DIFFERENTIAL EQUATIONS SECTION 4 SPRING 2023 UPDATE PAGE

SITARAMAN


Here you will see information on what was covered in class, upcoming quizzes, and solutions to exams
CHECK HERE EVERYDAY !

COURSE PAGE WITH SYLLABUS, GRADING SCHEME, ETC.,

SCROLL DOWN BELOW TO SEE SOLUTIONS OF TESTS AND QUIZZES FROM THIS COURSE

OPTIONAL: It will be useful to have access the online homework website Webassign.
CLASS KEY: HOWARD 7336 6935.
You will also need access code that you got when you bought book or e-book.

SYLLABUS
Will try to stick to this schedule as much as possible.

You can see everything we did last semester in this course here:Fall 2022 Differential Equations Notes and Tests.

OLD FINAL EXAMS

TRY PROBLEMS EVERY DAY!
EXAMS WILL BE ANNOUNCED BELOW


PLEASE READ ALL INSTRUCTIONS ABOVE AND KEEP UP WITH CLASS.


ZOOM LINK FOR VIRTUAL MEETINGS, VIRTUAL OFFICE HOURS ETC., HAS BEEN POSTED ON CANVAS. LOOK IN ANNOUNCEMENTS



5/2/23 TUESDAY
Please read solutions for Final exam given below.
Final exam solutions

Final exam problems
GRADES AS OF 4/24/23 HAVE BEEN POSTED ON CANVAS ; GO TO CANVAS -> MODULES -> GRADES (at the top).
IT IS THE TOTAL OF TOP 7 QUIZZES PLUS TOP TWO TESTS PLUS 20 POINTS FOR ATTEMPTING AT LEAST 8 QUIZZES.

Happy summer!! I will send you an email once the grading is done.

GRADUATING SENIORS PLEASE CONTACT ME TO SET UP TIME FOR FINAL EXAM BETWEEN 4/24 AND 4/28.

 FINAL EXAM ON TUESDAY, 5/2, 1-3pm SAME ROOM ; COVERING ALL MATERIAL DONE IN CLASS. NO CALCULATORS ALLOWED.
NO MAKE-UPS FOR FINALS.
REVIEW IN CLASS ON WED, THU AND FRI April 26, 27, 28.
Please use this exam from last semester AND THIS final given to graduating seniors.
Also try 1,5,7,8,9,11,12,13,16,17,19,20,22,24,25,28,29,30,31 of this additional problems set.
(You can try all of them but some are more challenging).

Please also study class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THE PROBLEM SETS THERE, AND MAKE USE OF ADDITIONAL FEATURES.

4/24/23 MONDAY
Today we went over test 3 and also 8.2 (systems with matrices that have complex eigenvalues).
Rest of the week will be for reviewing course material.

4/21/23 FRIDAY
Please read solutions for Test 3 given below.
Test III solutions

TEST III problems
Happy weekend!!

TEST3 ON FRIDAY, 4/21 COVERING CHAPTERS 6,7, AND 8. NO CALCULATORS ALLOWED.
NO MAKE-UPS FOR TEST 3. ALL OUTSTANDING ISSUES IN COURSE MUST BE RESOLVED BY THURSDAY 4/20.
REVIEW IN CLASS ON THU April 20.
I HAVE MADE A POLL TO FIGURE OUT DATE FOR FINAL THAT WORKS FOR ALL. SEE IN CANVAS.

Please use this study-guide .
Please also study class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THIS THERE, AND MAKE USE OF ADDITIONAL FEATURES.

4/19/23 WEDNESDAY
We saw how to solve systems of differential equations using matrices, 8.2.
I have expanded the notes with more explanations and examples.
(Please reload page) Solving Systems of Differential Equations using matrices.
Practice problems:
8.2: 1, 3, 21, 23, 35.

4/17/23 MONDAY
We saw how to write systems of differential equations using matrices, 8.1.
Solving Systems of Differential Equations using matrices.
Practice problems:
8.1: 1, 3, 7, 9, 11, 21.

4/13/23 THURSDAY
I will be on zoom from 3pm tomorrow if anyone needs help.
Please read solutions for Quiz 10 given below.
QUIZ 10 solutions

QUIZ 10 problems

We will start 8.1 on monday.

If I don't see you tomorrow, Happy weekend!!
QUIZ 10 ON THURSDAY, COVERING 7.1 AND 7.2. NO CALCULATORS ALLOWED.

4/12/23 WEDNESDAY
We saw how to use Laplace transforms and their inverses to solve differential equations, 7.2.
Please see notes for parts of 7.2 that were not covered in class.
(Updated -- refresh page) Laplace transforms and Differential Equations.
Practice problems:
7.1: 7, 9, 11, 17, 25, 29, 37, 41.

4/10/23 MONDAY
We had an introduction to Laplace transforms, 7.1. Please see notes for parts of 7.1 that were not covered in class. Laplace transforms and Differential Equations.
Practice problems:
7.1: 3, 5, 11, 17, 23, 29, 31.

4/7/23 FRIDAY
Please read solutions for Quiz 9 given below.
QUIZ 9 solutions

QUIZ 9 problems

We will start 7.1 on monday.

Happy weekend!!

QUIZ 9 ON FRIDAY, COVERING 6.1 AND 6.2. NO CALCULATORS ALLOWED FROM NOW ON.

4/6/23 THURSDAY
We talked about 6.2 (power series and second order differential equations) today. See (updated -- refresh browser) Power series and Differential Equations.
Practice problems:
6.2: 3, 5, 7, 9, 11.
4/5/23 WEDNESDAY
We continued with same topic as yesterday and showed how to solve a first order equation using power series. Practice problems same as below.

GRADES AS OF 4/4/23 HAVE BEEN POSTED ON CANVAS ; GO TO CANVAS -> MODULES -> GRADES (at the top).
IT IS THE TOTAL OF TOP 7 QUIZZES PLUS TWO TESTS.

4/3/23 MONDAY
We talked more about 6.1 (power series and differential equations) today. See (updated -- refresh browser) Power series and Differential Equations.
Practice problems:
6.1: 1, 3, 5, 11, 13, 17, 19, 35, 37.

3/31/23 FRIDAY
We talked about 6.1 (power series and differential equations) today. See Power series and Differential Equations.
Will put practice problems on monday.

Please read solutions for Test 2 given below.
Test II solutions

TEST II problems
Happy weekend!!

TEST II ON THURSDAY MARCH 30 ON CHAPTERS 3, 4, 5.
REVIEW IN CLASS ON WED March 29.
Please use this study-guide .
Please also study class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THIS THERE, AND MAKE USE OF ADDITIONAL FEATURES.

3/27/23 MONDAY
We talked about 5.1.3 (forced, damped motion) today. See Intro to Modeling with higher order Differential Equations.
In addition, try 31 and 35 from 5.1.

3/25/23 SATURDAY
Please read solutions for Quiz 8 given below.
QUIZ 8 solutions

QUIZ 8 problems

We will start 5.1 section 3 on monday.

Happy weekend!!

QUIZ 8 ON FRIDAY MARCH 24, ON 5.1.1, 5.1.2

3/23/23 THURSDAY
We talked about 5.1.2 (free, damped motion) today. See Intro to Modeling with higher order Differential Equations.
. Please try 25 and 27 from 5.1.

3/23/23 THURSDAY
We talked about 5.1.1 (free, undamped motion) yesterday. See notes and practice problems below.
In addition, try 9 and 11 from 5.1.

3/20/23 MONDAY
Today we started talking about applications of the method of undetermined coefficients to find solutions of second order linear differential equations with constant coefficients.
Notes --we covered part of 5.1 today : Intro to Modeling with higher order Differential Equations.
I have corrected quiz 7 problem 3 (bonus) solutions below.
Please try the following from 5.1 if you coud; we will go ove rthem in class wednesday :
5.1: 1,3,5.


3/17/23 FRIDAY
Please read solutions for Quiz 7 given below.
QUIZ 7 solutions

QUIZ 7 problems

We will start 5.1 on monday.

Happy weekend!!

QUIZ 7 friday, on 4.3 and 4.4. Please try practice problems below and study the notes as well.
3/16/23 THURSDAY
Today we did the method of undetermined coefficients to find solutions of second order linear differential equations with constant coefficients.
Notes --we covered 4.4 today. (Updated -- please refresh): Intro to higher order Differential Equations.
(I have corrected 4.4 problem 6 solutions)
Please try the following from 4.4 in addition to ones from wednesday and monday:
4.4: 27, 29, 37.


3/15/23 WEDNESDAY
Today we continued to talk about solutions of second order linear differential equations with constant coefficients.
Notes --we covered 4.3 and part of 4.4 today. (Updated -- please refresh): Intro to higher order Differential Equations.
Please try the following from 4.4:
4.4: 1, 3, 7, 13, 19, 31, 35.


3/13/23 MONDAY
Today we talked about solutions of second order linear differential equations with constant coefficients.
Notes --we covered part of 4.3 today. (Updated -- please refresh): Intro to higher order Differential Equations.
Please try the following from 4.3:
4.3: 1, 3, 5, 7, 31, 37.



3/2/23 THURSDAY
Please read solutions for Quiz 6 given below.
QUIZ 6 solutions

QUIZ 6 problems

We will start 4.3 monday after the break.

Happy spring break!!

QUIZ 6 will be this thursday, 3/2, on 4.1 and part of 4.2.

3/1/23 WEDNESDAY
Today we talked about fundamental solutions of higher order linear differential equations and linear independence.
Notes --we covered 4.1 and part of 4.2 today. (Updated -- please refresh): Intro to higher order Differential Equations.
Please try the following from 4.1 and 4.2:
4.1: 13, 23, 27, 31, 33
4.2: 1, 3



2/27/23 MONDAY
Today we introduced higher order linear differential equations.
Notes --we covered 4.1 and part of 4.2 today--: Intro to higher order Differential Equations.
Please try the following from 4.1 and 4.2:
4.1: problems 1, 3, 7, 17, 19, 21




2/24/23 FRIDAY
Please read solutions for Quiz 5 given below.
QUIZ V solutions

QUIZ V problems

We will start 4.1 monday.



GRADES AS OF 2/22/23 HAVE BEEN POSTED ON CANVAS ; GO TO CANVAS -> MODULES -> GRADES (all the way at bottom).

QUIZ 5 will be this friday, 2/24, on 3.1 and part of 3.2.

2/23/23 THURSDAY
Today we saw how to use first order linear and non-linear differential equations to solve real world problems.
Notes --we covered 3.1 and part of 3.2 today-- (Updated, refresh browser) : Modeling with first order Differential Equations.
Please try the following from 3.1 and 3.2:
3.1: problems 13, 19, 21, 25.

3.2: problems 1, 3.


2/22/23 WEDNESDAY
Today we saw how to use first order differential equations to solve real world problems.
Notes (we covered 3.1 today ) : Modeling with first order Differential Equations.
Please try the following from 3.1:
3.1: problems 1, 3, 5, 9, 11.



2/16/23 THURSDAY
Please read solutions for Test 1 given below.
TEST I solutions

TEST I problems

We will start 3.1 tomorrow.


TEST I WILL BE ON THU FEB 16; REVIEW IN CLASS ON WED FEB 15. WILL COVER ALL OF CHAPTERS 1 AND 2.

Please use this study-guide from last semester.
Please also study Euler's method (2.6), class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THIS THERE, AND MAKE USE OF ADDITIONAL FEATURES.

2/13/23 MONDAY
Today we saw how to approximate solutions to first order differential equations using Euler's method.
Notes (Updated ; Please reload page) : Solving first order Differential Equations.
Please try the following from 2.6:
2.6: problems 1, 3, 5, 7.


2/10/23 FRIDAY
Please read solutions for Quiz 4 given below.
QUIZ IV solutions

QUIZ IV problems

We will start 2.6 monday.


QUIZ 4 TOMORROW (FRI) ON 2.4 AND 2.5.
Study class notes, practice problems, and following from fall 22:
Quiz 4 problem 3, Test I problems 5, 6, 7.
PROF. JAMES WILL GIVE IT IN CLASS.

2/8/23 THURSDAY
Today we saw how to solve first order differential equations using substitution.
Video of class after 5pm will be emailed to you. it will also be in canvas announcements as well.
Notes (Updated ; Please reload page) : Solving first order Differential Equations.
Please try the following from 2.5:
2.5: problems 7, 11, 15, 17, 21, 23, 25.


2/8/23 WEDNESDAY
Today we saw how to solve exact first order differential equations.
Notes (Updated ; Please reload page) : Solving first order Differential Equations.
Please try the following from 2.4:
2.4: problems 7, 9, 15, 21, 25.
2/2/23 THURSDAY
Please read solutions for Quiz 3 given below.
QUIZ III solutions

QUIZ III problems

We will start 2.4 monday.


2/1/23 WEDNESDAY
QUIZ TOMORROW ON 2.2 and 2.3
STUDY CLASS NOTES, PRACTICE PROBLEMS AND QUIZ 3 and 4 from last semester (except the exact equation problem).
Today we saw how to solve linear first order differential equations.
Notes (Updated ; Please reload page) : Solving first order Differential Equations.
Please try the following from 2.3:
2.3: problems 3. 5, 7, 9, 25, 27.


1/30/23 MONDAY
Today we did some more problems involving separable differential equations.
Notes (Updated ;Please reload page) : Solving first order Differential Equations.
Please try the following from 2.2:
2.2: problems 23, 31, 33, 37.


1/27/23 FRIDAY
LINK FOR WATCHING VIDEO WILL BE POSTED ON CANVAS
Today we looked at solving separable differential equations.
Notes (Updated ;Please reload page) : Solving first order Differential Equations.
Please try the following from 2.2:
2.2: problems 1, 3, 7, 9, 17, 19, 21.


1/26/23 THURSDAY
TOMORROW, FRIDAY, NO IN PERSON CLASS
I WILL BE RECORDING ON ZOOM AROUND 11 AM
YOU ARE WELCOME TO JOIN OR WATCH VIDEO LATER.
BOTH ZOOM LINK AND VIDEO LINK WILL BE POSTED ON CANVAS.

Please read solutions for Quiz 2 given below.
QUIZ II solutions

QUIZ II problems

We will start 2.2 tomorrow.


1/25/23 WEDNESDAY
QUIZ II THURSDAY ON 1.3 AND 2.1.
Sample problems in Quiz 2 and Quiz 3 of last semester (except you won't need to do any integration).
Today we looked at direction fields and phase portraits and what they tell us about differential equations.
Notes : Solving first order Differential Equations.
Please try the following from 2.1:
2.1: problems 1, 3, 19, 21, 23.


1/24/23 TUESDAY
QUIZ II THURSDAY ON 1.3 AND 2.1.
Yesterday we continued to discuss how to write differential equations for various real world situations.
Notes : Differential Equations as Models
Please try the following from 1.3 in addition to the ones from friday:
1.3: problems 9, 11, 23.


1/20/23 FRIDAY
Today we discussed how to write differential equations for various real world situations.
Notes from Today : Differential Equations as Models

Please try the following:
1.3: problems 1, 3, 7, 17, 21.


1/18/2023 THURSDAY
Please read solutions for Quiz 1 given below.
QUIZ I solutions

QUIZ I problems

We will start 1.3 tomorrow.


1/18/23 WEDNESDAY
QUIZ I THURSDAY BASED ON ALL 1.1 AND 1.2 PRACTICE PROBLEMS ASSIGNED SO FAR.

Today we discussed interval of definition, explicit and implicit solutions and existence and uniqueness of solutions of differential equations.
Notes from Today (with more worked examples -please reload!): Definitions and existence of solutions

Please try the following:
1.1: problem 15, 17, 19, 21, 23.
1.2: problems 15, 17, 21, 25, 27.
Apologize for typo on friday. Problems from friday are in 1.1.


1/13/23 FRIDAY
QUIZ I THURSDAY BASED ON 1.1 AND 1.2 PRACTICE PROBLEMS.

Today we discussed numerical solutions, interval of definition, normal form (using differentials) and explicit and implicit solutions of differential equations.
Notes from Today (with more worked examples): Introduction to Differential Equations and Definitions and different types of solutions to Differential Equations.
The notes are slightly modified from last semester. For example I added the solution of 1.1 problem 16 in the second powerpoint.

Please try the following:
1.1: problem 15, 17, 19, 21, 23.


1/12/23 THURSDAY
Today we continued to discuss the basics of differential equations using the example of the equations relating to motion of an object under gravity.
Notes from Monday, Wednesday and Today: Introduction to Differential Equations.
Please try the following:
1.1: problems 7, 9.
1.2: problem 1.


1/12/23 THURSDAY
Yesterday we discussed the basics of differential equations using the example of the equations relating to motion of an object under gravity.
I will post updated notes soon, but meanwhile please check out the "Introduction to Differential Equations" notes from 8/22/2022.
You can get there by clicking on "Fall 2022 notes and tests" above.
Please try the following:
1.1: problems 1, 3, 5, 7.
1.2: problems 9, 11, 13.


1/10/2023 TUESDAY
Here is the article about "supertall" skyscrapers that I talked about:HOW TALL IS TOO TALL?

Here is a nice article about the origins of the theory of gravity:University of Virginia Physics Lecture Notes on Gravity

Please study following to prepare for class: Watch this video on coronavirus, exponential growth, and differential equations

REVIEW MATERIAL FROM CALCULUS I: Powerpoint on integration basics
Notes from Fall 2020 on definite integrals.
A Brief Introduction to Calculus from Spring 2021.