August 25 |
First Day of Class Policies |
- Class policies for the semester
- Tentative day-by-day outline of the course
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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
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August 27 |
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- Finding useful substitutions to simplify integrals
- Evaluating indefinite integrals
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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')
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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
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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
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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
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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
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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
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September 26 |
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- 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
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October 8 |
Summary of Euler's Method, Slope Fields and Separation of Variables
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- 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
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October 22 |
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- Non-revolution volumes
- Volume of revolution
- Arc length
- Applications of integrals to physics (work)
- Separation of variables
- Integrating factors
- Method of undetermined coefficients
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November 6 |
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- nth term test for divergence
- Integral test
- Ratio test
- Comparison test
- Alternating series test for convergence
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November 19 |
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- Infinite series
- Power series
- Taylor series
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December 5 |
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