Download Calculus II (Lamar University, 2007, 371 pages, 2.53 MB pdf file)

As a prerequisite to this text, you should have worked through the material in Calculus I (or any other introductory calculus text, please see the link at the bottom of this page). As Dawkins correctly says, Calculus II is not easy, and if you do not have a good foundation in Calculus I it will be even more difficult.

Dawkins first covers the standard integration techniques like integration by parts, trigonometric substitutions and partial fractions. Very interesting is the section on "Integration Stategy", starting at p. 55. Even if you already have some experience with integration techniques you might want to take a look at Dawkins approach and see if you find it useful. One final step that Dawkins does not mention in his strategy is "Give up and ask Mathematica (or Maple or an advanced calculator or Wolfram Alpha )". There is a good reason he does not mention this, because it is simply not an option if you have to take an exam. But if you study mathematics on your own and you just need it as a tool, it does not make much sense to spend an hour with a complicated integral when a computer can perform this task in a split second. However, you should be able to solve some simple integrals in your head, so that you can follow the discussion in a textbook without having to switch to your computer constantly.

The next chapters cover applications of integrals (arc length, surface area, centre of mass, some hydrostatic calculations and probability), parametric equations and polar coordinates, sequences and series, vectors and the three dimensional space (including cylindrical and spherical coordinates).

As in his Calculus I text, Dawkins offers many good examples with detailed solutions. One thing that has changed is that the proofs are now integrated in the main text. I liked his approach in Calculus I better, where all the proofs are in one special chapter at the end of the text.

You may also be interested in Calculus III by Dawkins and some other recommendations for Introductions to Calculus.

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