Take a few minutes to reflect on your experiences with mathematics. Who were your teachers? What have you learned? What would you like to learn? Write about yourself and your experience with mathematics. To get full credit on this assignment, you must do the following:
- Your experience with mathematics. Examples of topics you could write about include:
- Compare the best mathematics teacher you ever had with the worst mathematics teacher you ever had. What makes a good math teacher?
- What was the best experience you ever had with mathematics? What was the worst experience?
- What was the hardest math problem you ever attempted? Were you successful? How did you feel about it?
- What do you find easiest about mathematics, and what gives you the most difficulty, and why?
- The practicality of mathematics. Examples of topics you could write about include:
- Have you ever attempted to solve a math problem just for the fun of it, or do you only do math problems if they are assigned?
- Have you ever done a math problem that had an impact (however small) on your life? If so, describe the impact it had.
- Do you know of any mathematics that has had an impact on your life?
- Your expectations in this course.
- What do you expect to put into this course, and what would you really like to get out of this Calculus course?
- How do your expectations compare with those of the instructor that are printed in lthe syllabus?
- What do you think would be the most helpful thing that could be done in this course to help you succeed?
Review the rules for calculating limits in 1.4. Then read 3.7 L'Hopital's Rule.
Turn in 3.7 #3, 6, 9, 14, 37, 39, 40, 41, 47, 49
- Distinguish between determinate and indeterminate forms of limits.
- Use L'Hopital's rule to calculate limits of the proper form.
- Manipulate a limit with indeterminate form so that L'Hopital's rule applies.
- Find limits (whether you need L'Hopital's rule or not!).
Extra Credit(2): In problem 49, find an example of a non-differentiable function where the indicated limit exists.
Read 6.6 Improper Integrals.
Turn in 6.6 #2, 4 (In 4b, make a table and integrate exactly), 8, 9, 12, 13, 39, 41, 42, 43, 44, 58 (You may use your calculator's integral instead of Simpson's rule, but tell which you use.)
- Distinguish proper vs. improper integrals.
- Evaluate improper integrals using the fundamental theorem of calculus.
- Use the comparison test to determine if an improper integral converges or diverges.
- Bound a tail of an improper integral, and evaluate it numerically.
Read 8.1 Sequences.
Turn in #3, 6, 9, 12, 15, 18, 21, 24, 27, 34, 35, 38, 43
- Find the general term of a sequence.
- Learn to reindex a sequence.
- Find the limit of a sequence.
- Determine when a sequence is bounded.
- Determine when a sequence is monotonic.
- Learn the bounded monotononic sequence theorem.
Read 8.2 Series.
Turn in 8.2 #3, 7, 10, 16, 17, 18, 19, 24, 39, 44, 45, 47
- Tell when a series is convergent or divergent.
- Recognize and sum any geometric series.
- Recognize the harmonic series and know that it diverges.
- Be able to use the nth term test for divergence.
- Sum a telescoping series.
Read 8.3 The integral and Comparison tests; Estimating sums.
Turn in 8.3 #9, 10, 11, 12, 13, 14, 15, 16, 17, 26, 31
- Apply the comparison test.
- Apply the limit comparison test.
- Apply the integral test.
- Estimate the sum of a series given an error bound.
Read 8.4 Other Convergence Tests
Turn in 8.4 #4, 5, 8, 12, 16, 17, 21, 22
- Identify Alternating series.
- Apply the alternating series test.
- Distinguish between Convergence and Absolute Convergence.
- Use the Ratio test to determine convergence or divergence of a series.
- Estimate the sum of a series that converges by the ratio test.
Read 8.5 Power Series
Turn in 8.5 #3, 6, 9, 12, 15, 18, 20, 23
- Identify the center of a power series
- Find the radius of a power series.
- Find the interval of convergence of a power series.
- Estimate values of functions given as power series.
Read 8.6 Representation of functions as power series
Turn in 8.6 #3, 4, 5, 6, 7, 12, 19, 27, 28
- Integrate any power series
- Differentiate any power series
- Find power series related to 1/(1-x) by differentiation, integration, and composition.
Read 8.7 Taylor and Maclaurin Series
Turn in 8.7 #4, 5, 8, 20, 32, 38, 40
- Find a Taylor series for a function
- Use known Taylor series of exp(x), sin(x), cos(x) to find related series.
- Compute binomial coefficients for non-integer powers.
- Compute the binomial series for a (1+x)^k and related series.
Read 8.8 Applications of Taylor Polynomials
Turn in 8.8 #3, 6, 9, 17, 22, 23, 25, 27
- Approximate a function with Taylor Polynomials.
- Estimate the error in a Taylor polynomial approximation.
Read Section 9.1 Parametric Curves
Do 9.1 #5, 6, 9, 10, 16, 19, 22, 24, Write parametric equations for a fancy smiley face.
- Graph parametric equations
- Write parametric equations of circles, ellipses, and lines
- Write parametric equations of functions
Read Section 9.2 Calculus with parametric curves
Do 9.2 #3, 6, 15, 21, 29, 30, 34, 40, 48
- The derivative of a parametric curve
- The area under a parametric curve representing a function
- The arc length of a parametric curve
Read Section 9.3 Polar Coordinates
Do 9.3 #2, 3, 6, 12, 13, 16, 31, 36, 40, 47, 51, 57 (look at only)
- Definition of Polar Coordinates, pole, polar axis
- Why polar coordinates are not unique
- When is a point on a polar graph
- How to graph a polar coordinate graph on your calculator
- How to write polar coordinate equations of
- Circles centered at the origin
- Circles through the origin
- How to convert between Polar and Rectangular coordinates
- The slope of the tangent line to a polar graph (dy/dx)
Read 9.4 Calculus in Polar Coordinates. Find
Do 9.4 #2, 8, 9, 15, 21, 23, 29, 33, 34
- Distinguish between dr/dt, dy/dt, dx/dt, dy/dx
- (H.2) How to set up an integral for the area in polar coordinates
- How to set up an integral for the arc length in polar coordinates
Read 9.5 Conic sections in polar coordinates. Find
Do 9.5 #2, 3, 4, 9, 10, 13, 25
- The general equations of the ellipse, parabola, and hyperbola in Cartesian coordinates.
- How to write an equation for a conic section in polar coordinates
- Given a polar equation, identify the eccentricity
- Given a polar equation, identify the type of conic section
Last Update: September 1, 2008
Ronald K. Smith
Lamoni, IA 50140