11.3 Solids Of Revolution Washerap Calculus

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MATH – 20B.Calculus

11.3 Solids Of Revolution Washerap Calculus Solver


Summer, July, 2015

MWF,2:00pm-3:50pm, APM B402a.

11.3 Solids Of Revolution Washerap Calculus

Reset Show examples. This calculator is a work in progress and things may not work as expected! In addition, please note that some solids may take longer to graph than others. I introduce the process of finding the volume of a solid, also called volume of revolution, using the Disk Method and Washer Method. There are a few minor c.


Instructor:Professor VladimirRotar; office: APM-7450,e-mail: [email protected]

Officehours:MWF, 4:15-5:15. If itis needed, office hours may be extended.Some short questions may be answered right after the lectures.

Text:Rogawski, Calculus: EarlyTranscendentals, 2ndedition, and

11.3 Solids Of Revolution Washerap Calculus 2nd Edition

The supplement to Rogawski’s book. (downloadhere).

Examinations: Therewill be several quizzes, and a final exam. Homework will be assigned eachlecture and posted in the HW site.

11.3 Solids Of Revolution Washerap Calculus Calculator



The listbelow is rather one of topics than of lectures: the real experience may dictatea slower or faster pace. A slight change of the order of exposition is alsopossible.

  1. Sec. 5.2-5.4: Review of the Fundamental Theorem of Calculus.Sec. 5.5: Total change as the integral of a rate.
  2. Sec. 5.6: The substitution algorithm for integrals.Sec. 6.1: Areas between curves.
  3. Sec. 6.2-6.3: Volumes; average value of a function; the mean value theorem. The basic method is slicing a solid into pieces of known cross-sectional area; solids of revolution are a special case.
  4. Sec. 11.3-11.4: Polar coordinates; areas in polar coordinates.Supp. 1–2: Complex numbers and complex exponentials: De Moivre’s theorem, complex roots, and Euler’s formula.
  5. Sec. 7.1: Integration by parts.Sec. 7.2, 7.4, Supp 3. Trigonometric integrals, Sec. 7.3: Trigonometric substitution (may be omitted).
  6. Supp. 4-5, Sec. 7.5: The fundamental theorem of algebra; partial fractions and integration of rational functions using partial fractions.
  7. MIDTERM (can be replaced by quizzes).
  8. Sec. 7.6: Improper integrals. Sec. 7.8. Numerical integration.
  9. Sec. 10.1: Sequences: limits, convergence, and divergence.
  10. Sec. 10.2: Series. Sec. 10.3: Series with positive terms: the integral and comparison tests.
  11. Sec. 10.4-10.5: Absolute convergence; the ratio and root tests. Sec. 10.6: Power series.
  12. Sec.10.7: Taylor series.
  13. Sec. 9.1-9.2: Solving differential equations; exponential models.