 2:00p   - 2:50p YORK 3000A;  622299 DI C06 Tu 3:00p - 3:50p YORK 3000A     

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Computer Lab: Matlab Website is  math20d.   This lab complements the theoretical aspects of the course,  MATLAB will be used. Your TA will be in the lab to assist you during the reserved time but you can also do the lab problems on your own computer.   Where do the labs meet?  Our labs are located in CLICS (in Galbraith Hall).  They'll be on the NW Mezzanine (no room number) it's an open lab and the TA can carve out a corner of the room.  We will meet this first week - to introduce students to the program, etc. See the website above for the lab assignments.   Your Matlab class meets at the same time as discussion except Thursday rather than Tuesday.

LA C50 Th 10:00a - 10:50a;     LA C51 Th 11:00a - 11:50a;       LA C52 Th 12:00p - 12:50p

LA C53 Th 1:00p - 1:50p;         LA C54 Th 2:00p - 2:50p ;       LA C55 Th 3:00p - 3:50p

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Our TAs  are:

C01 and C04: Chang, Christopher:  office  APM 6436;  email: chc007@math.ucsd.edu

C02 and CO3: Butler, Steven:  office  APM 6436;  email: sbutler@math.ucsd.edu

C05 and C06: Shakeel, Asif:  office  APM 6434;  email: ashakeel@math.ucsd.edu

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Text:   Boyce and DiPrima, Elementary Differential Equations  (8th edition), Chapters 1-7.   This text should be on reserve in S&E library.  You might also want to look at other texts.  There are plenty in S&E. 

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Course Description.  Ordinary differential equations: exact, separable, and linear; constant coefficients, undetermined coefficients. Variations of parameters. Series solutions. Systems. Laplace transforms. Techniques for engineering sciences. Computing symbolic and graphical solutions using Matlab.

Prerequisite: Math. 20C (or Math. 21C) with a grade of C– or better. It is strongly suggested that you be familiar with the material from Math 20A, 20B, and 20C, or equivalent courses.

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Good News Everyone:  We will drop the lowest 2 homework and lowest 2 Matlab grades.  The student solutions manual has lots of good hints for homework problems. Solutions to Homeworks 1-7  can be found below - after each assignment.

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Here’s what I’m thinking the 1st midterm grades mean:

A  35-40     B   28-34    C   22-27    D   16-21    F    0-15    

Exam 1 solutions:  blue midterm solutions

Practice midterm 1   practice exam 1

Solutions to practice exam 1   practice exam 1 solutions

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Exams:     2 Midterms plus a final.  Wed. April 23   and   Wed. May 21.

Final Exam:  Thursday,  June 12, 2008  11:30a - 2:29p.

Mid Term Exams will be closed book, no notes, no calculators, no computers, no headphones.

Grading Weights   Midterms 1+2: 20% each,   Final 30%,   text homework 20%,   lab homework 10%.                          Grades will be curved.

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Homework Assignments:  Although you are required to turn in only the HW problems assigned, you are strongly advised to attempt solving as many problems from each section as possible.   Keep a loose leaf notebook of homework solutions. But don’t hand the notebook in.  That would fill up the TA’s offices with notebooks.  Instead, just hand in the pages for the assignment of the week.  When the graded assignment is returned, put it in your notebook. I may look at your homework notebook near the end of the quarter. Your notebook will be useful when reviewing for exams.  I don’t care what sort of notebook you use.  It can be loose lined pages held together in a binder. It should just be neat.  You can use the graded homework papers or copies thereof and add any extra homework problems you may do.

                Please hand in MATLAB and textbook homeworks separately. Keep a 2nd notebook of MATLAB homework solutions. Again, don’t hand in the notebook - just the pages for the week’s Matlab assignment. I may want to look at the notebook near the end of the quarter.

        Homework Drop Boxes are located on the 6th floor of AP&M.  There are 2 drop boxes for each of our 3 TAs.  One box is for text homework and one for Matlab homework. Hand your homework in to the appropriate drop box for the TA in whose section you are officially enrolled. The homework must be in the drop box by noon of the day after the homework is due; Wed. at noon for text homework and Fri. at noon for Matlab assignments.  Make sure you print your name and student ID number on your homework, along with official section number.  Also make sure you staple the homework together (no notebooks).  Neatness counts !!!!!!!!!!!!!!!!!

        Since homework answers are often in the back of the book and can be produced in a flash using Matlab’s dsolve, you need to show your work to get credit for homework problems.  Because we have only 1 grader for 200 students, sadly, we will only grade 3 problems per assignment.

 

HW #1.  (DUE Tues., April 8)   Section 1.1:  4, 6, 23; Section 1.2: 6, 8, 13;  Section 1.3: 4, 8, 15; Section 2.1:  6, 13, 18, 21 (b and c), 24

Solutions to Homework #1:  hw 1 solns.pdf

 

HW #2.  (DUE Tues., April 15)   Section 2.2:  2,10,11,20;   Section 2.3:  4,7,10,12; 

Section 2.4: 2,7,22,25;  Section 2.5:  3,4,7,8,15

Solutions to Homework #2:  hw 2 solns.pdf

 

HW #3.  (DUE Tues., April 22)  Section 2.6:  4,10,21;  (Optional, Misc. Probs. p. 131: 2,6,14,20,33);

Section 3.1: 3,12,18,20;  Section 3.2: 1,2,9,10,22;  Section 3.3: 1,4,9,11,16, 24;

Solutions to Homework #3:   hw 3 solns.pdf

 

HW #4.  (DUE Tues., April 29)  Section 3.4: 2,4,10,20,27; Section 3.5: 6,11,18,21,23,38;

Section 3.6: 2,5,17,31

Solutions to Homework #4:   hw 4 solns.pdf

 

HW #5.  (DUE Tues., May 6)  Section 3.7: 1,2,5,10; Section 7.1: 1,3,5,19, 20;

Section 7.2: 2,7a,c , 10;  Section 7.3:  1,7,16,25,26,30

Solutions to Homework #5:   hw 5 solns.pdf

 

HW #6.  (DUE Tues., May 13)  Section 7.4: 2,3,4,6;  Section 7.5: 6,11,28,29;

Section 7.6: 2,10,13,28,29

Solutions to Homework #6:   hw 6 solns.pdf

 

HW #7.  (DUE Tues., May 20)  Section 7.7: 1,3,11,16;  Section 7.8: 2,7,19;

Section 7.9:  7,11,15

Solutions to Homework #7:   hw 7 solns.pdf

 

HW #8.  (DUE Tues., May 27)  Section 5.1:  3,4,10,13,16,26;  Section 5.2: 4,7,15,25

Solutions to Homework #8:   hw 8 solns.pdf

 

HW #9.  (DUE Tues., June 3)  Section 5.3:  2,5,12,19,22;  Section 6.1: 5a,c; 8,11,22,23;

Section 6.2:  9,18,19,21,31;  Section 6.3:   1,4,7,12,23;   Section 6.4:  1,5,9

Solutions to Homework #9:   hw 9 solns.pdf

 

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Tentative Calendar.             Please read the text BEFORE the lecture!

 

week

ending

Monday

Tuesday

Wednesday

Thursday

Friday

1

April 4

introduction

 

Sec 1.1-1.3

 

Sec 2.1

2

April 11

Sec 2.2-2.3

HW 1 due

Sec 2.4-2.5

Matlab 1 due

Sec 2.6

3

April 18

Sec 3.1-3.2

HW 2 due

Sec 3.3

Matlab 2 due

Sec 3.4

4

April 25

Review

HW 3 due

Exam 1

Matlab 3 due

Sec 3.5

5

May 2

Sec 3.6

HW4 due

Sec 3.7

Matlab 4 due

Sec 7.1-7.2

6

May 9

Sec 7.3

HW 5 due

Sec 7.4

Matlab 5 due

Sec 7.5

7

May 16

Sec 7.6

HW 6 due

Sec 7.7-8

Matlab 6 due

no class

8

May 23

Sec 7.9

Review

HW 7 due

Exam 2

Matlab 7 due

Sec 5.1-5.2

9

May 30

holiday

HW 8 due

Sec 5.3

Matlab 8 due

Sec 6.1-2

10

June 6

Sec 6.3-4

HW 9 due

resonance & chaos

 

resonance & chaos

finals week

June 13

 

 

 

final exam

11:30a-2:29p

 

 

 

 

Some Motivation.     

 

Differential equations have been the language of science since Newton and Leibnitz.  Most problems in applied math. are modeled by systems of differential equations.  Of course you cannot always expect to solve such equations exactly.  We will be looking at various methods to attack such problems from infinite sums and integrals such as the Laplace transform to graphical methods.  Another method is to approximate the differential equation by a difference equation and change the problem to linear algebra.

            As an example consider Bessel’s equation which arises in the analysis of vibrating circular drums.  The problem involving y(x)=J0(x)  is to find a function y(x) such that      

                (xy’)’ + k2xy = 0 .

Here k is a parameter determined by the drum.  A method due to Frobenius says seek a solution which is an infinite series   

            y(x) = xa(c0 + c1x + c2x2 + ...     )  

 and determine the power a   and the coefficients   c0, c1, c2, …   etc.   Assuming it is legal to differentiate the infinite sum term by term you can do this with some effort.  See the Math 110 text,  Powers, Boundary Value Problems,  for more information on that problem. 

 

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