Syllabus Precalculus – Fall ‘13 Section 6484

Instructor: Geoff Hagopian
Office: Math 12
Office Hours: MWF: 11:30 – 12:30 and TR: 2 – 3
Email: ghagopian@collegeofthedesert.edu
Web Page: http://faculty.collegeofthedesert.edu/ghagopian
Telephone: (760) 776-7223

Main Text

Precalculus: Mathematics for Calculus, 6th Edition
James Stewart; Lothar Redlin; Saleem Watson
ISBN-10: 0-8400-6807-7
ISBN-13: 978-0-8400-6807-1

Catalog Description:

This course is the second in a two semester sequence preparing students for Calculus.  In this course, students will extend the concept of a function to polynomial, rational, exponential and logarithmic functions as well as studying analytic trigonometry.  Topics include analysis of equations and word problems involving polynomial, rational, exponential and logarithmic functions, trigonometric identities, inverse trigonometric functions, and solving trigonometric equations.
Tutoring:
Math/Science Study Center in Math 4 --computers and tutors.
MESA club in MSTC --study guides a tutoring staff.
Technology:
You need a graphing utility of some sort.  There are many alternatives these days, ranging from the TI/Casio/HP graphing calculators to various iphone/android apps and gcalc.net - get with me and or others and find something you're comfortable with.

Prerequisites:

Before entering the course students must be able to:

1. Apply facts about angles, parallel lines and triangles to deduce further results about a geometric figure.
2. Prove when two triangles are congruent or similar.
3. Justify the lengths of sides in an isosceles right triangle and in a 30 – 60 – 90 triangle.
4. Deduce the lengths of sides in quadrilaterals such as trapezoids and rectangles using basic definitions, Pythagorean Theorem, perimeter and/or area.
5. Calculate the measure of a central angle in a circle using the measure of the intercepted arc and calculate the areas of geometric figures involving circles.
6. Apply facts about plane geometric figures to deduce the surface area and volume of three dimensional geometric figures.
7. Demonstrate an understanding of the concept of a function by identifying and describing a function graphically, numerically and algebraically.
8. Calculate the domain and range for a function expressed as a graph or an equation. From a graph, estimate the intervals where a function is increasing, decreasing and/or has a maximum or minimum value.
9. Use and interpret function notation to find “inputs” and “outputs” from the graph, table and/or an equation describing a function
10. From an equation, graph or table, calculate average rates of change by using a difference quotient or by using slopes of secant lines. Analyze average rates of change to determine the concavity of a graph.
11. Demonstrate an understanding of the six basic transformations of functions by graphing translated functions including the quadratic functions.
12. Determine when a function has an inverse (one to one functions) and find the inverse function graphically or
13. Form new functions through addition, subtraction, multiplication, division and composition.
14. Recognize classical and analytic definitions of the trigonometric functions.
15. Solve triangles using right triangle trigonometry, the law of sines and the law of cosines.
16. Convert from radian to degree measure and vice-versa.
17. Graph the 6 trigonometric functions and demonstrate the ability to change parameters and predict corresponding graphic behavior.
18. Use trigonometric functions to model periodic behavior.
19. Recognize the basic features of the graphs of the conic sections (including parabolas, ellipses, circles and hyperbolas) and use those features to graph shifted conics.
20. Analyze independently and set up application problems, thus applying problem solving technique to new situations. Demonstrate the ability to anticipate and check their proposed solutions.

Homework
We’ll use the ILRN.COM homework system which is detailed in lecture.

Most of your grade points will be determined by chapter tests and the final exam, whose dates are indicated in the tentative schedule.  The homework assignments are the crucial touchstone that will guide daily class discussions.  Everyone should come prepared to lead and/or follow a discussion on the topic for each scheduled meeting.  To be successful, you’ll want to have test scores whose weighted average exceeds 70% (C), 80% (B) or 90% (A) where pre-final exam points are awarded by the following weighting scheme:
5% attendance
10% homework
85% chapter tests and final exam

Overview
Precalculus is a course designed to do just what it suggests: prepare you for a first course in calculus.  This means learning many definitions and properties of basic functions and methods of solving equations, but it also—perhaps most importantly—means learning how to solve problems.  The basic outline for general problem solving devised by Polya is a four step program:

1. Understand the problem
2. Devise a plan for solving the problem
3. Carry out the plan
4. Look back

Let's flesh this out:

Polya’s Four Step Program for Problem Solving

1. UNDERSTANDING THE PROBLEM
• Do you have good definitions for all the words in the problem statement?.
• What is the unknown?  That is, what does the problem want to be produced? What are the given data? What condition(s) must be satisfied?
• Is it possible to satisfy the conditions? Are the condition(s) sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
• Draw a figure or make a diagram to help conceptualize what is going on. Introduce suitable notation.
• Could you restate the problem in an equivalent way that makes more sense to you?

1. DEVISING A PLAN

Polya mentions (1957) that there are many reasonable ways to solve problems. The skill at choosing an effective strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:

 Guess and check Make and orderly list Eliminate possibilities Use symmetry Consider special cases Use direct reasoning Solve an equation Look for a pattern Draw a picture Solve a simpler problem Use a model Work backward Use a formula Be ingenious

Often times an algebra problem is best solved using the algebraic method:

• Introduce a variable to represent the unknown.
• Write related quantities in terms of this variable.
• Set up an equation using the variable.
• Solve the equation.
1. CARRYING OUT THE PLAN
• Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?   If your plan isn’t working, you may need to go back to step 2 and devise a better plan.
2. Looking Back
• Can you check the result?   Can you derive the solution differently?
• Can you use the result, or the method, for some other problem?
• Can you generalize your solution to a larger class of problems?

### The Importance of Looking Back

Looking back may be the most important part of problem solving and is the best opportunity to learn from the problem. The phase was identified by Polya with admonitions to examine the solution by such activities as checking the result, checking the argument, deriving the result differently, using the result, or the method, for some other problem, reinterpreting the problem, interpreting the result, or stating a new problem to solve.
Teachers and researchers report, however, that developing the disposition to look back is very hard to accomplish with students. Some researchers have found little evidence of looking back among students--even when it is stressed by instruction. One teacher put it succinctly: "In schools, there is no looking back." This likely stems from a culture of mathematics education that holds “answer getting” as the paramount objective.  Also, pressure to cover a prescribed course syllabus; the absence of tests that measure processes and student frustration contribute to the tendency not to reflect on what a problem means in a larger context..
The importance of looking back should outweigh these difficulties.. It is often what you learn after you have solved the problem that really counts.