DIFFERENTIAL EQUATIONS SECTION 4 SPRING 2024 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 5190 2388
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 2023 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.



5/2/2024 Friday
Grades will be posted on bisonweb soon. Please wait for it to appear.
Final exam solutions

Final exam problems


FINAL EXAM MAY 3, FRI, 5 TO 7PM. SAME ROOM.
You can see past final exams by going to Old courses page and looking at update pages of past semesters.
PLEASE ALSO STUDY ALL CLASS NOTES, QUIZZES AND TESTS FROM THIS SEMESTER.

ALL OUTSTANDING ISSUES MUST BE CLEARED BY FRI APR 19, 3pm.

GRADES AS OF 4/24 POSTED ON CANVAS, UNDER ANNOUNCEMENTS.

4/24/2024 Wednesday
Please read the solutions for the quiz 12.
Quiz 12 solutions

Quiz 12 problems

We will do review for final on thursday and friday.

4/18/2024 Thursday
QUIZ 12 wednesday Apr 24 on 7.6 and 8.2.
Friday and Monday we will do problems from 7.6 and 8.2.
You will be expected to have studied those sections and do problems in class.

Today we talked about using complex eigenvalues to find solutions for two equations in two unknown functions and also using Laplace transforms to solve the same.
Notes for today : (Updated-- Refresh!) Systems of Differential Equations.
Written notes from class
Please study relevant parts of 8.2.
Practice problems:
7.6: 1, 3, 7, 9, 15.
8.2: 35, 37, 39.

TEST 3 APRIL 17 WEDNESDAY. REVIEW MONDAY APR 15.
COVERING ALL MATERIAL AFTER TEST 2
Upcoming quizzes: 4/12, 4/24.
TEST III WILL COVER 6.2, 7.1, 7.2, 8.1, 8.2.
Please use this study-guide .
Please also study class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THE PRACTICE TEST AS AN ASSIGNMENT THERE, AND MAKE USE OF ADDITIONAL FEATURES.

4/17/2024 Wednesday
Please read the solutions for the test 3.
Test 3 solutions

Test 3 problems

We will talk about complex eigenvalues and Laplace transforms for systems tomorrow.

4/15/2024 Monday
Today we did a review for test 3 that is on wednesday.
Written notes from class (Updated -- Refresh).

4/12/2024 Friday
Please read the solutions for the quiz 11.
Quiz 11 solutions

Quiz 11 problems

We will do review for test 3 on monday.

4/11/2024 Thursday
QUIZ 11 friday on 8.1 and 8.2.
Today we talked about using eigenvalues to find solutions for two equations in two unknown functions when there is onl one eigenvalue and eigenvector.
Notes for today : Systems of Differential Equations.
Please study relevant parts of 8.2.
Practice problems:
8.2: 1, 3, 5, 7, 11, 13, 21, 23, 31.

4/8/2024 Wednesday
QUIZ 11 friday on 8.1 and 8.2.
Today we talked about using eigenvalues to find solutions.
Notes for today (Updated -- refresh!): Systems of Differential Equations.
Also please read Written notes from class (Updated -- Refresh).
Please study relevant parts of 8.2.
Practice problems:
8.2: 1, 3, 5, 7, 11, 13.

4/8/2024 Monday
Today we talked about verifying solutions for systems of equations and using eigenvalues to find solutions.
Notes for today (Updated -- refresh!): Systems of Differential Equations.
Also please read Written notes from class.
Please study relevant parts of 8.2 and 8.1.
Practice problems:
8.1: 21, 23, 25.
8.2: 1, 3, 5, 7.

4/5/2024 Friday
Please read the solutions for the quiz 10.
Quiz 10 solutions

Quiz 10 problems

We will continue with 8.1 (systems) on monday.

QUIZ 10 friday on 7.1, 7.2 (only related to practice problems below) and 8.1.

4/4/24 Thursday
GRADES AS OF NOW POSTED ON CANVAS.

Today we introduced systems of equations.
Notes for today (Updated -- refresh!): Systems of Differential Equations.
Please study relevant parts of 3.3 and 8.1.
Practice problems:
8.1: 1, 3, 5, 7, 9, 11, 13, 15.


4/3/24 Wednesday
Today we talked about Laplace Transforms and second order equations.
Notes for today (Updated -- refresh!): Laplace Transform.
Also please read Written notes from class.
Please study relevant parts of 7.2.
Practice problems:
7.2: 39, 41, 45, 47.


4/1/24 Monday
Today we talked about Laplace Transforms using Gamma function.
Notes for today (Updated -- refresh!): Laplace Transform.
Also please read Written notes from class.
Please study relevant parts of 7.1.
Practice problems:
7.1: 43, 45, 46.


3/29/2024 Friday
Please read the solutions for the quiz 9.
Quiz 9 solutions

Quiz 9 problems

We will continue with 7.2 on monday.

3/28/24 Thursday
GRADES AS OF NOW POSTED ON CANVAS.

QUIZ 9 FRIDAY WILL BE ON 7.1 AND 7.2.

Today we talked about solving differential equations using Laplace Transforms.
Notes for today (Updated -- refresh!): Laplace Transform.
Please study relevant parts of 7.2.
Practice problems:
7.2: 1, 3, 5, 9, 13, 15, 17, 35, 37.
Please also try finding the Laplace transform of t^2 from laplace transform of t using formula for Laplace transform of derivative.

3/27/24 Wednesday
GRADES AS OF NOW POSTED ON CANVAS.

QUIZ 9 FRIDAY WILL BE ON 7.1 AND 7.2.

Today we talked about properties of Laplace Transforms.
Notes for today (Updated -- refresh!): Laplace Transform.
Also please read Written notes from class.
Please study relevant parts of 7.1.
Practice problems:
7.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23.
I will give practice problems from 7.2 tomorrow but for today try finding the Laplace transform of t^2 from laplace transform of t using formula for Laplace transform of derivative.

3/25/24 Monday
Today we talked about Laplace Transforms of piecewise functions and exponential functions.
Notes for today (Updated -- refresh!): Laplace Transform.
Also please read Written notes from class.
Please study relevant parts of 7.1.
Practice problems:
7.1: 1, 3, 5, 7, 9, 11, 19, 21, 23, 25.


3/22/2024 Friday
Please read the solutions for the quiz 8.
Quiz 8 solutions

Quiz 8 problems

We will continue with 7.1 on monday.

QUIZ 8 on 6.2 and 7.1 on friday. See below for more.

3/20/24 Thursday
Today we talked a bit about Airy's function and started Laplace Transforms.
Notes for today (Updated -- refresh!): Laplace Transform.
Also please read Written notes from class.
Please study relevant parts of 7.1.
Practice problems:
7.1: 19, 21, 23, 25.


3/20/24 Wednesday
Today we finished talking about power series and second order equations, including singular points.
Notes for today (Updated -- refresh!): Power series and Differential Equations.
Notes for today (Updated -- refresh!): Written notes from class.
Please study relevant parts of 6.2.
Practice problems:
6.2: 1, 3, 5, 7, 9, 11, 13, 15.


3/18/24 Monday
Today we started talking about power series and second order equations.
Notes for today (Updated -- refresh!): Power series and Differential Equations.
Please study relevant parts of 6.2.
Practice problems:
6.1: 3, 5, 7, 9, 11.


3/15/2024 Friday
Please read the solutions for the test 2.
Test 2 solutions

Test 2 problems

We will start 6.2 on monday.

TEST II FRIDAY MAR 15.
QUIZ 7 will be on 5.1 and 6.1.
TEST II WILL COVER 3.1, 3.2, 4.1 to 4.4 and 5.1 and 6.1.
Please use this study-guide .
Please also study class notes, practice problems and quiz solutions.
IF YOU HAVE ACCESS TO WEBASSIGN, YOU CAN DO THE PRACTICE TEST AS AN ASSIGNMENT THERE, AND MAKE USE OF ADDITIONAL FEATURES.

.

3/13/2024 Wednesday
Please read the solutions for the quiz 7.
Quiz 7 solutions

Quiz 7 problems

We will do a review for the test tomorrow (Thursday).

3/11/24 Monday
Today we started talking about power series and first order equations.
Notes for today (Updated -- refresh!): Power series and Differential Equations.
Please study relevant parts of 6.1.
Practice problems:
6.1: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 35, 37.


3/1/24 Friday
Today we started talking about power series and functions.
Notes for today (Updated -- refresh!): Power series and Differential Equations.
Please study relevant parts of 6.1.
Practice problems:
6.1: 1, 3, 5, 7, 9, 11, 13, 15.


2/29/24 Thursday
Today we finished talking about application of 2nd order linear ODE to simple harmonic motion such as spring, pendulum, etc.,.
Notes for today (Updated -- refresh!): Applications of Higher Order Differential Equations.
Please study relevant parts of 5.1.
Practice problems:
5.1: 1, 5, 9, 11, 25, 27, 31, 35, 37.


2/28/24 Wednesday
Today we talked about application of 2nd order linear ODE to simple harmonic motion such as spring, pendulum, etc.,.
Notes for today (Updated -- refresh!): Applications of Higher Order Differential Equations.
Please study relevant parts of 5.1.
Practice problems:
5.1: 1, 5, 9, 11.


2/26/2024 Monday
Please read the solutions for the quiz 6.
Quiz 6 solutions

Quiz 6 problems

We will start 5.1 wednesday.

2/23/24 Friday
For QUIZ 6 on monday please study 4.2, 4.3 and 4.4.
Today we talked about solution of 2nd order linear non-homogenous ODE using undetermined coefficients.
Notes for today (Updated -- refresh!): Higher Order Differential Equations.
Extra Notes (slightly trickier probems): More on Nonhomogenous Equations.
Please study relevant parts of 4.4.
Practice problems:
4.4: 5, 15, 21, 31, 33.


2/22/24 Thursday
Today we talked about solution of 2nd order linear homogenous ODE using auxiliary equation.
Notes for today (Updated -- refresh!): Higher Order Differential Equations.
Please study relevant parts of 4.3.
Practice problems:
4.3: 1, 3, 5, 7, 9, 11, 29, 31, 33, 37, 39.


2/21/24 Wednesday
Today we talked about solution of 2nd order linear ODE using reduction of order.
Notes for today (Updated -- refresh!): Higher Order Differential Equations.
Please study relevant parts of 4.2.
Practice problems:
4.2: 1, 3, 5, 9.


2/16/2024 Friday
Please read the solutions for the quiz 5.
Quiz 5 solutions

Quiz 5 problems

We will do 4.2 wednesday.

QUIZ 5 on FRIDAY Feb 16; TEST II FRIDAY MAR 15.

2/15/24 thursday
Today we talked about linear independence, Wronskian, and fundamental solutions of higher order linear ODE solutions.
Notes for today (Updated -- refresh!): Higher Order Differential Equations.
Notes from whiteboard: Linear independence and Wronskian.
Please study relevant parts of 4.1.
Practice problems:
4.1: 1, 3, 5, 9, 13, 31, 33, 15, 17, 23, 25, 27.


2/14/24 Wednesday
Today we started with higher order linear ODE solutions.
Notes for today: Higher Order Differential Equations.
Please study relevant parts of 4.1.
Practice problems:
4.1: 1, 3, 5, 9, 13, 31, 33


2/12/24 Monday
Today we discussed the applications of first order ODEs.
(Updated, reload!) Modeling using First Order Differential Equations

Included solution of problem 35 (pages 17 AND 18) discussed in class.
Please study relevant parts of 3.1 and 3.2.
Practice problems:
3.1: 1, 3, 5, 7, 9, 10, 11, 13, 19, 21, 25, 35.
3.2: 1, 3.


2/9/2024 Friday
Please read the solutions for the test 1.
Test I solutions

Test I problems

We will do 3.1 monday.

TEST I NEXT FRIDAY FEB 9 ; REVIEW FOR TEST 1, ON THURSDAY FEB 7 ; STUDY ALL OF CHAPTERS 1 AND 2.

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

2/7/2024 WEDNESDAY
TEST I FRIDAY. SEE ABOVE FOR DETAILS.

We discussed numerical methods to solve differential equations.
(Updated; please refresh) Notes for today: First order linear equations . See last section on Euler's method.
Please try 1, 3, 5, 7 of 2.6.

2/5/2024 Monday
Please read the solutions for the quiz 4.
Quiz 4 solutions

Quiz 4 problems

We will do 2.6 wednesday.

2/1/2024 THURSDAY
QUIZ 4 MONDAY ON 2.3, 2.4 AND 2.5.

We discussed substitution methods to solve differential equations.
(Updated; please refresh) Notes for today: First order linear equations
Included in the notes (after section on exact equations) is the question for today about volume of a cylinder.
Please try 3, 7, 9, 13, 15, 19, 27, 29 of 2.5.

1/29/2024 WEDNESDAY
We discussed exact differential equations.
Notes for today: First order linear equations
Please try 3, 7, 11, 13, 17, 25, 27 of 2.4.

1/26/2024 Friday
1/29/2024 MONDAY
We discussed linear differential equations.
Notes for today: First order linear equations
Please try 5, 7, 13, 17, 25, 27, 37 of 2.3.

1/26/2024 Friday
Please read the solutions for the quiz 3.
Quiz 3 solutions

Quiz 3 problems

We will finish 2.2 and start 2.3 on wednesday.

1/25/2024 THURSDAY
Quiz tomorrow based on 1.3, 2.1, 2.2.
We discussed phase portraits and separable differential equations.
Notes for today: First order equations (phase prtraits and separable equations)
Please try 7, 17, 23, 27, 31, 33 of 2.2.

1/24/2024 WEDNESDAY
We discussed direction fields and isoclines of differential equations.
Notes for today: First order equations (autonomous equations)
Please try 2.1: 1, 3, 19, 21, 23 of 2.1.

1/22/2024 Monday
Please read the solutions for the quiz 2.
There was an error in problem 2. I have given credit for any work on it that was reasonable.

Quiz 2 solutions

Quiz 2 problems

We will start 2.1 on wednesday.

1/19/2024 FRIDAY
QUIZ 2 ON MONDAY will be based on 1.1 and 1.2. See practice problems below.
We discussed modeling of differential equations.
Notes for today: Modeling and Differential Equations
Please try 1, 3, 5, 7, 9, 11, 13, 17, 21 of 1.3.

1/18/2024 THURSDAY
If all goes well there will be a quiz tomorrow. If university moves classes online due to snow we will just have a regular class.
We discussed existence and uniqueness of solutions.
Notes for today: Existence and interval of definition of solutions for Differential Equations
Please try 17, 19, 21, 23, 25, 27 of 1.2.

1/17/2024 WEDNESDAY
If all goes well there will be a quiz on friday. We discussed interval of definition of solutions, and solutions given in different forms -- differential form , implicit form, and piecwise.
Notes for today: Existence and interval of definition of solutions for Differential Equations
Please try 15, 17, 19, 21, 23, 25, 29, 31, 33 of 1.1.

1/12/2024 friday
Please read the solutions for the quiz 1.
Quiz 1 solutions

Quiz 1 problems

Have a great weekend!

1/11/2024 THURSDAY
For the quiz tomorrow please study class notes, the video, and try the practice problems 1,3,5,7 from 1.1 and 1, 7, 11 from 1.2. We went over similar problems in class.
I have sent the video of the class by email (via canvas). If you didn't get it please check your spam forlder.

1/9/2024 Tuesday
We will have a quiz on friday, if all goes well.

Here are solutions for the calculus review problems.
Review solutions

Review problems

We will go over these in class tomorrow.

1/8/2024 MONDAY
We will discuss how integration process is basically the solving of differential equations and then started talking about how the models for the spread of coronavirus infections were made using differential equations.
Notes for wednesday and today: Introduction to Differential Equations


Here are solutions for Final exam given last semester.
Final exam solutions

Final exam problems

Look forward to seeing you in class!

In order to build tall buildings or planes, architects and engineers use modeling and simulation inside wind tunnels, the design of which uses Differential Equations .
There is an excerpt from the NASA article on differential equations used in design of wind tummels in the "Introduction to Differential Equations" above.
Here is an article about "supertall" skyscrapers : 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.