Math 122 

Fall 2008

Handouts from Lectures

Instructor: 
Dale Winter
6124 Wean Hall
(412) 268-8419
amanita@andrew.cmu.edu

Many of the files on this site are posted in PDF format. If you have any trouble reading them, try downloading the latest version of the free Adobe Acrobat Reader software.

  The handouts distributed and used in lectures are listed in the table below.

Click on the title of the handout to download a copy in PDF format.

Date Title Summary
August 25 First Day of Class Policies
  • Class policies for the semester
  • Tentative day-by-day outline of the course
August 25 Acceleration Ranking Activity
  • Ranking people, animals and vehicles on acceleration to 20 km/hr
  • Example of how integrals can be used to solve problems
August 27
  • Finding useful substitutions to simplify integrals
  • Evaluating indefinite integrals
August 27 Integration by parts
  • Identifying u and v' in integrals
  • Finding u' and v
  • Substituting into the integration by parts formula
  • Using classical integration by parts tricks (e.g. including a factor of 1 as v')
September 5 Integration by partial fractions
  • Recognizing when partial fractions are feasible
  • Factoring the denominator of a rational function
  • Recognizing the case(s) of partial fractions that need to be used
  • Setting up and solving linear equations to find the coefficients in the partial fraction decomposition
  • Integrating the partial fraction decomposition to find antiderivatives
September 10 Approximating integrals using Riemann Sums and the Trapezoid Rule
  • Evaluating left and right hand Riemann sums on a calculator
  • Approximating areas under curves using the Trapezoid rule and a calculator
September 17 Miscellaneous Review Problems for Unit Test 1
  • Over and under estimates of definite integrals
  • Integration using trigonometric substitution
  • U-substitution
  • Completing the square
  • Error estimate for Midpoint rule
  • Estimating area under a curve using a sum on a calculator
September 24 Volumes of revolution
  • Envisioning a volume of revolution in three dimensions
  • Breaking a complicated shape into simpler shapes
  • Creating and evaluating a definite integral to calculate a volume of revolution
September 26 Volumes of revolution by the shell method
  • Breaking a given shape down into a collection of cylindrical shells
  • Finding a formula for the volume of a cylindrical shell
  • Creating and evaluating a definite integral to calculate a volume of revolution
September 26
  • Using a density function to decide how to slice up a given volume
  • Creating a formula for the volume of a spherical shell
  • Creating a formula for the mass contained within a spherical shell
  • Setting up and evaluating a definite integral to compute total mass when density varies
October 8 Summary of Euler's Method, Slope Fields and Separation of Variables
  • Estimating numerical function values from a derivative and one function value
  • Approximating the graph of a function defined by its rate of change
  • Working backwards from the derivative to find a formula for a function
October 22
  • Non-revolution volumes
  • Volume of revolution
  • Arc length
  • Applications of integrals to physics (work)
  • Separation of variables
  • Integrating factors
  • Method of undetermined coefficients
November 6
  • nth term test for divergence
  • Integral test
  • Ratio test
  • Comparison test
  • Alternating series test for convergence
November 19
  • Infinite series
  • Power series
  • Taylor series
December 5
  • Everything!