Calculus I with Precalculus, 3 edition ©2012

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Calculus I with Precalculus, 3 edition ©2012

Author: Ron Larson - The Pennsylvania State University, The Behrend College | Size: 102.26 MB | Format: PDF | Publisher: ©2012 Brooks/Cole, Cengage Learning | Year: 2012, 2006, 2002 | pages: 1064 | ISBN: ISBN-10: 0840068336 ISBN-13: 9780840068330

1.Overview

1.1.About the Product
CALCULUS I WITH PRECALCULUS, developed for one-year courses, is ideal for instructors who wish to successfully bring students up to speed algebraically within precalculus and transition them into calculus. The Larson Calculus program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. Two primary objectives guided the authors in writing this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and saves the instructor time.

1.2.Features
The explanations, theorems, and definitions have been thoroughly and critically reviewed. Exercise sets have been carefully and extensively examined to ensure they cover calculus and precalculus topics appropriately.
Questions involving skills, writing, critical thinking, problem-solving, applications, and real-data applications are included throughout the text. Exercises are presented in a variety of question formats, including matching, free response, true/false, modeling, and fill-in the blank.
To address the changing needs of today's instructors and students and recognizing that the calculus course is presented in a variety of teaching and learning environments, the program resources are available in print and online formats.

1.3.About the Author
Ron Larson
Ron Larson received his Ph.D. in mathematics from the University of Colorado and has been a professor of mathematics at The Pennsylvania State University since 1970. He has pioneered the use of multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson has also conducted numerous seminars and in-service workshops for math teachers around the country about using computer technology as a teaching tool and motivational aid. His INTERACTIVE CALCULUS (a complete text on CD-ROM) received the 1996 Texty Award for the most innovative mathematics instructional material at the college level, and was the first mainstream college textbook to be offered on the Internet.

1.4. Previous Editions
2006
2002

2.Table of Contents

P. PREREQUISITES.
Solving Equations. Solving Inequalities. Graphical Representation of Data. Graphs of Equations. Linear Equations in Two Variables.
1. FUNCTIONS AND THEIR GRAPHS.
Functions. Analyzing Graphs of Functions. Transformations of Functions. Combinations of Functions: Composite Functions. Inverse Functions. Mathematical Modeling and Variation.
2. POLYNOMIAL AND RATIONAL FUNCTIONS.
Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial and Synthetic Division. Complex Numbers. The Fundamental Theorem of Algebra. Rational Functions.
3. LIMITS AND THEIR PROPERTIES.
A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits.
4. DIFFERENTIATION
The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Related Rates.
5. APPLICATIONS OF DIFFERENTIATION.
Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Differentials.
6. INTEGRATION.
Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Applications of Integration.
7. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions and Their Graphs. Logarithmic Functions and Their Graphs. Using Properties of Logarithms. Exponential and Logarithmic Equations. Exponential and Logarithmic Models.
8. EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND CALCULUS.
Exponential Functions: Differentiation and Integration. Logarithmic Functions and Differentiation. Logarithmic Functions and Integration. Differential Equations: Growth and Decay.
9. TRIGONOMETRIC FUNCTIONS.
Radian and Degree Measure. Trigonometric Functions: The Unit Circle. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Graphs of Sine and Cosine Functions. Graphs of Other Trigonometric Functions. Inverse Trigonometric Functions. Applications and Models.
10. ANALYTIC TRIGONOMETRY.
Using Fundamental Identities. Verifying Trigonometric Identities. Solving Trigonometric Equations. Sum and Difference Formulas. Multiple-Angle and Product-Sum Formulas.
11. TRIGONOMETRIC FUNCTIONS AND CALCULUS.
Limits of Trigonometric Functions. Trigonometric Functions: Differentiation. Trigonometric Functions: Integration. Inverse Trigonometric Functions: Differentiation. Inverse Trigonometric Functions: Integration. Hyperbolic Functions.
12. TOPICS IN ANALYTIC GEOMETRY.
Introduction to Conics: Parabolas. Ellipses and Implicit Differentiation. Hyperbolas and Implicit Differentiation. Parametric Equations and Calculus. Polar Coordinates and Calculus. Graphs of Polar Coordinates. Polar Equations of Conics.
13. ADDITIONAL TOPICS IN TRIGONOMETRY.
Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot Products. Trigonometric Form of a Complex Number.

3.New to this Edition

Table of Contents Update: Chapter 14 has been omitted.
NEW! Chapter Summary gives a concise review of key terms and concepts covered in each chapter.
NEW! Chapter Tests have been added to each chapter and are one page assessments of problems covering key topics.
NEW! Explorations, an optional discovery feature, help students develop intuitive understanding of calculus concepts. These can be deleted without loss of continuity.
UPDATED! Appropriate exercises will be labeled as Writing About the Concepts.
NEW! CalcChat.com reference has been added to text exercise sets.

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