Calculus I  Math 151
 Course Contract
 Lab Schedule
 Walker_221 Computer Lab 11/19/2008 2:00 PM
 4:00 PM
Walker_216 Computer Lab 12/01/2008 2:00 PM  4:00 PM
Walker_216 Computer Lab 12/03/2008 2:00 PM  4:00 PM Walker_216 Computer Lab 12/08/2008 2:00 PM  4:00 PM
 Writing A Calculus I (Math 151)
Project
1. Objective: To learn how Calculus is linked to your chosen major or field.
2. Guidelines:
a. You may choose up to three classmates to form a group.
b. You need to identify a reallife problem in your fields that you would like to do. (For example, it could be an optimization problem.)
c. You need to use technological tools to demonstrate how you use Calculus to achieve your answer.
3. Writing up your report: You need to prepare a Word or PowerPoint file
4. Oral presentation: December 10.
Topics
 CASIO files
 Line Equations (Casio file).

Finding Domains and Shifting Techniques.
 A Casio file. (lab 1)
 A Maple file. (lab 1)
 Drills of finding domain of a function.
 A Java Applet (lab 1)
 Practices on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
 Drill on composite functions.
 (skip) Exercises on Quadratic Functions
 Polynomial functions (CASIO) (Maple)lab 2
 Rational functions (CASIO) (Maple)lab 2
 Find two rational functions f which
satisfy all the following conditions, and use Maple to
check your answers:
 the vertical asymptotes of f are at x=1 and x=3;
 the horizontal asymptote of f is at y=2;
 f(0) = 3.
 Peer instruction (an old review sheet).
 (read on your own) How the number e is being found.
(A
Java applet, developed by
IES)

Exponential Functions I.
(maple file)
 An Exercise.
 Exponential Functions II
 An Exercise.

Exponential Functions I.
(maple file)

Inverse Functions
 Drill. Explore with CP.
 Inverse functions II (Maple worksheet).
 Peer instruction.
 Review on Trigonometric Functions using Java Applets.
 More on inverse functions.
 **Explore Inverse Trig with ClassPad.
 Limits (Maple
file)
 Numerical Exploration on Limits. (html file)
 Explore limit with Casio
 Drill.
 Continuous Function (html
file)
 Explore with CASIO
 Explore with Maple
 Finding the limits (Maple)
 Drill (Do only the first two exercises, skip the trig functions).
 Practices on limits and continuity
 Concept of tangent lines. (html)
 Explore with CASIO. A video clip.
 Explorationhtml file.
 Tangent line at a point and the function (zooming in).
 An animation on finding the slope of the tangent line. (Maple file)
 Derivative Functions:
 Interpreting the graphs.
 Drill on the definition.
 How do we find the derivative at one point? (an avi file)
 Finding the derivative at one point
numerically and algebraically. (Maple
file)
 Problem 5 on section 2.1 (Maple file)
 An animation on finding the slope of the tangent line. (Maple file)
 A link to an old test 2.
 Explore the derivatives of sin(x) and tan(x) graphically with ClassPad (CP file, a Video Clip).
 Relationship between f and f'. (Maple file)
 (Investigating max/min and inflection points (Maple file)
 Review for an old Test 3
 Peer InstructionsReview for an old test 4.
 Drill on product Rule

Derivative of trigonometric functions
 ClassPad file
 Maple file
 Drill using product rule.
 Drill using quotient rule.
 *A video clip showing the derivatives of sin(x) and tan(x).
 Chain Rule

A Review Sheet.
 An Old Test Practice Problems
 An interest rate problem. (A Maple file)
 Implicit Differentiation with Maple
 (December 1) Hints on some exercisesimplicit differentiation
 Hints on an old test 3. (CP file)
 Derivatives of an inverse function. (html)
 Derivative of logarithmic differentiation. (Drill)
 Derivatives and Antiderivatives
 (December 1) Review for an old final exam.
 More practices on finding derivatives, horizontal tangents and etc.
 Maximum, Minimum, First Derivative Test
 Second Derivative
 Sharp Corners and Vertical Tangents.
 Applications to Product and Quotient Rules
 Chain Rule and etc
 Help on Word Problems Using Maple
 Projects on Limits:
8
Limits
Limits (PiecewiseDefined Functions and Squeeze Principle)
ClassPad e8
Video v8
9
Limit2
Finding Limits Using Geometric Approaches
10
Shrinking Circle
A Shrinking Circle: A Limit problem
 Projects on Optimizations:
12
Shortest_Dist1
Shortest distance between a point and a curve
ClassPad e12
13
Shortest_Dist2
Minimum Distance Between Two Curves
14
Ladder
A Ladder Problem
15
Rope
A Calculus Problem
 Trigonometric Functions using Java Applets
 ** Assessment (WebWork)
 Students will login as:
Ussername = (their RU login, e.g. cmett)
Password = (their 6digit RU id number)
and of course they should also change passwords at their first opportunity.
 Students will login as:
 A link to my Trigonometry Class.
 A link to my Precalculus Class.
Review from College Algebra:
 Factoring
 Rational Expressions
 Line equations
 Quadratic Equations
 Higher Order Inequalities.
 Parabolic Functions
 Lab 1 (A Maple worksheet) [** You can access to Maple from labs on campus.]
 Lab 2 (A Maple worksheet)
 **Online help on solving a math problem.