First exam

Topics and Sections for the first exam.

  1. Differentiation, integration and applications of the natural logarithm ln, log to the base e, and its inverse, the exponential function, e to the x. Chapter 8.
  2. Integration by substitution; effectively the chain rule in reverse. General power rule, logarithm form, exponential form, basic trigonemtric forms. Using the five trig identities on page 298 to help with integration. Inverse trig functions, mainly arcsin and arctan. Applications of these techniques. Chapter 9.
  3. Integration by parts. Pay attention to the guidelines on page 311. More on integration by substitution. Trig substitutions. Using partial fractions to prepare for integration. Integration by use of tables. Caution: you may need to make a substitution in order to use the tables. Or you many need to apply integration by parts in order to make effective use of the tables. Make sure you can make the transition from indefinite integrals to definite intergals so you can make use of the FTC . Plus applications of the above integration techniques techniques. Sections 10.1 to 10.6.
  4. Improper integrals--integrals for which the FTC does not apply. Indefinite integrals with infinite upper, infinite lower limits and integrands that have one or more vertical asymptoes between the upper and lower limits do not satisfy the conditions of the FTC . Applications of improper integrals. Section 10.7.
  5. Partial derivatives and their applications. Section 11.3.

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