Pre-Calculus Algebra
7. Content and Method
Topic | Lectures | |
Chapter 1: Fundamentals | 3 | |
1.1 | Sets of Real Numbers | |
1.2 | Absolute Value | |
1.3 | Solving Equations (Review and Preview) | |
1.4 | Rectangular Coordinates. Visualizing Data | |
1.5 | Graphs and Graphing Utilities | |
1.6 | Equations of Lines | |
1.7 | Symmetry and Graphs. Circles | |
Chapter 2: Equations and Inequalities | 3 | |
2.1 | Quadratic Equations: Theory and Examples | |
2.2 | Other Types of Equations | |
2.3 | Inequalities | |
2.4 | More on Inequalities | |
Chapter 3: Functions | 5 | |
3.1 | The Definition of a Function | |
3.2 | The Graph of a Function | |
3.3 | Shapes of Graphs. Average Rate of Change | |
3.4 | Techniques in Graphing | |
3.5 | Methods of Combining Functions (Skip iteration) | |
3.6 | Inverse Functions | |
Chapter 4: Polynomial and Rational Functions : Applications to Optimization | 4 | |
4.1 | Linear Functions | |
4.2 | Quadratic Functions | |
4.4 | Setting Up Equations That Define Functions | |
4.5 | Maximum and Minimum Problems | |
Chapter 12: Roots of Polynomial Equations | 4 | |
12.1 | The Complex Number System | |
12.2 | Division of Polynomials | |
12.3 | The Remainder Theorem and the Factor Theorem | |
12.4 | The Fundamental Theorem of Algebra | |
12.5 | Rational and Irrational Roots (optional) | |
12.6 | Conjugate Roots and Descartes's Rule of Signs (Descartes's Rule optional) | |
12.7 | Introduction to Partial Fractions (optional) | |
12.8 | More About Partial Fractions (optional) | |
Chapter 4: Polynomial and Rational Functions: Applications to Optimization | 3 | |
4.6 | Polynomial Functions | |
4.7 | Rational Functions | |
Chapter 5: Exponential and Logarithmic Functions | 7 | |
5.1 | Exponential Functions | |
5.2 | The Exponential Function y = e^{x} | |
5.3 | Logarithmic Functions | |
5.4 | Properties of Logarithms | |
5.5 | Equations and Inequalities with Logs and Exponents | |
5.6 | Compound Interest | |
5.7 | Exponential Growth and Decay | |
Chapter 10: Systems of Equations | 5 | |
10.1 | Systems of Two Linear Equations in Two Unknowns | |
10.2 | Gaussian Elimination | |
10.3 | Matrices | |
10.4 | The Inverse of a Square Matrix (optional) | |
10.5 | Determinants and Cramer’s Rule | |
10.6 | Nonlinear Systems of Equations (optional) | |
10.7 | Systems of Inequalities (optional) | |
Total 34 |
8. Methods of Assessment
The primary methods of assessment are, in decreasing order
of importance : essay
examinations, quizzes and homework. Typically, there will be two or three
hour-long
examinations during the quarter, and a comprehensive final examination. Students
are required
to show their work, and are graded not only on the correctness of their answers,
but also on
their understanding of the concepts and techniques. Quizzes are usually given
once or twice a
week to provide a spot check of student learning. Homework is required daily.
Since this class
satisfies a General Education requirement, at least 10% of the grade must be
based on writing
using correct mathematical notation.
9. Additional Comments
a. The syllabus is tightly packed, and the course moves at
a rapid pace; students should be
forewarned of this at the first class meeting. Students finding difficulty with
the pace should
instead take Math 116 followed by Math 117.
b. The text has many interesting applications. Also note
the review sections at the end of
each chapter.
c. The text is readable; students should be advised to read each section before coming to class.
d. The text is bundled with an interactive Video Skill-Builder CD-ROM.
e. Additional supplements (test banks, Instructor’s
Resource CD, etc.) are available from the
course supervisor.
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