Catalog Description

An integrated treatment of the concepts necessary for calculus beginning with a review of algebraic and transcendental functions including trigonometric functions. Topics also include the binomial theorem, analytic geometry, vector algebra, polar and parametric equations, mathematical induction and sequences and series.

Course Learning Outcomes

The student will:

• Demonstrate and apply knowledge of properties of functions.

• Recognize and apply algebraic and transcendental functions and solve related equations.

• Apply graphing techniques to algebraic and transcendental functions.

• Compute the values of trigonometric functions for key angles in all quadrants of the unit circle measured in both degrees and radians.

• Prove trigonometric identities.

• Solve right and oblique triangles.

• Apply the binomial theorem.

• Determine equations of conic sections, and graph conics, including translation and identification of vertices, foci and asymptotes.

• Perform basic operations and solve applications using vector algebra.

• Perform operations and graph equations using polar and parametric equations.

• Prove statements using mathematical induction.

• Use properties of arithmetic and geometric sequences and series to identify terms, find sums and solve applications.

Contact Hour Information

Credit Hours: 4

Lecture Hours: 4

Lab Hours: 1

External Hours: 0

Total Contact Hours: 80

Prerequisites

Math 1314 and Math 1316 OR placement by testing;

ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing

Corequisites

ENGL 0307

**Required Materials**

**Textbook: **Sullivan, Michael and Sullivan, Michael III,

**Calculator:**

Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.

Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.

Neither cell phones nor PDA’s can be used as calculators. Calculators may be cleared before tests.

Review Sections and Readiness Check

There are sections of the textbook that should be covered in class (listed below as Textbook Sections) and sections that should be assigned to the students to review on their own at the beginning of the semester (listed below as Self Review Sections). Self Review Sections must NOT be covered in class but students MUST be assessed on these sections as part of their grade. Faculty have the option of using the departmental College Algebra and Trigonometry Readiness Check for Precalculus as an assessment instrument. This instrument is available in print form or in web-based form through MyMathLab.

To access the print version click College Algebra and Trigonometry Readiness Check for Precalculus.

To access the web-based version copy the College Algebra and Trigonometry Readiness Check from the Course ID burghduff61044 in MyMathLab.

**Textbook Sections**

** Note:** The following sections are to be covered in class. Self Review Sections, listed below, are to be reviewed by the students on their own outside of class and evaluated.

**Chapter 4. Polynomial and Rational Functions**

4.4 Properties of a Rational Function

4.5 The Graphs of a Rational Functions

**Chapter 5. Exponential and Logarithmic Functions**

5.6 Logarithmic and Exponential Equations

5.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay

Chapter 7. Analytic Trigonometry

7.3 Trigonometric Equations

7.4 Trigonometric Identities

7.6 Double-angle and Half-angle Formulas

**Chapter 9. Polar Coordinates and Vectors**

9.1 Polar Coordinates

9.2 Polar Equations and Graphs

9.3 The Complex Plane; DeMoivre's Theorem

9.4 Vectors

9.5 The Dot Product

Chapter 10. Analytic Geometry

10.1 Conics

10.2 The Parabola

10.3 The Ellipse

10.4 The Hyperbola

10.6 Polar Equations of Conics

10.7 Plane Curves and Parametric Equations

**Chapter 11. Systems of Equations and Inequalities**

11.1 Systems of Linear Equations: Substitution and Elimination

11.2 Systems of Linear Equations: Matrices

11.3 Systems of Linear Equations: Determinants

11.4 Matrix Algebra

11.5 Partial Fraction Decomposition (*optional*)

11.6 Systems of Nonlinear Equations (*optional*)

11.7 Systems of Inequalities

**Chapter 12. Sequences, Induction, the Binomial Theorem**

12.1 Sequences

12.2 Arithmetic Sequences

12.3 Geometric Sequences, Geometric Series

12.4 Mathematical Induction

12.5 The Binomial Theorem

Self Review Sections

Note: Students are expected to review the following sections on their own. Instructors must evaluate these sections.

Chapter 2. Functions and their Graphs

2.1 Functions

2.2 The Graph of a Function

2.3 Properties of Functions

2.4 Library of Functions; Piece-wise Defined Functions

2.5 Graphing Techniques: Transformations

2.6 Mathematical Models: Building Functions

Chapter 4. Polynomial and Rational Functions

4.1 Polynomial Functions and Models

Chapter 5. Exponential and Logarithmic Functions

5.3 Exponential Functions

5.4 Logarithmic Functions

5.5 Properties of Logarithms

Chapter 6. Trigonometric Functions

6.1 Angles and their Measures

6.2 Trigonometric Functions: Unit Circle Approach

6.3 Properties of the Trigonometric Functions

6.4 Graphs of the Sine and Cosine Functions

6.5 Graphs of the Tangent, Cotangent, Cosecant and Secant Functions

6.6 Phase Shift; Sinusoidal Curve Fitting

Chapter 7. Analytic Trigonometry

7.1 The Inverse Sine, Cosine and Tangent Functions

7.2 The Inverse Trigonometric Functions (continued)

Chapter 8. Applications of Trigonometric Functions

8.1 Right Triangle Trigonometry: Applications

8.2 The Law of Sines

8.3 The Law of Cosines

8.4 Area of a Triangle