Spring 07 Classes:

126, 140, 151

Courses taught in the past:

Calculus 152,251,252, Linear algebra (460) Advanced Calc. 430/431.


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


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Walker 203; Phone: (540) 831-5232


Business Calculus

  1. Course Contract
  2. Quiz 1: January 22
  3. Note. When opening a math 'html' file in this web page, it is preferable to use 'Internet Explorer'.
  4. Review on Pre-Calculus or College Algebra:
  5. Exponents and Radicals
    • page 0-18:,31,33,35,37,39.
  6. Standard Equation of a circle:
  7. Line Equations
    • Word Problems: Break Even Analysis, Rental Car Problem and etc.
    • Example: 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.
    • Example 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.
      • Find the cost, revenue and profit functions.
      • Sketch these functions.
      • Find the break-even point.
    • Practice Problems
  8. Functions
    • Recall vertical line test, when will the graph represent a function?
    • Domain and Range:
      (a) When you know the graph of a function, you can tell what the domain (inputs or x) and range (outputs or y) are.
    • Drills on finding the domain of a function.
  9. Shifting and Reflection Techniques:
      • Horizontal Shifting: y = f(x + a) is a horizontal shifting of y = f(x). If a > 0, then the graph will be shifted to the left; if a <0, then the graph will be shifted to the right.
      • Vertical Shifting: y = f(x) + a is a vertical shifting of y = f(x). If a > 0, then the graph will be shifted up; if a <0, then the graph will be shifted down.
      • y = - f(x) is a reflection of y = f(x).
  10. Practices on Shifting, Expansions and etc (CASIO file)
  11. Tutorial on polynomial functions.
  12. More on polynomial functions
  13. Review for an old test 2.
  14. Extra Credits
  15. Limits (skip Maple file)
    • Numerical Explorations on Limits. (html file)
    • Drill.
    • Exercises from pages 58-60, #5,9,17,19,21,25,27,31,35,41,43,45.
  16. Continuous Function (html file)
    • Drill (Do only the first two exercises, skip the trig functions).
    • Exercises from pages 69-70: #1 through 25 odd; 49, 50.
  17. Concept of tangent lines. (html) An animation on finding the slope of the tangent line. (Maple file)
  18. Derivative Functions:
  19. NOTES on Understanding the Concepts of Derivatives
  20. Rules of finding derivatives and etc.
  21. An old test 3.
  22. An old practice test 4.  [Study this for quiz on March 23.]
  23. HW for Section 2.4: page 129, #23-37 odd numbers.
  24. Practice for test 3. (Added on April 2, 2007)
  25. Review for an old test 4.  
  26. Marginal Analysis.
  27. Investigating max/min and inflection points (Maple file)
  28. More practices on finding derivatives, horizontal tangents and etc.
  29. Applications to Product and Quotient Rule.
  30. Chain Rule and etc
  31. Maximum, Minimum, First Derivative Test
  32. Second Derivative
  33. Sharp Corners and Vertical Tangents.
  34. (Skip) Help on Word Problems
  35. (Skip) Rational Functions.
  36. Second Derivative
  37. April 11: An old practice test 5 (Do number 3 through 7)
  38. **April 20: Quiz 4/Test 4 (Due April 23).
  39. Word Problems.
  40. Applications:
    • Open box problem: An open box is to be made from a 16 in. by 30 in. piece of cardboards by cutting out squares of equal size from the four corners and bending up the sides. What size should the squares be to obtain a box with largest possible volume?
  41. **Review for the final exam.
  42. Some animations and graphs related to Mathematics