MATH 101, January - April 2009 — Integral Calculus with Applications to Physical Sciences and Engineering

INFORMATION ABOUT THE APRIL 2009 MATH 101 FINAL EXAM

Comments about this year’s final exam:

1. The exam will begin with several short-answer questions, as in recent April final exams. Full marks will be given for correct answers, and at most 1 point for an incorrect answer. Answers should be simplified.
2. Later questions are full-solution problems, for which all work must be shown. Answers do not need to be simplified unless requested otherwise. At least 2/3 of the questions on the final exam will be similar to the suggested homework problems. The homework problems are a good indication of material for which students are responsible.
3. Students are responsible for all topics included in this year’s course outline. All of these topics are contained within the relevant sections of the textbook. Note the following:
   • in §5.2, students are not responsible for memorizing formulas 5, 6, and 7 (etc.) on p. 369 (if such a formula is required to do a question on the final exam, it will be given);
   • in §7.2, students are not responsible for the boxed material in the middle of p. 465;
   • in §7.5, students are not responsible for formulas 15, 16, 19, or 20 on p. 484;
   • in §7.7, students are not responsible for memorizing the error-bound formulas (if such a formula is required to do a question on the final exam, it will be given);
   • in §7.8, students are not responsible for the use of l’Hopital’s rule to evaluate improper integrals;
   • for Integration Using Taylor Series, students are responsible only for the material in section 4 of the Course Notes, but should also know the Taylor series listed in section 3 for e^x, sin x, cos x, 1/(1-x), ln(1-x), and tan^-1 (x). In particular, students should know the alternating series estimation theorem (p. 14 of the Course Notes), but are not responsible for the Lagrange remainder formula (page 6);
   • in §8.3, students are not responsible for moments for a system of n particles or Pappus’s Theorem;
   • in §8.5, students are not responsible for memorizing the probability density function for normal distributions (if this function is required to do a question on the final exam, it will be given);
   • in §9.2, students need not memorize Euler's method for numerical solution of differential equations. Students will not be asked to draw direction fields, but may be asked to use direction fields to analyze aspects of solutions, such as equilibria and rough sketches.
   • in §9.3, ignore orthogonal trajectories, but note that Toricelli’s Law is included (if a question on the final exam requires Toricelli’s Law, the law will be stated);
   • in §9.2, and 9.5, students are not responsible for memorizing the differential equations governing electric circuits.
4. Note that past exams may have problems involving second order differential equations (as in sections 17.1 - 17.3). This is no longer part of the syllabus. On the other hand, sections 9.2 and 9.5 are now part of the course, whereas they previously were not. This should be kept in mind when reviewing past exams.
5. No calculators or formula sheets are allowed. Also, cell phones are not permitted.
6. In applications problems, students are expected to be familiar with both the Metric and Imperial systems. Note in particular that in the Imperial system, pounds are a unit of force.
7. The final exam will comprise 50% of students’ final course grades. The final exam will not generally be weighted higher for students who perform better on the final exam than they did during the term, although some allowance may be made for students who perform much better on the final exam than they did during the term. Note however that term marks for each of the sections of MATH 101 will be scaled depending on the section’s performance on the final exam, as explained in the Course Policies section of the MATH 101 homepage.