- Address each of the three areas (1, 2, 3) below.
- Email your paper (no more than 2 pages) to me by midnight Thursday night with the subject line:
MATH2510 HW0 [last name], [first name]

- 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?

- 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.

- 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.

- 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.

- 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.

- Apply the comparison test.
- Apply the limit comparison test.
- Apply the integral test.
- Estimate the sum of a series given an error bound.

- 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.

- 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.

- Integrate any power series
- Differentiate any power series
- Find power series related to 1/(1-x) by differentiation, integration, and composition.

- 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.

- Approximate a function with Taylor Polynomials.
- Estimate the error in a Taylor polynomial approximation.

Find

- Graph parametric equations
- Write parametric equations of circles, ellipses, and lines
- Write parametric equations of functions

Find

- The derivative of a parametric curve
- The area under a parametric curve representing a function
- The arc length of a parametric curve

Find

- 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
- Cardioids
- Limacons
- Roses

- How to convert between Polar and Rectangular coordinates
- The slope of the tangent line to a polar graph (dy/dx)

- 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

- 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

Graceland University

Lamoni, IA 50140

rsmith@graceland.edu