Calculus: Preliminary Edition, 1/e
Robert Decker, University of Hartford
Dale Varberg, Hamline University
Published March, 1996 by Prentice Hall Engineering/Science/Mathematics
Copyright 1996, 651 pp.
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A second generation reform text, Decker/Varberg is designed to motivate
an intuitive understanding of calculus topics with the aid of visualization
technology and rich problems and applications. Stronger than all other texts in its coverage of numeries.
fully incorporates the Rule of Three (graphical, numeric
and symbolic) with an emphasis on a numeric approach. (Example:
Chapter 2.5; 4 and Lab 11, 6.3)
group projects (usually technology-based) throughout the
book that focus on mathematical exploration and discovery, not just
button pushing. These have been developed by the author through a
series of NSF-sponsored workshop and technology training sessions.
(Example: Lab #13, chapter 7.5; and Lab #18, chapter 9.2)
full coverage of important calculus topics that is sometimes
omitted from other reform texts, such as sequences and series, mean
value theorem, hyperbolic functions, parametric equations, L'Hopital's
Rule, conic sections and centers of mass.
a early, careful introduction to exponential and logarithmic
functions (Sect. 1) to motivate more interesting applications and
modeling in subsequent chapters. (The topics are discussed further
in Chapter 7.2).
the introduction of limits is followed quickly by an introduction
to derivatives to help motivate an understanding of the connection
between the two concepts. (Example: 1.1)
a complete chapter on Graphical and Numerical Techniques
of Problem Solving (Chapter 2). The chapter includes a comprehensive
discussion on how to interpret and use graphs and tables in problem
solving. Also introduces local linearity; intermediate value theorem;
linear curve fitting; and an expansion of exponential function topics.
special emphasis is placed throughout the book on showing
the students both the value and the limitations of using technology
to learn calculus (Example: Chapter 4.6).
book includes discussion and group project on dynamical
systems and chaos to students that capitalizes on recent discussions
and interesting applications in this diverse area. (Example: Chapter
9.1, Lab 17).
Graphs and Equations. Functions. The Straight Line and Linear
Functions. The Trigonometric Functions.
1. Calculus: A First Look.
Introduction to Limits Part I. Lab 1: Limits. Introduction
to Limits Part II. The Derivative: Two Problems With One Theme. Exponential
Functions. Logarithms and the Logarithmic Function. Chapter Review.
2. Numerical and Graphical Techniques.
Calculator and Computer Graphs. Lab 2: Calculator
and Computer Graphs. Calculator and Computer Tables. Parameters. Lab
3: The Damped Harmonic Oscillator. Zooming and Local Linearity.
Lab 4: Roots and Slopes: When and How Fast? Solving Equations.
Linear Curve Fitting. Nonlinear Curve Fitting. Chapter Review.
The Derivative as a Function. Lab 5: The Derivative
as a Function. Rules for Finding Derivatives. Derivatives of Sines,
Cosines, Logs and Exponentials. The Chain Rule. Higher-Order Derivatives.
Implicit Differentiation and Related Rates. Differentials and Approximations.
4. Applications of the Derivative.
Maxima and Minima. Lab 6: Increasing, Decreasing,
and the Derivative. Monotonicity and Concavity. Local Maxima and Minima.
Lab 7: Ideal Gases and Real Gases. More Max-Min Problems. Applications
from Economics. Graphing with Parameters. The Mean Value Theorem. Chapter
5. The Integral.
Antiderivatives (Indefinite Integrals). Introduction to
Differential Equations. Lab 8: The Draining Can. Area and Reimann
Sums. Lab 9: Area and Distance. The Definite Integral and Numerical
Integration. Lab 10: Area Functions. The Fundamental Theorem
of Calculus. More Properties of the Definite Integral. Substitution. Chapter
6. Applications of the Integral.
The Area of a Plane Region. Volumes of Solids: Slabs, Disks,
Washers. Length of a Plane Curve. Lab 11: Arc Length. Work.
Moments, Center of Mass. Chapter Review.
7. Transcendental Functions and Differential Equations.
Inverse Functions and Their Derivatives. A Different Approach
to Logarithmic and Exponential Functions. Lab 12: Falling Objects.
General Exponential and Logarithmic Functions. Exponential Growth
and Decay. Numerical and Graphical Approaches to Differential Equations.
Lab 13: Planning Your Retirement. The Trigonometric Functions
and Their Inverses. The Hyperbolic Functions and Their Inverses. Chapter
8. Techniques of Integration.
Substitution and Tables of Integrals. Integration by Parts.
Lab 14: Integration by Parts. Some Trigonometric Integrals.
Integration of Rational Functions. Lab 15: Population Models.
Indeterminate Forms. Improper Integrals. Lab 16: Probability
and Improper Integrals. Chapter Review.
9. Infinite Series.
Infinite Sequences and Dynamical Systems. Lab 17:
Discrete Population Models. Infinite Series. Lab 18: Bouncing
Balls and Infinite Series. Altering Series, Absolute Convergence.
Taylor's Approximation to Functions. Lab 19: Taylor Series and
Fourier Series. The Error in Taylor's Approximation. Lab 20: Newton's
Method. General Power Series. Lab 21: The Gamma Function and
Taylor Series. Approximations. Operations on Power Series. Chapter
10. Conics, Polar Coordinates and Parametric Curves.
Conic Sections. Translation of Axes. The Polar Coordinate
System and Graphs. Technology and Graphs of Polar Equations. Lab
22: Graphs in Polor Coordinates. Calculus in Polar Coordinates.
Lab 23: Orbits of the Planets. Plane Curves: Parametric Representation.