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Precalculus Concepts, Preliminary Edition, 1/e
Warren W. Esty, Montana State University
Published August, 1996 by Prentice Hall Engineering/Science/Mathematics
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Precalculus with Graphing Calculators-Mathematics
The goal of this text is to develop the students' ability to read,
write, think and do mathematics and to give the student command
of the facts and methods of algebra and trigonometry. The text emphasizes
the appropriate and creative use of technology, but even more, the
understanding of concepts and symbolism. In general, the goals of
the text are to equip students for calculus and to promote understanding
and retention of mathematical thoughts.
Emphasis on learning to read and use the symbolic and abstract
language of algebra.
Connects mathematical concepts between review and new material.
Emphasis on graphs and their interpretations, and the
use of graphing calculators.
Assumes graphing calculator usage to illustrate behavior
of functions and develop important mathematical concepts.
Emphasizes proven aids to retention rather than just
repetitive practice methods. Presentation of non-traditional homework
that emphasizes retention of concepts through reading, writing,
explaining and visually illustrating ideas, formulas.
Presents numerous “A level” practice problems
Supplements practice with “B level problems”
that encourage an additional conceptual approach including:
Emphasis on learning to work word problems.
1. Fundamental Concepts.
The Conceptual Level of Algebra. Order Matters! Abstraction
and Written Mathematics.
Methods as Formulas. Methods as Identities. Methods as Theorems
That Relate Equations.
Variables, Patterns, and Theorems.
Placeholders (Dummy Variables).
Expressions, Equations, and Graphs.
Graphing with Calculators.
Four Ways to Solve Equations.
2. Functions and Graphs.
Functions, Functions, Graphs, and Tables. Composition and
Decomposition.
Composition and Graphs.
Relations and Inverses.
3. Fundamental Functions.
Lines, Distance, and Circles.
Distance in the Plane. Circles.
Quadratics.
Ellipses.
Graphical Factoring.
Advanced Factoring Methods.
Word Problems. Word Problems with Constraints.
4. Powers.
Powers and Polynomials.
Polynomials.
Polynomial Equations.
Calculator-Aided Factoring Techniques.
Fractional Powers. Percents, Money, and Compounding. Rational
Functions. Inequalities.
Graphical Solutions. Absolute Values. Zeroes and Inequalities.
5. Exponential and Logarithmic Functions.
Exponents and Logarithms. Base 2 and Base e.
Exponential Growth.
Applications.
6. Trigonometry.
Geometry for Trigonometry. Trigonometric Functions.
Sine. Inverse Sine. Cosine. Inverse Cosine. Tangent. Inverse
Tangent.
Solving Triangles.
The Law of Sines. The Law of Cosines.
Solving Figures.
7. Trigonometry for Calculus.
Arc Length and Radians. Trigonometric Identities.
List of Trigonometric Identities.
Waves.
8. Other Topics.
Complex Numbers.
Trigonometric and Exponential Forms.
Polar Coordinates. Parametric Equations.
9. Conic Sections.
Conic Sections: Parabolas. Ellipses and Hyperbolas. Polar
Equations of Conic Sections.
Index.
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