by Soo T. Tan
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Author Bio
Soo T. Tan, Professor of Mathematics at Stonehill College, has published numerous papers in Optimal Control Theory and Numerical Analysis. He received his S.B. degree from Massachusetts Institute of Technology, his M.S. degree from the University of Wisconsin-Madison, and his Ph.D. from the University of California at Los Angeles. "One of the most important lessons I learned from my early experience teaching these courses is that many of the students come into these courses with some degree of apprehension. This awareness led to the intuitive approach I have adopted in all of my texts."
Preface.
1. PRELIMINARIES.
Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines. Chapter 1 Summary of Principal Formulas and Terms. Chapter 1 Concept Review Questions. Chapter 1 Review Exercises. Chapter 1 Before Moving On.
2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Portfolio. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Chapter 2 Summary of Principal Formulas and Terms. Chapter 2 Concept Review Questions. Chapter 2 Review Exercises. Chapter 2 Before Moving On.
3. DIFFERENTIATION.
Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Using Technology: Finding the Differential of a Function. Chapter 3 Summary of Principal Formulas and Terms. Chapter 3 Concept Review Questions. Chapter 3 Review Exercises. Chapter 3 Before Moving On.
4. APPLICATIONS OF THE DERIVATIVE.
Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Chapter 4 Summary of Principal Terms. Chapter 4 Concept Review Questions. Chapter 4 Review Exercises. Chapter 4 Before Moving On.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Using Technology. Logarithmic Functions. Compound Interest. Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment. Differentiation of Exponential Functions. Using Technology. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Portfolio. Using Technology: Analyzing Mathematical Models. Chapter 5 Summary of Principal Formulas and Terms. Chapter 5 Concept Review Questions. Chapter 5 Review Exercises. Chapter 5 Before Moving On.
6. INTEGRATION.
Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Portfolio. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Business and Economic Applications/Technology Exercises. Chapter 6 Summary of Principal Formulas and Terms. Chapter 6 Concept Review Questions. Chapter 6 Review Exercises. Chapter 6 Before Moving On.
7. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Calculus to Probability. Chapter 7 Summary of Principal Formulas and Terms. Chapter 7 Concept Review Questions. Chapter 7 Review Exercises. Chapter 7 Before Moving On.
8. CALCULUS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Portfolio. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Chapter 8 Summary of Principal Formulas and Terms. Chapter 8 Concept Review Questions. Chapter 8 Review Exercises. Chapter 8 Before Moving On.
Appendix A.
The Inverse of a Function. The Graphs of Inverse Functions. Functions That Have Inverses. Finding the Inverse of a Function.
Appendix B.
Indeterminant Forms and l'Hôpital's Rule. The Indeterminant Forms 0/0 and ?/ ?.
Index.
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Author Bio
Soo T. Tan, Professor of Mathematics at Stonehill College, has published numerous papers in Optimal Control Theory and Numerical Analysis. He received his S.B. degree from Massachusetts Institute of Technology, his M.S. degree from the University of Wisconsin-Madison, and his Ph.D. from the University of California at Los Angeles. "One of the most important lessons I learned from my early experience teaching these courses is that many of the students come into these courses with some degree of apprehension. This awareness led to the intuitive approach I have adopted in all of my texts."
Table of Contents
Preface.
1. PRELIMINARIES.
Precalculus Review I. Precalculus Review II. The Cartesian Coordinate System. Straight Lines. Chapter 1 Summary of Principal Formulas and Terms. Chapter 1 Concept Review Questions. Chapter 1 Review Exercises. Chapter 1 Before Moving On.
2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
Functions and Their Graphs. The Algebra of Functions. Functions and Mathematical Models. Portfolio. Using Technology: Finding the Points of Intersection of Two Graphs and Modeling. Limits. Using Technology: Finding the Limit of a Function. One-Sided Limits and Continuity. Using Technology: Finding the Points of Discontinuity of a Function. The Derivative. Using Technology: Graphing a Function and Its Tangent Line. Chapter 2 Summary of Principal Formulas and Terms. Chapter 2 Concept Review Questions. Chapter 2 Review Exercises. Chapter 2 Before Moving On.
3. DIFFERENTIATION.
Basic Rules of Differentiation. Using Technology: Finding the Rate of Change of a Function. The Product and Quotient Rules. Using Technology: The Product and Quotient Rules. The Chain Rule. Using Technology: Finding the Derivative of a Composite Function. Marginal Functions in Economics. Higher-Order Derivatives. Using Technology: Finding the Second Derivative of a Function at a Given Point. Implicit Differentiation and Related Rates. Differentials. Using Technology: Finding the Differential of a Function. Chapter 3 Summary of Principal Formulas and Terms. Chapter 3 Concept Review Questions. Chapter 3 Review Exercises. Chapter 3 Before Moving On.
4. APPLICATIONS OF THE DERIVATIVE.
Applications of the First Derivative. Using Technology: Using the First Derivative to Analyze a Function. Applications of the Second Derivative. Using Technology: Finding the Inflection Points of a Function. Curve Sketching. Using Technology: Analyzing the Properties of a Optimization I. Using Technology: Finding the Absolute Extrema of a Function. Optimization II. Chapter 4 Summary of Principal Terms. Chapter 4 Concept Review Questions. Chapter 4 Review Exercises. Chapter 4 Before Moving On.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Using Technology. Logarithmic Functions. Compound Interest. Using Technology: Finding the Accumulated Amount of an Investment, the Effective Rate of Interest, and the Present Value of an Investment. Differentiation of Exponential Functions. Using Technology. Differentiation of Logarithmic Functions. Exponential Functions as Mathematical Models. Portfolio. Using Technology: Analyzing Mathematical Models. Chapter 5 Summary of Principal Formulas and Terms. Chapter 5 Concept Review Questions. Chapter 5 Review Exercises. Chapter 5 Before Moving On.
6. INTEGRATION.
Antiderivatives and the Rules of Integration. Integration by Substitution. Area and the Definite Integral. The Fundamental Theorem of Calculus. Portfolio. Using Technology: Evaluating Definite Integrals. Evaluating Definite Integrals. Using Technology: Evaluating Integrals for Piecewise-Defined Functions. Area between Two Curves. Using Technology: Finding the Area between Two Curves. Applications of the Definite Integral to Business and Economics. Using Technology: Business and Economic Applications/Technology Exercises. Chapter 6 Summary of Principal Formulas and Terms. Chapter 6 Concept Review Questions. Chapter 6 Review Exercises. Chapter 6 Before Moving On.
7. ADDITIONAL TOPICS IN INTEGRATION.
Integration by Parts. Integration Using Tables of Integrals. Numerical Integration. Improper Integrals. Applications of Calculus to Probability. Chapter 7 Summary of Principal Formulas and Terms. Chapter 7 Concept Review Questions. Chapter 7 Review Exercises. Chapter 7 Before Moving On.
8. CALCULUS OF SEVERAL VARIABLES.
Functions of Several Variables. Partial Derivatives. Portfolio. Using Technology: Finding Partial Derivatives at a Given Point. Maxima and Minima of Functions of Several Variables. The Method of Least Squares. Using Technology: Finding an Equation of Least-Squares Line. Constrained Maxima and Minima and the Method of Lagrange Multipliers. Double Integrals. Chapter 8 Summary of Principal Formulas and Terms. Chapter 8 Concept Review Questions. Chapter 8 Review Exercises. Chapter 8 Before Moving On.
Appendix A.
The Inverse of a Function. The Graphs of Inverse Functions. Functions That Have Inverses. Finding the Inverse of a Function.
Appendix B.
Indeterminant Forms and l'Hôpital's Rule. The Indeterminant Forms 0/0 and ?/ ?.
Index.
Digital Rights
eTextbooks and eChapters can be viewed by using the free reader listed below.
Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.
Download Requirements:Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.
Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.
User Help:
Click Here to access the VitalSource Bookshelf FAQ
Digital Rights Management (DRM) Key
Printing - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."
Expires - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).
Reading Aloud - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."
Sharing - Books that cannot be shared with other computers will show "Not Allowed."
Min. Software Version - This is the minimum software version needed to read this book.
Suitable Devices - Hardware known to be compatable with this book. Note: Reader software still needs to be installed.