Math 140: Unit 10

Due Date: Wednesday, December 11, 2002

Topics

Unit 10 continues the work on systems of equations that was begun in Unit 9. A primary focus in this unit is applications. The unit starts with a study of real-world applications of 3x3 linear systems, and then continues with a mathematical application called the partial fraction decomposition. The partial fraction decomposition is a method of decomposing a complicated rational function into a sum of simpler ones. This technique is useful in a number of areas of mathematics (calculus in particular).

The unit concludes with a study of methods for solving nonlinear systems of equations (namely, 2x2 systems involving second-degree equations), and application of such systems.

• 3x3 Systems of Linear Equations (10.2-3)
  • Applications of 3x3 linear systems
• Partial Fraction Decomposition (10.6)
• Nonlinear Systems Involving Second-Degree Equations (10.7)
  • Definition and number of solutions
  • Substitution method
  • Elimination method
  • Graphical solutions
  • Applications

Calculators may be used on this unit.

Unit 10 will be followed by the Final Exam.

Study guidelines

• Sections 10.2 and 10.3: Applications of 3x3 Systems of Linear Equations
  • Read example 4 in section 10.2, and example 10 in section 10.3.
  • Problems: 10.2 #17, 18, 21-27
  • Problems: 10.3 #69-77 odds
    
    
• Section 10.6: Partial Fraction Decomposition
  • Read Section 10.6.
  • It is critical that you start with the correct form for a partial fraction decomposition, as described in Cases 1-4. If you choose the incorrect form, you will waste a lot of time and get the wrong answer. Read through the examples carefully. Partial fractions is just a mechanical procedure, but it takes practice to do it right.
  • More explanation and examples of partial fractions
  • Problems: 10.6 #1-41 odds
    
    
• Section 10.7: Systems of NonlinearEquations
  • Read Section 10.7.
  • Unlike the situation for linear systems, there is no one method that will work for all systems involving second-degree equations. Thus, you need to try the various techniques described in the textbook on lots of practice problems.
  • Problems: 10.7 #1, 5, 9, 11, 15, 19, 25, 33, 37, 43, 45, 49, 51, 55, 59, 63, 65-81 odds
    
    
• Supplementary material (optional) for Chapter 10:
  • Student Solutions Manual for Chapter 10 (see note)
  • Video lectures are available in the Media Reserve room of the ISU library. They are listed under Math 140: Poon.
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help
  • The MathPak5 web site contains other resources such as Reading Quizzes and links to other interesting and fun math sites.

Unit Exam #10
After completing the above work, do the following:

1. Read the exam description:
   • This exam has 8 questions, and will count 15 points toward your grade. 
   • This exam has a one-hour time limit.
   • Calculators may be used on this unit.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems ask you to solve a system of equations for which there may be more than one solution (for example, the systems in section 10.7). Each solution will be a point (x,y), so if there is more than one solution, you must separate the points with a semicolon. For example, if the system has solutions x=1,y=3 and x=5,y=-2, then your answer would be (1,3);(5,-2) or ( 5,-2);(1,3).
2. Complete the online Unit 10 Pretest assignment. You may use your book if you wish, and redo the pretest as many times as you like. Your pretest score will be scaled to 5 points maximum.
3. You can repeat the online Unit 10 Pretest assignment without using your book until you feel that you are ready for the unit exam.
4. If you are having trouble with any of the problems listed above or on the pretest or practice exams, spend some time working with the online tutors listed on the Help page.
5. Go to the Math Computer Lab (449 Carver) to take the online proctored unit exam (go to Unit 10 Exam). Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.

   Note: Remember that you can always go back and take practice exams (go to Unit 10 Practice Exam) on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

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