StudyGuide_FinalExam

# StudyGuide_FinalExam - MATH 4BDierential Equations Fall...

• Test Prep
• 22
• 100% (1) 1 out of 1 people found this document helpful

This preview shows page 1 - 4 out of 22 pages.

MATH 4B–Di erential Equations, Fall 2016 Final Exam Study Guide GENERAL INFORMATION AND FINAL EXAM RULES The exam will have a duration of 3 hours. No extra time will be given. Failing to submit your solutions within 3 hours will result in your exam not being graded. The Final Exam is comprehensive. The sections are 1.1–1.3, 2.1–2.6, 3.1–3.7, 6.1–6.4, 7.1–7.9. 35% of the questions will be from Chapters 1 and 2, 35% from Chapters 3 and 6, and 30% from Chapter 7. You can bring ONE index card of dimensions up to 5 00 6 00 . This index card should be handwritten and can be filled on both sides. However, note cards of higher dimensions than the ones mentioned above or typewritten WILL NOT be allowed. Calculators WILL NOT be needed, nor allowed for this exam. Last but not least, CHEATING WILL NOT BE TOLERATED. 1
SKILL’S LIST Verify that a given function is a solution for an Initial Value Problem (IVP). Sketch the direction (slope) fields of an ODE. Find equilibrium solutions for Au- tonomous ODEs, and determine whether equilibrium solutions are semistable or not. Solve a separable ODE and corresponding IVP. Find the general solution to a first order linear ODE. Determine if an ODE is exact. Solve an exact ODE. Read information from a word problem, and establish the corresponding ODE modeling the situation in the following cases: 1. Free falling object. 2. Population growth and decay. 3. Tank model. 4. Newton’s law of cooling. 5. Springs. Determine whether two functions y 1 ( t ) , y 2 ( t ) form a fundamental set of solutions for a second order linear ODE. Find the general solution for a second order homogeneous ODE with constant coe ffi - cients. Given a solution y 1 ( t ) for a second order linear ODE, use reduction of order to find a second (independent) solution of the form y 2 ( t ) = u ( t ) y 1 ( t ). Find a particular solution for a second order ODE with constant coe ffi cients using the method of undetermined coe ffi cients, and/or variation of parameters. Find the general solution to a second order ODE with constant coe ffi cients. Solve Initial Value Problems associated to a second order ODE with constant coe ffi - cients. 2
Compute the Laplace transform of a given function. Compute inverse Laplace transforms to rational functions and piecewise continuous functions. Use Laplace transforms to solve second order IVP. Compute the determinant of a matrix (2 2 or 3 3 would su ffi ce). Find the eigenvalues and eigenvectors of a matrix. Find the inverse of a matrix. Find the canonical Jordan form of a 2 2 matrix. Find the general solution of a homogeneous system of linear ODEs with constant coe ffi cients. Find the fundamental matrix of a system of linear ODEs with constant coe ffi cients.

Want to read all 22 pages?

Want to read all 22 pages?

#### You've reached the end of your free preview.

Want to read all 22 pages?

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern