Active Learning Materials for Second Semester Calculus

Source files and solution files

Materials produced at the University of Colorado Boulder for second-semester calculus

As of June 2015, all materials here are in draft form. Please give feedback about errors or typos.

Tactivities:

• Indefinite integral dominoes and User's guide
• Put these sequences in increasing order of rate of growth. (When it is correct, the letters at the bottom spell something.)
• Put these sequences in increasing order of rate of decay. (When it is correct, the letters at the bottom spell something.)
• Sorting sequences:
  • Sort these sequences into four piles: sequences that converge to 0, sequences that converge to something other than 0, sequences that diverge to infinity, sequences that diverge to other than infinity. (Please look at just the third page of this file. When it is correct, the numbers in each pile all have something in common.)
  • You can use this placemat to help with the sorting
• Taylor series matching
  • Match functions with their Taylor Series representations (both sigma notation and expanded form)
  • Taylor series matching user guide
• Slope Field Matching cards (adapted from a project by Nancy Stephenson)
• Matching cards for parametric equations

• For our first-semester calculus materials, please see First semester calculus activities
  
• Indefinite integral dominoes and User's guide
• Antiderivative review
• Worksheet on practicing them mechanics of /du substitutions
• Worksheet on choosing substitutions for u/du substitutions
• Worksheet on integrating flow rates in/flow rates out

• Discovery worksheet for trig integrals
• Discovery worksheet for partial fractions
• Using tables, computer algebra systems, and practice comparing alternate solutions
• Discovery worksheet on approximate integation
• Discovery worksheet on determinging convergence of improper integrals by comparison
• Practice worksheet on choosing which technique of integration to use (includes solutions)

• Practice worksheet on finding areas of regions and volumes of solids
• A variety of applications of integration (getting the big picture of applications)

• Put these sequences in increasing order of rate of growth. (When it is correct, the letters at the bottom spell something.)
• (TACTIVITY) Put these sequences in increasing order of rate of decay. (When it is correct, the letters at the bottom spell something.)
• (TACTIVITY) Sorting sequences:
  • Sort these sequences into four piles: sequences that converge to 0, sequences that converge to something other than 0, sequences that diverge to infinity, sequences that diverge to other than infinity. (Please use just the third page of this file. When it is correct, the numbers in each pile all have something in common.)
  • You can use this placemat to help with the sorting
• Recursive sequences

• Discovery worksheet for geometric series
• Discovery worksheet for Integral test
• Discovery worksheet for Comparison tests for series
• Practice writing full detailed solutions for comparison tests
• Comparison tests - practice choosing what series to compare to
• Series - the big picture
  • Practice choosing what test to use (solutions on last page
  • Reference sheet - list of all tests

• Discovery worksheet for Taylor polynomials
• Turning a geometric series into something new (substitution, multiplication by a constant or a power of x, differentiation, integration)
• Turning a Taylor series into something new (substitution, multiplication by a constant or a power of x, differentiation, integration)
• (TACTIVITY) Taylor series matching
  • Match functions with their Taylor Series representations (both sigma notation and expanded form)
  • Taylor series matching user guide
• Taylor series remainder estimate practice
• An application of Taylor Series

• (TACTIVITY) Slope Field Matching cards (adapted from a project by Nancy Stephenson)
• Discovery project on Euler's method
• Practice modeling with differential equations
• Draining a tank - Toricelli's law (includes a review of related rates
• Mixing problems
• SIR model of Ebola

• (TACTIVITY) Matching cards for parametric equations
• Polar coordinate practice

Materials produced at the University of Nebraska Omaha (UNO)
Note: These materials are largely guided worksheets (mix mini-lecture with group practice)
Note: these materials have only been used for one semester, so consider these a rough draft
Guidance on using the worksheets below

• Review of integration
• Practice with derivatives, definite and indefinite integrals

• Volumes of solids of revolution - disks and washers
• Volumes of solids of revolution - shells
• Volumes of solids - perpendicular slices
• Volumes of all solids - practice
• Arclength
• Work - lifting objects
• Work - pumping fluid
• Area in polar coordinates

• Integrating powers of sin(x) and cos(x)
• Trigonometric substitution
• Practice Trig Integrals
• Integration By Parts
• Improper Integrals
• Mixed Practice Integration
• More Mixed Practice Integration, including improper integrals

• Introduction to sequences (explicit and recursive forms)
• Geometric sequences and series
• Geometric and Telescoping series practice
• Series practice (positive terms)
• More series practice (positive terms)
• Alternating series practice
• Series dominoes (TACTIVITY)

• Introduction to power series and intervals of convergence
• Practice finding intervals of convergence
• Practice finding Taylor series using the formula and by manipulating known series. Practice bounding error.

Materials collected from other sources

Active learning worksheets from University of Arizona