Calculus

=__**Objectives**__:=

** As an IB Learner you are reflective. On your own page of your blog you will need to explain each of these important ideas __ in your own words __: **


** TYPES OF QUESTIONS TO SOLVE: **


 * ===Describe the limit process, including Zeno's paradox.===
 * ===Describe the derivative, including the tangent problem.===
 * ===Describe the integral, including the area problem.===
 * ===Be able to guess the limit of a sequence.===
 * ===Be able to draw the line tangent to a curve at a specified point.===
 * ===Approximate an area by using rectangles.===
 * ===Explain the process of mathematical modeling.===
 * ===Write out the first 5 terms of a sequence when given a general term.===
 * ===Find the limit of a sequence.===
 * ===Solve applied problems involving limits of sequences.===
 * ===Estimate a rate of change by looking at a graph.===
 * ===Estimate the slope of a tangent line by looking at a graph.===
 * ===Find an average rate of change for a given function over an interval.===
 * ===Find an instantaneous rate of change for a given function at a particular point.===
 * ===Find the derivative by using the definition of derivative.===
 * ===Find the equation of a tangent line.===
 * ===Evaluate an area function.===
 * ===Find an antiderivative.===
 * ===Find the area under a curve.===
 * ===Approximate the value of a definite integral by using areas.===

What is Calculus?
**Isaac Newton:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Newton.html**



**Gottfried Leibniz:** **@http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Leibniz.html**

Reference Topic Sites:
@http://www.brightstorm.com/math/calculus/


 * "The limit"**
 * "Archimedes' calculation of pi"**
 * "Secants and tangents"**
 * @http://www.math.psu.edu/dna/graphics.html**

**Discussions on Zeno's paradox:** **@http://mathforum.org/isaac/problems/zeno1.html**

**Article on mathematical modeling and why it is important:** **@http://www.mtholyoke.edu/courses/jmorrow/math_models.html**

Video:

 * Introduction to the limit of a function** (time: 8:44)

Video:

 * Introduction to derivative ** (time: 8:44)

Reference Topic Sites:

 * Check out the following on this site:**
 * "Secants and tangents"**
 * "Zooming in on a tangent line"**
 * @http://www.math.psu.edu/dna/graphics.html**

Reference Topic Sites:

 * Check out** **"Archimedes' calculation of pi"** **on this site:**
 * @http://www.math.psu.edu/dna/graphics.html**