# Differential Equations Midterm

MIDTERM DIFFERENTIAL EQUATIONS SUMMARY (1)FirstOrder (a)Linear Homogeneous: y0+p(t)y= 0 Non-homogeneous(usevariationofparameters): y0+p(t)y= g(t). (b)Separable: dy dt = f(t) g(y) (c)Exact: M(t;y)+N(t;y)dy dt = 0 with @M @y @N @t = 0 (d)(Separable)Homogeneous dy dt = f(y=t) (e)Generalequation: dy dt = f(x;y) Picarditerates Existenceofsolutions (2)SecondOrder (a)Liner. MMAT 5520 Differential Equations & Linear Algebra Mid-term Exam (31 Oct 2012) Solution Time allowed: 90 mins Each question carries 10 marks 1. Solve dy dx = 2 xy x 2 - y 2. Solution: Rewrite the equation as dy dx = 2 y/x 1 - ( y/x ) 2 which is a homogeneous equation. Using substitution y = xu, we have u + x du dx = dy dx = 2 u 1 - u 2 x du dx = u + u 3 1 - u 2 (1 - u 2 ) du u (1 + u 2 ) = dx x Z 1 u - 2 u 1 + u 2 du = Z dx x log ( u ) - log (1 + u 2 ) = log ( x ) + C log ( y.

Studying MATH2060U Differential Equations at University of Ontario Institute of Technology? On StuDocu you find all the lecture notes, summaries and study guides for this course.

**Spring 2015**

**Instructor: Enrique TreviĆ±o****Lectures:**MWF 9:00 - 9:50 pm in Young Hall 111**Office Hours:**MWF between 11:00am and 12pm. You can also arrange a meeting by appointment.**Office:**Young Hall 105**Email:****Phone Ext.:**#6187

**Announcements**

The **final exam** will be on Tuesday May 5 from 1:30pm to 4:30pm. Remember that you can bring a cheat sheet to the final. You can write whatever you want on both sides of the sheet, but you can only use one sheet.

The second midterm will be split into two parts (just like Midterm 1). The first part will cover problems from Chapter 7 (systems of first-order differential equations) and will be on Wednesday April 15. The second part of the midterm will cover problems from Chapter 5 (series solutions of second-order differential equations) and will be on Friday April 17.

You are allowed to bring a one-sided cheat sheet for part 1 and another one-sided cheat sheet for part 2 (only write on one side of your sheet).

For the midterm you are allowed to write down formulas on one sheet of paper (you can use both sides). You will turn in the sheet with your exam. You will use the same sheet on the second part of the exam (I will hand it back at the beginning of the test).

The first midterm will be split into two parts. Part 1 will be on Monday February 23 and cover the topics from the first and second homework assignments. Part 2 will be on Wednesday Feb. 25 and it will cover the topics from the third and fourth homework assignments.

Practice Exam 1.

Practice Exam 1 Solutions.

Some Mathematica Files which I've used in class: (to access them, right-click to save on a computer that has Mathematica. Then open them in Mathematica)

Cannonball with and without air-resistance. Has the equations that come from having the initial value condition of initial velocity and also the case where the initial value condition is the time it takes to reach the apex.

Streamplots and Integral Curves. Some examples we did in class shown visually.

If you need a tutor to help, there is drop-in tutor help for this class in YH 107 or YH 118 at the following times (with the following tutors):

- Sunday: Daniel Acevski from 6pm to 8pm.
- Monday: Brandon Bauerly from 8pm to 10pm.
- Wednesday: Brandon Bauerly from 8pm to 10pm.

**Textbook**

## What Makes A Differential Equation Linear

*Elementary differential equations and boundary value problems* 10-th edition, by W. Boyce and R. DiPrima.

**Topics we will cover**

This course is a survey of important types of differential equations, both linear and nonlinear. Topics include the study of systems of ordinary differential equations, numerical solutions of first and second order equations and of systems, and the solution of elementary partial differential equations using Fourier series. From the textbook, we will cover chapters 1, 2, 3, 4, 5, 7, and 10.

**Grading**

The course grade will be based on:

Homework 15%,

Midterm 1 25%,

Midterm 2 25%,

Final Exam 35%.

**Homework and Quizzes**

There will be written homework roughly every week. The most recent homework will be posted in the announcements and a copy of all homeworks can be accessed here. Collaboration in the homework is permitted, however you must write in your own solutions to the exercises and submit it as your own.

**Exams**

There will be two midterms and one final exam. On the midterms and the final exam you must work on the problems on your own.

**No collaboration permitted**in the exams.

The dates are:

- The first midterm will be on Monday February 23 and on Wednesday February 25.
- The second midterm will be on Wednesday April 15 and on Friday April 17.
- The
**final exam**will be on Tuesday May 5 from 1:30pm to 4:30pm.

**Attendance**

If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

## Differential Equations Midterm 1

**Accommodations Statement**

If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit http://www.lakeforest.edu/academics/resources/disability/.

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.

## Differential Equations Midterm Exam

*Last modified on May 5, 2015. *