Final, May 11, 7-10pm, 314 Altgeld

Content of the final

The exam will cover the entire course. The content for the previous hour exams, lecture notes, quizzes, and homework problems are a good guide as to the general types of problems. I will provide some basic trigonometric identities, some integrals, and other formulas as needed for the specific problems on the final.

I have provided below some excercises which could be used to prepare for the exam. Solving all these problems, however, is neither necessary nor sufficient to succeed on the exam.

  • Simple substitutions, integration by parts for definite and indefinite integrals. Excercises 6.1: 1-49; Excercises 6.2: 1-26
  • Trigonometric techniques of integration: powers of trigonometric functions, trigonometric substitutions. Excercises 6.3:1-30
  • Integration of rational functions, partial fractions. Excercises 6.4:1-16
  • Improper integrals: discontinuous integrand, infinite limit of integrations, comparison test Excercises 6.6: 1-34
  • Differential equations. Exponential growth and decay. Excercises 7.1: 1-8.

  • Sequences: convergence, divergence, all the section 8.1 except for the proof of theorem 1.4. Excercises 8.1: 11-25, 33-38
  • Series: definition of convergence, geometric series, k-th term test, harmonic series, all the section 8.2. Excercises 8.2: 1-22
  • Integral test and comparison tests, p-series test, limit comparison test. Excercises 8.3: 1-34
  • Alternating series, convergence test. Excercises 8.4: 1-24
  • Absolute convergence, conditional convergence, ratio test, root test, all the section 8.5. Excercises 8.5: 1-38
  • Power series. Interval and radius of convergence. Excercises 8.6: 15-30

  • Taylor series and its applications. Construction. Remainder term. Estimating the error. Limits. Binomial Series. Excercises 8.7: 1-8,9-14 and Excercises 8.8: 7-12, 33-36
  • Parametric equations, different parametrizations, orientation. Excercises 9.1: 1-10,25-30,31-40,41-44
  • Calculus of parametric equations, tangents to a curve, velocity, enclosed area. Excercises 9.2: 1-6,9-14,15-20,21-24

  • Arc length and surface area for parametric equations. Finding surface area of the surface of revolution given by parametric equations. Excercises 9.3: 1-12 (without evaluating integrals)
  • Extra credit problem: Polar coordinates. Converting equations from polar to rectangular coordinates. Finding slope, area, and arc length in polar coordinates. Excercises 9.4: 19-26
  • Extra credit problem: Conic sections. Definitions and derivations of equations for ellipses, parabolas, and hyperbolas. Definitions of focai, directrix, vertices. Being able to write the equations of conics knowing vertices, focai, etc. Asymptotes of hyperbolas.

    • Length of the final

    I expect to have 16-18 problems for the final and I will prepare it as a 2-2.5 hour exam. It is possible, of course, to take all three hours to finish the exam. There will be one or two extra credit problems on the material that was not covered by homeworks and quizzes (see above).

    Grades

    Since the week of finals is very busy and it takes a long time to grade the final, the grades may appear rather late, but before the university deadline.