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The only text on the market that truly integrates calculus with precalculus and algebra in a two-semester course appropriate for math and science majors, Integrated Calculus uses a student-friendly approach without sacrificing rigor. Students learn about logic and proofs early in the text then apply these skills throughout the course to different types of functions. This structure enhances conceptual understanding and reinforces skills at point of use, while allowing for a systematic development of calculation skills. This combined approach allows students to eliminate a pure precalculus course and focus on calculus, with a "point-of-use" presentation of necessary algebra and precalculus concepts. Algebra and precalculus topics are integrated into the text to provide instruction and review just prior to using these concepts in a calculus context. This helps students see the relevance and connectedness of the mathematics. Because of the text's integration of algebra, limits, and derivatives, students are able to fully review all the components of a specific function. This comprehensive approach helps students better learn and retain the material. Concept Questions begin each exercise set and test students' understanding of definitions, theorems, and concepts from the reading. The remaining exercises are divided into Skills, Applications, and Proofs sections.

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Book details

List price: $123.16 Copyright year: 2005 Publisher: CENGAGE Learning Binding: Hardcover Pages: 894 Size: 8.50" wide x 10.50" long x 1.06" tall Weight: 4.972 Language: English

AuthorTable of Contents

Functions, Limits, and Derivatives

The Basics

Numbers and Sets

Equations

Inequalities

Logic

Proofs

Functions

What Is a Function?

Graphs of Functions

Linear Functions

A Basic Library of Functions

Combinations of Functions

Transformations and Symmetry

Inverse Functions

Limits

Intuitive Notion of Limit

Formal Definition of limit

Delta-Epsilon Proofs

Limit Rules

Calculating Limits

Continuity

Two Theorems About Continuous Functions

Appendix: Proofs of Selected Limit Rules

Derivatives

Tangent Lines and the Derivative at a Point

The Derivative as an Instantaneous Rate of Change

Differentiability

The Derivative as a Function

Basic Differentiation Rules

Three Theorems about Tangent Lines

The First Derivative and Function Behavior

The Second Derivative and Function Behavior

Algebraic Functions

Power Functions

The Algebra of Power Functions

Limits of Power Functions

Derivatives of Power Functions

Graphs of Power Functions with Integer Powers

Graphs of Power Functions with Rational Powers

Polynomial Functions

The Algebra of Polynomial Functions

Limits and Derivatives of Polynomial Functions

Graphing Polynomial Functions

Optimization with Polynomial Functions

Rational Functions

The Algebra of Rational Functions

Limits and Asymptotes of Rational Functions

Derivatives of Rational Functions

Graphs of Rational Functions

General Algebraic Functions

Working with Algebraic Functions

The Product Rule and the Chain Rule

Implicit Differentiation

Related Rates

Optimization and Curve Sketching

Transcendental Functions

Exponential Functions

The Algebra of Exponential Functions

The Natural Exponential Function

Limits of Exponential Functions

Derivatives of Exponential Functions

Graphs of Exponential Functions

Applications of Exponential Functions

L' Hocirc;pital's Rule

Logarithmic Functions

The Algebra of Logarithmic Functions

Limits and Derivatives of Logarithmic Functions

Using Logarithms as a Calculational Tool

Trigonometric Functions

Right Triangle Trigonometry

Unit Circle Trigonometry

The Algebra of Trigonometric Functions

Limits of Trigonometric Functions

Derivatives of Trigonometric Functions

Graphs of Trigonometric Functions

Inverse Trigonometric Functions

Defining the Inverse Trigonometric Functions

Derivatives of Inverse Trigonometric Functions

Integration

Definite Integrals

Geometric Approximation and Sigma Notation

Approximating Area with Riemann Sums

The Definite Integral

Area and Average Value

The Fundamental Theorem of Calculus

Indefinite Integrals

The Fundamental Theorem of Calculus

Functions Defined by Integrals

Basic Integration Techniques

Integration by Substitution

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Applications of Integration

Arc Length

Volumes by Slicing

Volumes by Shells

Practical Applications

Selected Answers

Table of Contents provided by Publisher. All Rights Reserved.

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