DIFFERENTIAL EQUATIONS SECTION 2 FALL 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 0807 4050.
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:SPRING 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.
TUESDAY CLASSES WILL BE ON ZOOM UNLESS OTHERWISE MENTIONED.



12/10/23 Sunday
Please read the solutions below. I might be in office tomorrow.
Final exam Solutions
Final exam Problems


Final exam on Dec 8, 2to 4pm (date for course exams on calendar). Please go to my office if room is locked.
Please study class notes, quiz and test solutions from this semester.
You can also access previous semester's material including final exams from my old course page.

Review in class this friday (Dec 1).
ALL OUTSTANDING ISSUES MUST BE CLEARED BY FRIDAY DEC 1, 4PM.

11/29/23 Wednesday
Please read the solutions below. We will review for final exam on friday.
Test 3 Solutions
Test 3 Problems

TEST 3 ON NOV 29 WED. REVIEW IN CLASS NOV 28 TUESDAY.
WILL COVER 7.1, 7.2, 7.6, 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.

11/27/23 Monday
Today we talked about solving systems of equations coming from electrical networks theory using Laplace transforms.
Please study relevant parts of 7.6.
Practice problems today:
7.6: 15, 17.

11/21/23 Tuesday
Happy Thanksgiving! Please read the solutions below. We will go over some applications on monday.
Quiz 10 Solutions
Quiz 10 Problems

QUIZ 10 tomorrow (tuesday)in person on 7.6 and 8.2.3.
11/20/23 Monday
Today we talked about solving systems using complex eigenvalues as well as Laplace transforms.
(Updated--refresh) Notes for today : systems of ODE's and matrices

Please study relevant parts of 8.2.3 and 7.6.
Practice problems today:
7.6: 1, 3.
8.2: 35, 37, 39.

11/17/23 Friday
Please read the solutions below. We will go over 7.6 (only 1st order ODE applications) and 8.2.3 on monday.
Quiz 9 Solutions
Quiz 9 Problems

QUIZ 9 on friday, 11/17, on 8.2.
11/15/23 Wednesday
Today we talked about solving systems using eigenvalues and eigenvectors of matrices.
(Updated--refresh) Notes for today : systems of ODE's and matrices

Please study relevant parts of 8.2.2.
Practice problems today:
8.2: 21, 23, 31.

11/14/23 Tuesday
Today we talked about eigenvalues and eigenvectors of matrices and systems of ODE's.
Notes for today : systems of ODE's and matrices

Please study relevant parts of 8.2.1.
Practice problems today:
8.2: 1, 3, 5, 7, 9, 13.

11/13/23 Monday
Please read the solutions below. We will go over 8.1 and 8.2 on tuesday.
Quiz 8 Solutions
Quiz 8 Problems

QUIZ 8 on monday, 11/13, on 7.2, 3.3, 8.1.
11/8/23 Wednesday
Today we talked about matrices and systems of ODE's.
Notes for today : systems of ODE's and matrices

Please study relevant parts of 8.1 and 3.3.
Practice problems today:
8.1: 1, 3, 5, 7, 11, 13.

11/7/23 Tuesday
Today we did problems using laplace transform of some functions and also started on systems of ODE's.
Notes for today (Updated --refresh!): Laplace transforms

Please study relevant parts of 7.2 and 3.3.
Practice problems today:
7.2: 7, 11, 13, 17, 19, 23,31, 37 , 39, 41, 45, 47.
3.3: 1, 5, 7.

11/6/23 Monday
Today we found laplace transform of some functions.
Notes for today (Updated --refresh!): Laplace transforms

Please study relevant parts of 7.2.
Practice problems today:
7.2: 7, 11, 13, 17, 19, 23, 37 , 39, 41, 45.

11/3/23 Friday
Please read the solutions below. We will go over 7.2 on monday.
Quiz 7 Solutions
Quiz 7 Problems

QUIZ 7 ON FRIDAY ON 7.1.
11/1/23 Wednesday
Today we found laplace transform of some functions.
Notes for today (Updated --refresh!): Laplace transforms

Please study relevant parts of 7.1.
Practice problems today:
7.1: 1, 3, 5, 7, 11, 13, 19, 21, 25, 29, 31, 33, 35, 37, 43, 45.

10/31/23 Tuesday
Today we found laplace transform of some functions.
Notes for today (Updated --refresh!): Laplace transforms

Please study relevant parts of 7.1.
Practice problems today:
7.1: 1, 3, 5, 7, 11, 13, 19, 21, 25, 29, 31.

10/30/23 Monday
Today we discussed laplace transform and their use to find solutions of ODE's.
Notes for today: Laplace transforms

Please study relevant parts of 7.1.
No practice problems today:


10/27/23 Friday
Please read the solutions below. We will start 5.1 Laplace transforms on monday.
Test II Solutions
Test II Problems

TEST 2 ON OCT 27 FRI. REVIEW IN CLASS OCT 25 WEDNESDAY.
WILL COVER 2.6, 3.1, 3.2, 4.1, 4.2, 4.3, 4.4, 5.1, 6.1, 6.2.

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.

10/24/23 TUESDAY
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.
10/23/23 Monday
Today we discussed power series and how to find the series expansion for functions that are solutions of ODE's.
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.


10/20/23 Friday
Today we discussed power series and functions.
Notes for today: Power series and Differential Equations

Please study relevant parts of 6.1.
Practice problems:
6.1: 1, 3, 5, 7, 9, 11, 13, 15.


10/18/23 Wednesday
FRIDAY CLASS ONLINE DUE TO HOMECOMING!
We went over more of 4.4 today and it will be in next quiz.
Today we also started talking about series.
Notes for today: (Updated, please refresh) Higher Order Differential Equations

Please study relevant parts of 4.4.
Practice problems:
4.4: 7, 9, 13, 17, 27, 29.


10/17/23 Tuesday
We went over more of 4.4 and it will be in next quiz.
Today we also talked about application of second order linear ODE solutions to simple harmonic motion with damping and external force.
Notes for today: (Updated, please refresh) Models using higher Order Differential Equations

Please study relevant parts of 5.1.
Practice problems:
5.1: 31, 35, 37.
Please also try 4.4: 5, 15, 21, 31, 33.


10/16/23 Monday
Please read the solutions below. We will go over 4.4 some more on tuesday.
Quiz 6 Solutions
Quiz 6 Problems

QUIZ 6 MONDAY ON 5.1 AND 5.2. (No 4.4 -- see below).
10/13/23 Friday
We will go over more of 4.4 on wednesday and it will be in next quiz.
Today we talked about application of second order linear ODE solutions to simple harmonic motion with damping.
Notes for today: (Updated, please refresh) Models using higher Order Differential Equations

Please study relevant parts of 5.1.
Practice problems:
5.1: 25, 27.


10/11/23 Wednesday
Today we talked about application of second order linear ODE solutions to simple harmonic motion.
Notes for today: (Updated, please refresh) Models using higher Order Differential Equations

Please study relevant parts of 5.1.
Practice problems:
5.1: 1, 5, 9, 11.


10/10/23 Tuesday
Today we talked about non-homogenous second order linear ODE solutions.
Notes for today: (Updated, please refresh) Higher Order Differential Equations

Please study relevant parts of 4.4.
Practice problems:
4.4: 5, 15, 21, 31, 33.


10/6/23 Friday
Please read the solutions below. We will start 4.4 on monday.
Quiz 5 Solutions
Quiz 5 Problems

QUIZ 5 friday on 4.1, 4.2, 4.3.

10/4/23 Wednesday
Today we continued with higher order linear ODE solutions.
Notes for today: Higher Order Differential Equations

Please study relevant parts of 4.1, 4.2, and 4.3.
Practice problems: (see updates from mon and tue for more)
4.2: 1, 3, 5, 9.


10/3/23 Tuesday
Today we continued with higher order linear ODE solutions.
Notes for today: Higher Order Differential Equations

Please study relevant parts of 4.1 and 4.3.
Practice problems:
4.1: 15, 17, 23, 25, 27.
4.3: 9, 11, 29, 31, 33, 37, 39.


10/2/23 Monday
Today we started with higher order linear ODE solutions.
Notes for today: Higher Order Differential Equations

Please study relevant parts of 4.1 and 4.3.
Practice problems:
4.1: 1, 3, 5, 9, 13, 31, 33
4.3: 1, 3, 5, 7.


9/30/23 Saturday
Please read the solutions below.
Quiz 4 Solutions
Quiz 4 Problems

QUIZ 4 on FRIDAY, on 2.6, 3.1 and 3.2.
9/29/23 Wednesday
Today we continued with the applications of simple linear ODE solutions.
Notes for today: Modeling using First Order Differential Equations

Please study relevant parts of 3.1.
Practice problems:
3.1: 13, 19, 21, 25
3.2: 1, 3.


9/26/23 Tuesday
Today we reviewed the method of Euler and discussed the applications of simple linear ODE solutions.
Notes for today: Modeling using First Order Differential Equations

Please study relevant parts of 3.1.
Practice problems:
3.1: 1, 3, 5, 7, 9, 10, 11.


9/25/23 Monday
Today we discussed the method of Euler to find numerical solutions for differential equations.
(UPDATED-- REFRESH!) Notes for today: First Order Differential Equations

Please study relevant parts of 2.6.
Practice problems:
2.6: 1, 3, 5, 7.


9/22/23 Friday
Please read the solutions below. We will start 2.6 (Euler's method) on monday.
Test I Solutions
Test I Problems

TEST I ON FRIDAY SEP 22. REVIEW IN CLASS SEP 20 WEDNESDAY. WILL COVER ALL OF CHAPTERS 1 AND SECTIONS 1 to 5 of CHAPTER 2.

Please use this study-guide from fall 22 .
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.

9/18/23 Friday
Today we discussed the method of substitution for differential equations and their solutions.
(UPDATED-- REFRESH!) Notes for today: First Order Differential Equations

Please study relevant parts of 2.5.
Practice problems:
2.5: 7, 9, 15, 21, 25.


9/15/23 Friday
Today we discussed exact differential equations and their solutions.
(UPDATED-- REFRESH!) Notes for today: First Order Differential Equations

Please study relevant parts of 2.5.
Practice problems:
2.5: 3, 7, 11, 15, 17, 25, 27.


9/13/23 Wednesday
Please read the solutions below. We will start 2.4 (solving exact equations) on friday.
Quiz III Solutions
Quiz III Problems

QUIZ 3 ON WEDNESDAY, COVERS 2.1, 2.2, 2.3.
9/12/23 Tuesday
Today we reviewed isoclines, phase portraits of differential equations and solutions of linear equations.
Notes for today: First Order Differential Equations

Please study relevant parts of 2.3.
Practice problems:
2.1: 1, 3, 19, 21, 23.
2.2: 7, 17, 23, 27, 49.
2.3: 5, 7, 13, 17, 25, 27.


9/11/23 Monday
Today we talked about phase portraits of differential equations and some separable equations.
Notes for today: First Order Differential Equations

Please study relevant parts of 2.1 and 2.2.
Practice problems:
2.1: 1, 3, 19, 21, 23.
2.2: 7, 17, 23, 27, 49.


9/8/23 Friday
Today we started talking about slope fields and isoclines of differential equations.
Notes for today: First Order Differential Equations

Please study relevant parts of 2.1.
Practice problems:
2.1: 1, 3, 19.


9/6/23 Wednesday
Please read the solutions below. We will start 2.1 (solving first order equations) on friday.
Quiz II Solutions
Quiz II Problems

9/5/23, Tuesday
Today we went over some porblems on modeling with differential equations and also started separable equations.
Next quiz will be tomorrow (wednesday), including all material covered upto tuesday.
Please try practice problems from 1.2 and 1.3 below, given AFTER quiz 1.
Also go through notes from class sent by email. Video of class has been sent as well.

9/1/23 Friday
Today we continued talking about models and differential equations, including population models and mixing problems.
Notes for today: Modelling using of Differential Equations

Please study relevant parts of 1.3.
Practice problems:
1.3: 1, 3, 7, 9, 11, 17.


8/30/23 Wednesday
Today we continued talking about existence and uniqueness of solutions of differential equations of first order of the form y' = f(x,y) and started talking about models and differential equations.
Notes for today: Definition and solutions of Differential Equations

Please study relevant parts of 1.2 and 1.3.
Practice problems:
1.2: 3, 17, 19, 25, 27 (from yesterday).
1.3: 21, 23.


8/29/23 Tuesday
Today we talked about existence and uniqueness of solutions of differential equations of first order of the form y' = f(x,y).
Notes for today: Definition and solutions of Differential Equations

Please study relevant parts of 1.2.
Practice problems:
1.2: 3, 17, 19, 25, 27.


8/28/23 Monday
Quiz I Solutions
Quiz I Problems

QUIZ 1 WILL BE MONDAY, ON 1.1 AND 1.2.

8/25/23 Friday
Today we talked about solutions of differential equations that are defined implicitly and piecewise, as well as differential equations defined using differentials.
Please also read about intervals of solutions (from 1.1) in textbook or notes below.
Notes for today: Definition and solutions of Differential Equations

Please study relevant parts of 1.1 and 1.2.
Practice problems:
1.1: 9, 10, 15, 17, 19, 20, 29, 30. (some of these are in the notes)


8/23/23 Wednesday
Today we talked about linearity of differential equations,and solutions satisfying certain initial conditions.
Notes for today: Definition and solutions of Differential Equations

Please study relevant parts of 1.1 and 1.2.
Practice problems:
1.1: 11, 13, 21, 23.
1.2: 35, 37.


8/22/23 Tuesday
Today we continued talking about applications of differential equations to plotting spacecraft trajectories, developing models for spread of disease (such as coronavirus infection), and design of wind tunnels.
We also found the equation of motion for an object moving at constant acceleration.
Finally we discussed order and linearity of ordinary differential equations (ODE's).
Please study relevant parts of 1.1 and 1.2.
Practice problems:
1.1: 1, 3, 5, 7.
1.2: 1, 7, 11.

On monday we discussed 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 monday and today: Introduction to Differential Equations


8/17/23 THURSDAY
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.