Professor Wei-Chi Yang

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 real-life 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

1. CASIO files
2. Line Equations (Casio file).
3. 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)
4. Drill on composite functions.
5. (skip) Exercises on Quadratic Functions
   • Parabolic Functions I
   • Parabolic Functions II
   • 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).
6. (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.
7. Inverse Functions
   • Drill.  Explore with CP.
   • Inverse functions II (Maple worksheet).
8. Peer instruction.
   • Hint for an old test 1.
9. Review on Trigonometric Functions using Java Applets.
10. More on inverse functions.
    • Practice on composite and inverse functions.
    • Solution is here.
11. **Explore Inverse Trig with ClassPad.
    • A video clip.
12. Limits (Maple file)
    • Numerical Exploration on Limits. (html file)
    • Explore limit with Casio
    • Drill.
13. 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).
14. Practices on limits and continuity
15. Concept of tangent lines. (html)
    • Explore with CASIO. A video clip.
    • Exploration-html file.
    • Tangent line at a point and the function (zooming in).
    • An animation on finding the slope of the tangent line. (Maple file)
16. Derivative Functions:
    • Interpreting the graphs.
    • Drill on the definition.
    • How do we find the derivative at one point? (an avi file)
17. Finding the derivative at one point numerically and algebraically. (Maple file)
    • Problem 5 on section 2.1 (Maple file)
18. An animation on finding the slope of the tangent line. (Maple file)
19. A link to an old test 2.
20. Explore the derivatives of sin(x) and tan(x) graphically with ClassPad (CP file, a Video Clip).
21. Relationship between  f  and  f'. (Maple file)
22. (Investigating max/min and inflection points (Maple file)
23. Review for an old Test 3
24. Peer Instructions-Review for an old test 4.
25. Drill on product Rule
26. 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).
27. Chain Rule
    • Drill
    • Exploring the derivative for trigonometric functions and Chain Rule with Maple.
28. A Review Sheet.
    • An Old Test Practice Problems
    • An interest rate problem. (A Maple file)
29. Implicit Differentiation with Maple
    • Drill exercises for finding the derivative by using implicit differentiation.
    • Drill exercises for finding the equation of the tangent line at one point.
    • Explore Implicit Differentiation with ClassPad.
30. (December 1) Hints on some exercises-implicit differentiation
31. Hints on an old test 3. (CP file)
32. Derivatives of an inverse function. (html)
33. Derivative of logarithmic differentiation. (Drill)
34. Derivatives and Antiderivatives
35. (December 1) Review for an old final exam.
36. More practices on finding derivatives, horizontal tangents and etc.
37. Maximum, Minimum, First Derivative Test
38. Second Derivative
39. Sharp Corners and Vertical Tangents.
    • A problem.
    • Solutions to an old test.
40. Applications to Product and Quotient Rules
41. Chain Rule and etc
42. Help on Word Problems Using Maple
43. Projects on Limits:

    8	Limits	Limits (Piecewise-Defined Functions and Squeeze Principle)	ClassPad  e8	Video v8
    9	Limit2	Finding Limits Using Geometric Approaches	e9	v9
    10	Shrinking Circle	A Shrinking Circle: A Limit problem	e10	v10

44. Projects on Optimizations:

    12	Shortest_Dist1	Shortest distance between a point and a curve	ClassPad e12	Video v12
    13	Shortest_Dist2	Minimum Distance Between Two Curves	e13	v13
    14	Ladder	A Ladder Problem	e14	v14
    15	Rope	A Calculus Problem	e15	v15

45. Trigonometric Functions using Java Applets
46. ** Assessment (WebWork) 
    • Students will login as:
      Ussername = (their RU login, e.g. cmett)
      Password = (their 6-digit RU id number)
      and of course they should also change passwords at their first opportunity.
47. A link to my Trigonometry Class.
48. A link to my Precalculus Class.

Review from College Algebra:

1. Factoring
2. Rational Expressions
3. Line equations
   • *On-line practice on Point-Slope Formula.
   • *On-line practice on Drawing a line
4. Quadratic Equations
5. Higher Order Inequalities.
6. Parabolic Functions
   • Parabolic Functions I
   • Parabolic Functions II
7. Lab 1 (A Maple worksheet) [** You can access to Maple from labs on campus.]
8. Lab 2 (A Maple worksheet)
9. **On-line help on solving a math problem.

Some on line interactive calculator and software

1. Interactive Algebra
2. Java Applets
3. On Line Graphing Calculator
4. ON LINE CALCULATOR.