MATH 2270 Final Exam Checklist and Preparation, Exams of Algebra

Important details about the upcoming final exam for math 2270, including the exam format, what to bring and not bring, topics covered, and a recommendation for time management. Students are advised to review sections 6.1-6.5 and be prepared to compute laplace transforms and solve initial value problems using the laplace and inverse laplace transforms.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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MATH 2270 FINAL CHECKLIST
1. Overview
There will be two parts to the final, both closed book. The first
part will consist entirely of material covered subsequent to the material
covered on the last midterm. The relevant sections are 6.1-6.5. There
will be three questions in this part, and you will be asked to do two.
The second part will be comprehensive. You will be asked to do eight
of twelve questions. It is recommended that you take (roughly) half
an hour on Part I and one and a half hours on part II. However, the
division of labour is up to you.
Each question is worth five points, and so the maximum possible
score on the final is 50.
The final will take place in our usual room, B4 518. Our final is on
Monday 28 April from 0930 to 1130.
The late deadline for homework 14 is Monday 28 April 1700.
2. What to bring
You will need a writing implement of some kind. Paper will be
provided.
3. What not to bring
The exam is closed book and calculators are not allowed.
4. Topics List
All Topics from the midterms.
Definition of the Laplace transform. Note that computing a
Laplace transform involves an improper integral. Unless instructed
otherwise, you will compute said integrals in terms of limits.
Compute Laplace transforms. To this end, you will need to be able
to use table 6.2.1 on page 319. I will provide you with a copy of the
table, or at least a subsection of it. However, you should be able to
derive all the identities on table 6.2.1 except number 16 which we will
not use in any case. If the gamma function is involved, I will remind
you of the definition of the gamma function.
Solve initial value problems using the Laplace and inverse Laplace
transforms. I am particularly interested in the situation where the
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MATH 2270 FINAL CHECKLIST

  1. Overview There will be two parts to the final, both closed book. The first part will consist entirely of material covered subsequent to the material covered on the last midterm. The relevant sections are 6.1-6.5. There will be three questions in this part, and you will be asked to do two. The second part will be comprehensive. You will be asked to do eight of twelve questions. It is recommended that you take (roughly) half an hour on Part I and one and a half hours on part II. However, the division of labour is up to you. Each question is worth five points, and so the maximum possible score on the final is 50. The final will take place in our usual room, B4 518. Our final is on Monday 28 April from 0930 to 1130. The late deadline for homework 14 is Monday 28 April 1700.
  2. What to bring You will need a writing implement of some kind. Paper will be provided.
  3. What not to bring The exam is closed book and calculators are not allowed.
  4. Topics List
  • All Topics from the midterms.
  • Definition of the Laplace transform. Note that computing a Laplace transform involves an improper integral. Unless instructed otherwise, you will compute said integrals in terms of limits.
  • Compute Laplace transforms. To this end, you will need to be able to use table 6.2.1 on page 319. I will provide you with a copy of the table, or at least a subsection of it. However, you should be able to derive all the identities on table 6.2.1 except number 16 which we will not use in any case. If the gamma function is involved, I will remind you of the definition of the gamma function.
  • Solve initial value problems using the Laplace and inverse Laplace transforms. I am particularly interested in the situation where the 1

2 MATH 2270 FINAL CHECKLIST

forcing term is discontinuous, since our previous methods don’t work so efficiently in that case. Of course, all the ivps in this situation will be linear with constant coefficients.

  • Definition of a Heaviside function. Sketch graphs of functions defined in terms of step functions.
  • Derivation and definition of the Dirac delta function. Most of the problems in 6.5 have that silly little mouse icon. You will not need a computer for any problems involving the Dirac delta function that I ask on the final.
  1. Practice Final The practice final will feature questions similar in style and content to that of part I of the actual exam. For questions related to the other part of the exam, see the midterms and practice midterms. Topics covered on the midterms and the practice exams may or may not be covered on the actual exam, and topics on the actual exam may or may not have appeared on the practice exam.