Professor Wei-Chi Yang

• On Sabbatical Leave-Fall 2006.
• Spring 07 Schedule
• Professional Activities
• Education
• Teaching Experiences
• Founder, ATCM
• Curriculum Vitae

Remember:

Be sure to get all your homework done as soon as possible after class as this will lead to better grades.

Links:

- RU
- My book mark
- ATCM
- E-mail Me

Walker 203; Phone: (540) 831-5232

Calculus I - Math 151

Important Notes:

• There is a Lab session on every Wednesday 05:00-06:00 pm at PC  B04. (Pocahontas Hall), it will be conducted by a peer instructor.
• Computer Lab Sessions: Mark your calendar please:
  • 2/2/2007 Walker 221  
  • 2/7/2007 Walker 225
  • 2/9/2007 Walker 225: Test 1.
  • 2/12//2007 Walker 225
  • 2/14/2007 Walker 225

Topics

1. CASIO files
2. Line Equations (Casio file).
   1. Exercise 1: You are about to take a trip and you plan to rent a car, here are two rental offers: (i) Hertz will give you 30 cents per mile and $45 per day, and (ii) Avis will give you 25 cents per mile and $50 per day. Suppose you decide to rent a car for 4 days. Which company offers you a better deal? Explain. Answer.
   2. Exercise 2: A manufacturer of electronic components finds that in making x units of a product weekly it has a cost of $2 per unit, plus a fixed cost of $1800. Each unit sells for $5.
      (a) Find the cost, revenue and profit functions.
      (b) Sketch these functions.
      (c) Find the break-even point.
      (d) Find the total weekly revenue at the break-even point.
3. Finding Domains and Shifting Techniques.
   • A Casio file.
   • A Maple file.
   • Drills of finding domain of a function.
   • A Java Applet
   • Practices on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
4. Exercises on Quadratic Functions
   • Parabolic Functions I
   • Parabolic Functions II
   • Polynomial functions (CASIO) (Maple)
   • Rational functions (CASIO) (Maple)
   • 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).
5. 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.
6. Inverse Functions
   • Inverse functions I
   • Drill.  Explore with CP.
   • Inverse functions II (Maple worksheet).
7. Peer instruction.
   • Hint for test 1.
8. Review on Trigonometric Functions using Java Applets.
9. **Explore Inverse Trig (CP)
   • Composition of Functions
     • Drill
   • More on inverse functions.
     • Practice on composite and inverse functions.
     • Solution is here.
   • **A flash about the unit circle.
10. Derivative Functions:
    • Interpreting the graphs.
    • (A flash) Derivative at a point  a  is the slope of the tangent line at the point  a.
    • Drill on the definition.
    • How do we find the derivative at one point? (an avi file)
11. Finding the derivative at one point numerically and algebraically. (Maple file)
    • Problem 5 on section 2.1 (Maple file)
12. An animation on finding the slope of the tangent line. (Maple file)
13. Limits and Continuity
    • Casio file.
    • (Maple file)
    • Finding the limits  (Maple)
14. A link to an old test 2.
15. Relationship between  f  and  f'. (Maple file)
16. (Investigating max/min and inflection points (Maple file)
17. Review for an old Test 3
18. Peer Instructions-Review for an old test 4.
19. 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.
20. Hints on some exercises from page 243-implicit differentiation
21. Derivatives and Antiderivatives
22. Derivative of trigonometric functions
23. Exploring the derivative for trigonometric functions and Chain Rule
24. ** Review for an old final exam.
25. More practices on finding derivatives, horizontal tangents and etc.
26. Maximum, Minimum, First Derivative Test
27. Second Derivative
28. Sharp Corners and Vertical Tangents.
    • A problem.
    • Solutions to an old test.
29. Applications to Product and Quotient Rules
30. Chain Rule and etc
31. Help on Word Problems Using Maple
32. Trigonometric Functions using Java Applets
33. ** 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.
34. A link to my Trigonometry Class.
35. 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.

Copyright © 2006 (Wei-Chi Yang).