Calculus Website Checklist


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For help with , see my post on typesetting with in WordPress.

  1. Blog Post: 'Differential equations, slope fields, and Euler's Method.' It should contain:
    1. Nicely labeled link to your Slope Fields (#74) and Slope Fields lab (#76) handouts
    2. Under a heading of 'Big Ideas', copy and answer these questions:
      1. In algebra, the solutions we find to equations are numbers. How would you characterize solutions to a differential equation?
      2. What is a slope field, and how is it useful?
      3. What is the idea behind Euler's method, and why would we use Euler's method?
  2. Blog Post: 'Anti-derivatives, definite integrals, and -substitution.' It should contain:
    1. Nicely labeled links to your AP Practice (#60) and -substitution practice (#66) handouts
    2. Under a heading of 'Big Ideas', copy and answer these questions:
      1. What is the difference between an anti-derivative and a definite integral?
      2. Why is , but ?
      3. Describe your approach to finding an anti-derivative via -substitution. Illustrate your process by explaining how you find .
  3. Blog Post: 'Riemann sums.' It should contain:
    1. Nicely labeled links to your Riemann Sums intro (#55) and Riemann Sums lab (#56) handouts
    2. Embed your publicly shared Google spreadsheet, and provide a link to it as well.
    3. Embed your publicly shared desmos calculation, and provide a link to it as well.
    4. Under a heading of 'Conclusions', answer these questions:
      1. What do the left-hand and right-hand Riemann sums converge to for a positive-valued continuous function on an interval ?
      2. How do we interpret this limit if the function is not always positive-valued?
      3. Under what conditions can you be certain that the left-hand Riemann sum will be less than the right-hand Riemann sum?
  4. Blog Post: 'Related rates.' It should contain:
    1. Scan of your Related rates and related rates review handouts
    2. We discussed how to approach a related rates problem, using a framework of steps. Describe the steps of the framework you use when approaching a related rates problem.
    3. Embed an exemplary problem from your scanned handout, and explain how you applied your framework to solve the problem.
  5. Blog Post: 'Quotient Rule'. It should contain:
    1. Using LaTeX, write the quotient rule at the top of your post.
    2. Link to scan of your Quotient rule handout
    3. Create a function that requires the quotient rule to differentiate. Find the derivative, and in desmos, graph the function and its tangent line for values of , where has a slider. Link your blog post to this graph.
  6. Blog Post: 'Product Rule'. It should contain:
    1. Using LaTeX, write the product rule at the top of your post.
    2. Link to scan of your Product rule handout
    3. Create a function that requires the product rule to differentiate. Find the derivative, and in desmos, graph the function and its tangent line for values of , where has a slider. Link your blog post to this graph.
  7. Blog Post: 'Tangent line approximation.' It should contain:
    1. Scans of your tangent line approximation handouts (Tangent approximation practice and Tangent approximation)
    2. Embed a linked desmos graph from problem 3 of Tangent approximation practice
    3. Explain how you can use the tangent of a function to approximate the function for values of that are close to the point of tangency.
  8. Blog Post: 'Exponential functions'. It should contain:
    1. Link to scan of your Exponential functions handout
    2. Embedded graph linked to desmos showing
    3. Link to spreadsheet showing t-chart values for finding the limit.
    4. Commentary explaining how the graph and chart suggest a limit as goes to 0.
    5. Using LaTeX, write the differentiation rule you discovered for .
  9. Blog Post: 'The Binomial Theorem'. It should contain:
    1. Link to scan of your The Binomial Theorem handout
    2. Screenshot of your notes on Pascal's Triangle and the Binomial Theorem.
  10. Blog Post: 'The Derivative'. It should contain:
    1. Scan of your The Derivative handout
    2. Screenshot of your Grapher envelope you created
    3. Screenshot of your answer to problem #5.
    4. At the bottom of your post, answer the questions below. Wrap each question in a level 4 header, followed by the answer in paragraph form.
      1. What is a secant of a function?
      2. What is a tangent of a function?
      3. What is the derivative of a function?
  11. Blog Post: 'Secant and tangent lines of a function.' It should contain:
    1. Scan of your Dropping the ball handout
    2. Embed your desmos graph of your secant line from problem 4 of Dropping the ball handout.
    3. Embed your Google Spreadsheet graph of height vs. time.
    4. Scan of your Tangents to a Parabola handout

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