Course Number: MATH 1113

 

Course Title: Precalculus

 

Hours Credit: 4 hours

 

Prerequisites: Four years of high school mathematics including algebra and trigonometry

 

Courses Description: This course is designed to prepare students for calculus, physics and related technical subjects. Topics include an intensive study of algebraic and transcendental functions.

 

Text: Precalculus (3rd edition) by Robert Blitzer, Prentice-Hall

 

Learning Outcomes: Students should be able to demonstrate:

1. An understanding of functions and how to graph functions
2. An understanding of operations on functions including function composition
3. An understanding of polynomial and rational graphs, including intercepts and asymptotes
4. An understanding of how to find the zeros of a polynomial and how to factor polynomials
5. An understanding of inverse functions and how to find them graphically and algebraically
6. An understanding of the properties of exponential and logarithmic equations
7. An understanding of how to solve exponential and logarithmic equations
8. An understanding of how to find the values of the trigonometric functions from right triangles and circles
9. An understanding of how to graph the trigonometric functions
10. An understanding of how to prove trigonometric identities
11. An understanding of how to use the sum, difference, double-angle and half-angle formulas for sine and cosine
12. An understanding of how to solve triangle using the law of sines and law of cosines
13. An understanding of polar coordinates and graphs
14. An understanding of how to analyze and solve applied problems

 

Topics: The following sections of Blitzer’s book will be covered:

Section

1.2       Basics of Functions

1.3       More on Functions and Their Graphs

1.4       Lines and Slope

1.5       More on Slope

1.6       Transformations of Functions

1.7       Combinations of Functions; Composite Functions

1.8       Inverse Functions

1.9       Distance and Midpoint Formulas; Circles

2.1       Complex Numbers

2.2       Quadratic Functions

2.3       Polynomial Functions and Graphs

2.4       Dividing Polynomials

2.5       Zeros of Polynomials ( Optional Topics include: Rational Root Theorem and

Descartes’ Rule of Signs )

2.6       Rational Functions

3.1       Exponential Functions

3.2       Logarithmic Functions

3.3       Properties of Logarithms

3.4       Exponential and Logarithmic Equations

3.5       Modeling with Exponential and Logarithmic Functions

7.1       Systems of Linear Equations in Two Variables

7.2       Systems of Linear Equations in Three Variables

4.1       Angles and Their Measures

4.2       Trigonometric Functions: The Unit Circle

4.3       Right Triangle Trigonometry

4.4       Trigonometric Functions for any Angle

4.5       Graphs of Sine and Cosine Functions

4.6       Graphs of Other Trigonometric Functions

4.7       Inverse Trigonometric Functions

4.8       Applications of Trigonometric Functions

5.1       Verifying Trigonometric Identities

5.2       Sum and Difference Formulas

5.3       Double-Angle and Half-Angle Formulas

5.5       Trigonometric Equations

6.1       Law of Sines

6.2       Law of Cosines

6.3       Polar Equations

6.4       Graphs of Polar Equations

6.5       Complex Numbers in Polar Form; DeMoivre’s Theorem

 

Grading Method: To be determined by instructor. The final exam should be given during the time as scheduled by the Registrar’s Office and should count between 20% and 35% of the overall grade.