Brief Calculus An Applied Approach

by Larson, Ron; Edwards, Bruce H.

• ISBN13: 9780618547197
• ISBN10: 0618547193
• Edition: 7th
• Format: Hardcover
• Copyright: 2005-02-02
• Publisher: Cengage Learning

Summary

This text comprises Chapters 0–7 of Larson and Edwards' Calculus: An Applied Approach, 6/e. For a complete description of this text's features, refer to the entry for that text.

Table of Contents

A Word from the Authors (Preface)	vii
Features	xii
A Plan for You as a Student (Study Strategies)	xx
A Precalculus Review	1	(1)
The Real Number Line and Order	2	(6)
Absolute Value and Distance on the Real Number Line	8	(5)
Exponents and Radicals	13	(6)
Factoring Polynomials	19	(6)
Fractions and Rationalization	25
Functions, Graphs, and Limits	1	(80)
The Cartesian Plane and the Distance Formula	2	(9)
Graphs of Equations	11	(13)
Lines in the Plane and Slope	24	(12)
Functions	36	(13)
Limits	49	(12)
Continuity	61	(20)
Chapter 1 Algebra Review	72	(2)
Chapter Summary and Study Strategies	74	(2)
Review Exercises	76	(4)
Sample Post-Graduation Exam Questions	80	(1)
Differentiation	81	(90)
The Derivative and the Slope of a Graph	82	(11)
Some Rules for Differentiation	93	(12)
Rates of Change: Velocity and Marginals	105	(15)
The Product and Quotient Rules	120	(11)
The Chain Rule	131	(9)
Higher-Order Derivatives	140	(7)
Implicit Differentiation	147	(7)
Related Rates	154	(17)
Chapter 2 Algebra Review	162	(2)
Chapter Summary and Study Strategies	164	(2)
Review Exercises	166	(4)
Sample Post-Graduation Exam Questions	170	(1)
Applications of the Derivative	171	(86)
Increasing and Decreasing Functions	172	(9)
Extrema and the First-Derivative Test	181	(10)
Concavity and the Second-Derivative Test	191	(10)
Optimization Problems	201	(9)
Business and Economics Applications	210	(10)
Asymptotes	220	(11)
Curve Sketching: A Summary	231	(9)
Differentials and Marginal Analysis	240	(17)
Chapter 3 Algebra Review	248	(2)
Chapter Summary and Study Strategies	250	(2)
Review Exercises	252	(4)
Sample Post-Graduation Exam Questions	256	(1)
Exponential and Logarithmic Functions	257	(60)
Exponential Functions	258	(6)
Natural Exponential Functions	264	(9)
Derivatives of Exponential Functions	273	(8)
Logarithmic Functions	281	(9)
Derivatives of Logarithmic Functions	290	(9)
Exponential Growth and Decay	299	(18)
Chapter 4 Algebra Review	308	(2)
Chapter Summary and Study Strategies	310	(2)
Review Exercises	312	(4)
Sample Post-Graduation Exam Questions	316	(1)
Integration and Its Applications	317	(70)
Antiderivatives and Indefinite Integrals	318	(11)
The General Power Rule	329	(8)
Exponential and Logarithmic Integrals	337	(7)
Area and the Fundamental Theorem of Calculus	344	(12)
The Area of a Region Bounded by Two Graphs	356	(9)
The Definite Integral as the Limit of a Sum	365	(6)
Volumes of Solids of Revolution	371	(16)
Chapter 5 Algebra Review	378	(2)
Chapter Summary and Study Strategies	380	(2)
Review Exercise	382	(4)
Sample Post-Graduation Exam Questions	386	(1)
Techniques of Integration	387	(68)
Integration by Substitution	388	(8)
Integration by Parts and Present Value	396	(10)
Partial Fractions and Logistic Growth	406	(10)
Integration Tables and Completing the Square	416	(10)
Numerical Integration	426	(10)
Improper Integrals	436	(19)
Chapter 6 Algebra Review	446	(2)
Chapter Summary and Study Strategies	448	(2)
Review Exercises	450	(4)
Sample Post-Graduation Exam Questions	454	(1)
Functions of Several Variables	455
The Three-Dimensional Coordinate System	456	(8)
Surfaces in Space	464	(10)
Functions of Several Variables	474	(9)
Partial Derivatives	483	(11)
Extrema of Functions of Two Variables	494	(10)
Lagrange Multipliers	504	(10)
Least Squares Regression Analysis	514	(10)
Double Integrals and Area in the Plane	524	(8)
Applications of Double Integrals	532
Chapter 7 Algebra Review	540	(2)
Chapter Summary and Study Strategies	542	(2)
Review Exercises	544	(4)
Sample Post-Graduation Exam Questions	548
Appendices	1	(20)
Appendix A: Alternate Introduction to the Fundamental Theorem of Calculus	2	(10)
Appendix B: Formulas	12	(9)
Appendix C: Differential Equations
Solutions of Differential Equations
Separation of Variables
First-Order Linear Differential Equations
Applications of Differential Equations
Appendix D: Properties and Measurement
Review of Algebra, Geometry, and Trigonometry
Units of Measurements
Appendix E: Graphing Utility Programs
Graphing Utility Programs
Answers to Selected Exercises	21	(64)
Answers to Try Its	85	(12)
Index	97