This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# College Algebra -- Fall 2016

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MTH 130 College Algebra. 3 hrs. Polynomial, rational, exponential, and logarithmic functions. Graphs, systems of equations and inequalities, sequences. (PR: Math ACT 21 or above)

• Time and Place: 1:00 - 1:50 pm MWF at 516 Smith Hall.
• Instructor: Peter Saveliev (call me Peter)
• Office: 713 Smith Hall
• Office Hours: MW 2:30 - 5:00, or by appointment
• Office Phone: x4639
• E-mail: saveliev@marshall.edu
• Class Web-Page: math01.com
• Prerequisites: solid algebra skills, some knowledge of Cartesian coordinates, familiarity with basic functions
• Texts: College Algebra by Paul Sisson
• Computer Restrictions: graphic calculator TI-83 or TI-83+
• Outcomes: the student will learn to recognize and use functions, including the major classes of functions, graph these functions, solve equations
• Activities: the student will practice each outcome via the homework given in the textbook and online.
• Evaluation: the student achievement of each outcome will be assessed via:
• Grade Breakdown: TOTAL = .05×P + .40×(Q + H) + .20×M + .35×F
• participation: 5%
• quizzes and online homework: 40%
• midterm: 20%
• final exam: 35%

For details, see Course policy.

## Lectures

They will appear exactly as you see them in class and, as the course progresses, will be updated weekly.

## Schedule

$$\begin{array}{clllll} \text{Week}\# &\text{Date} &\text{Sections in class} &\text{HW Sections } \\ 1 & 8/22/16 & 1.2 \text{ pg. } 16-18, 2.1 & \\ & 8/24/16 & 2.1, 1.1 \text{ pg. } 6-8 & 2.1a \\ & 8/26/16 & 2.2, \text{ zero factor property in } 1.2, 1.5 & 1.1,2.1b \\ 2 & 8/29/16 & 1.5, 2.3 & 1.2 \\ & 8/31/16 & 2.3 & 1.5, 2.2 \\ & 9/2/16 & 2.3 & \\ 3 & 9/5/16 & \text{No class -- Labor Day }& \\ & 9/7/16 & 2.4/2.5 & 2.3 \\ & 9/9/16 & 2.5 & 2.4 \\ 4 & 9/12/16 & 2.5 & 1.4a \\ & 9/14/16 & 2.6 & 2.5 \\ & 9/16/16 & 2.6 & 2.6 \\ 5 & 9/19/16 & 3.1, 3.2 & \\ & 9/21/16 & 3.3 & 3.1, 3.2 \\ & 9/23/16 & 3.4, 3.5 & 3.3 \\ 6 & 9/26/16 & 3.6 & 3.4 \\ & 9/28/16 & 4.1 & 3.5 \\ & 9/30/16 & 4.1 & 3.6 \\ 7 & 10/3/16 & 4.2 & 4.1 \\ & 10/5/16 & 4.2, 4.3 & 4.2a \\ & 10/7/16 & 4.4 & 4.2b \\ 8 & 10/10/16 & 4.4 & 4.3a \\ & 10/12/16 & 4.5 & \\ & 10/14/16 & 4.6 & 4.4 \\ 9 & 10/17/16 & 5.1& 4.5 \\ & 10/19/16 & \text{Review }& 4.6 \\ & 10/21/16 & \text{Midterm }& \\ 10 & 10/24/16 & 5.2 & 5.1 \\ & 10/26/16 & 5.3 & 5.2 \\ & 10/28/16 & 5.4 & 5.3 \\ 11 & 10/31/16 & 6.1 & 5.4 \\ & 11/2/16 & 6.1 & 6.1a \\ & 11/4/16 & 1.3, 1.4 & 6.1b \\ 12 & 11/7/16 & 7.1 & 1.3a \\ & 11/9/16 & 7.2 & 1.4b \\ & 11/11/16 & 7.3 & 7.1 \\ 13 & 11/14/16 & 7.4 & 7.2 \\ & 11/16/16 & 7.4 & 7.3 \\ & 11/18/16 & 7.5 & 7.4 \\ 14 & 11/28/16 & 7.5 & \\ & 11/30/16 & 8.1 & 7.5 \\ & 12/2/16 & 8.1& \\ 15 & 12/5/16 & 8.1 & \\ & 12/7/16 & \text{Review for Final Exam } & 8.1 \\ & 12/9/16 & \text{Review for Final Exam }& \\ \end{array}$$

## Topics

Lesson Name

• 1.1 The Real Number System
• 1.2 The Arithmetic of Algebraic Expressions
• 1.3a Properties of Exponents
• 1.3b Scientific Notation and Geometric Problems Using Exponents
• 1.4b Rational Number Exponents
• 1.5 Polynomials and Factoring
• 1.6 The Complex Number System
• Chapter 1 Review
• 2.1a Linear Equations in One Variable
• 2.1b Applications of Linear Equations in One Variable
• 2.2 Linear Inequalities in One Variable
• 2.3 Quadratic Equations in One Variable
• 2.4 Higher Degree Polynomial Equations
• 2.5 Rational Expressions and Equations
• Chapter 2 Review
• 3.1 The Cartesian Coordinate System
• 3.2 Linear Equations in Two Variables
• 3.3 Forms of Linear Equations
• 3.4 Parallel and Perpendicular Lines
• 3.5 Linear Inequalities in Two Variables
• 3.6 Introduction to Circles
• Chapter 3 Review
• 4.1 Relations and Functions
• 4.2a Linear and Quadratic Functions
• 4.2b Max/Min Applications of Quadratic Functions
• 4.3a Other Common Functions
• 4.3b Direct and Inverse Variation
• 4.4 Transformations of Functions
• 4.5 Combining Functions
• 4.6 Inverses of Functions
• Chapter 4 Review
• 5.1 Introduction to Polynomial Equations and Graphs
• 5.2 Polynomial Division and the Division Algorithm
• 5.3 Locating Real Zeros of Polynomials
• 5.4 The Fundamental Theorem of Algebra
• Chapter 5 Review
• 6.1a Rational Functions
• 6.1b Rational Inequalities
• 6.2 The Ellipse
• 6.3 The Parabola
• 6.4 The Hyperbola
• Chapter 6 Review
• 7.1 Exponential Functions and their Graphs
• 7.2 Applications of Exponential Functions
• 7.3 Logarithmic Functions and their Graphs
• 7.4 Properties and Applications of Logarithms
• 7.5 Exponential and Logarithmic Equations
• Chapter 7 Review
• 8.1 Solving Systems by Substitution and Elimination
• 8.2 Matrix Notation and Gaussian Elimination
• 8.3 Determinants and Cramer's Rule
• 8.4 The Algebra of Matrices
• 8.5 Inverses of Matrices
• 8.6 Linear Programming
• 8.7 Nonlinear Systems of Equations
• Chapter 8 Review
• 9.1 Sequences and Series
• 9.2 Arithmetic Sequences and Series
• 9.3 Geometric Sequences and Series
• 9.4 Mathematical Induction
• 9.5a An Introduction to Combinatorics - Counting, Permutations, and Combinations
• 9.5b An Introduction to Combinatorics - The Binomial and Multinomial Theorems
• 9.6 An Introduction to Probability
• Chapter 9 Review
• A.1 Introduction to Polynomial Equations and Graphs (excluding complex numbers)
• A.2 Polynomial Division and the Division Algorithm (excluding complex numbers)
• A.3 Locating Real Zeros of Polynomials (excluding complex numbers)
• A.4 The Fundamental Theorem of Algebra (excluding complex numbers)

## Course Content

1. Solving equations in one variable of the following types:

• (a) linear equations and inequalities, basic equations with absolute value
• (b) quadratic equations with real solutions (factoring and quadratic formula only - omit completing the square)
• (c) equations with rational expressions
• (e) equations with exponential and/or logarithmic expressions

2. Basic Functions

• (a) definition of "function", "domain", and "range"
• (b) graphing lines
• (c) linear and quadratic functions and their applications
• (d) identification of other common functions graphically
• (e) graphing functions with translation and reflection (no stretching/compressing)
• (f) identifying symmetry in functions (even/odd)
• (g) graphically determine where a function is increasing, decreasing, and constant
• (h) composition of functions and inverse functions

3. Polynomial and rational functions

• (a) polynomial long division (synthetic division is optional)
• (b) remainder and factor theorems
• (c) basic graph sketching including end behavior at $\pm \infty$
• (d) intermediate value theorem
• (e) equations of asymptotes - vertical and horizontal (no oblique)

4. Exponential and logarithmic functions (a) basic properties of exponential functions and their graphs (b) basic properties of logarithmic functions and their graphs (c) applications of exponential and logarithmic functions (population growth, compound interest, laws of cooling, decibels, Richter scale, etc.)

5. Solving systems of linear equations in two variables using substitution and elimination

Current Textbook: College Algebra, 2nd edition by Paul Sisson.

## Tutoring

The math tutoring lab will be open this semester during the following hours:

• Smith Music 115: Monday-Thursday 10am-4pm, Friday 10am-12noon
• Smith Hall 620: Monday-Thursday 5:00pm-6:30pm

The lab will open the second week of classes.