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Integrated Calculus Calculus with Precalculus and Algebra

ISBN-10: 0618219501

ISBN-13: 9780618219506

Edition: 2005

Authors: Laura Taalman

List price: $123.16
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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

Functions, Limits, and Derivatives
The Basics
Numbers and Sets
What Is a Function?
Graphs of Functions
Linear Functions
A Basic Library of Functions
Combinations of Functions
Transformations and Symmetry
Inverse Functions
Intuitive Notion of Limit
Formal Definition of limit
Delta-Epsilon Proofs
Limit Rules
Calculating Limits
Two Theorems About Continuous Functions
Appendix: Proofs of Selected Limit Rules
Tangent Lines and the Derivative at a Point
The Derivative as an Instantaneous Rate of Change
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
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.