## Brief calculus and its applications

Author: Goldstein, Larry J. ; Lay, David C. ; Schneider, David I.Publisher: Prentice Hall, 1996.Language: EnglishDescription: 602 p. ; 24 cm.ISBN: 0133214230Type of document: BookBibliography/Index: Includes indexItem type | Current location | Collection | Call number | Status | Date due | Barcode | Item holds |
---|---|---|---|---|---|---|---|

Europe Campus Main Collection |
QA303 .G65 1996
(Browse shelf) 001221856 |
Available | 001221856 |

Includes index

Digitized

Brief Calculus and Its Application Contents PREFACE, ix INTRODUCTION 0 0.1 0.2 0.3 0.4 0.5 0.6 FUNCTIONS, 3 Functions and Their Graphs, 3 Some Important Functions, 22 The Algebra of Functions, 31 Zeros of Functions--The Quadratic Formula and Factoring, 37 Exponents and Power Functions, 46 Functions and Graphs in Applications, 55 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 THE DERIVATIVE, 71 The Slope of a Straight Line, 72 The Slope of a Curve at a Point, 84 The Derivative, 92 Limits and the Derivative, 103 Differentiability and Continuity, 114 Some Rules for Differentiation, 121 More About Derivatives, 128 The Derivative as a Rate of Change, 134 2 2.1 2.2 2.3 2.4 APPLICATIONS OF THE DERIVATIVE, 157 Describing Graphs of Functions, 158 The First and Second Derivative Rules, 173 Curve Sketching (Introduction), 189 Curve Sketching (Conclusion), 199 2.5 2.6 2.7 Optimization Problems, 207 Further Optimization Problems, 218 Applications of Calculus to Business and Economics, 230 3 3.1 3.2 3.3 TECHNIQUES OF DIFFERENTIATION, 249 The Product and Quotient Rules, 249 The Chain Rule and the General Power Rule, 261 Implicit Differentiation and Related Rates, 268 4 4.1 4.2 4.3 4.4 4.5 4.6 THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS, 287 Exponential Functions, 288 The Exponential Function ex, 292 Differentiation of Exponential Functions, 299 The Natural Logarithm Function, 305 The Derivative of In x, 311 Properties of the Natural Logarithm Function, 316 5 APPLICATIONS OF THE EXPONENTIAL AND NATURAL LOGARITHM FUNCTIONS, 325 5.1 5.2 5.3 5.4 Exponential Growth and Decay, 326 Compound Interest, 340 Applications of the Natural Logarithm Functions to Economics, 347 Further Exponential Models, 355 6 6.1 6.2 6.3 6.4 6.5 THE DEFINITE INTEGRAL, 373 Antidifferentiation, 374 Areas and Riemann Sums, 386 Definite Integrals and the Fundamental Theorem, 398 Areas in the xy-Plane, 413 Applications of the Definite Integral, 424 6.6 6.7 6.8 Techniques of Integration, 435 Improper Integrals, 447 Applications of Calculus to Probability, 454 7 7.1 7.2 7.3 7.4 7.5 7.6 FUNCTIONS OF SEVERAL VARIABLES, 467 Examples of Functions of Several Variables, 469 Partial Derivatives, 479 Maxima and Minima of Functions of Several Variables, 491 Lagrange Multipliers and Constrained Optimization, 502 The Method of Least Squares, 515 Double Integrals, 523 8 8.1 8.2 8.3 8.4 THE TRIGONOMETRIC FUNCTIONS, 535 Radian Measure of Angles, 535 The Sine and the Cosine, 540 Differentiation of sin t and cos t, 550 The Tangent and Other Trigonometric Functions, 563 ANSWERS TO EXERCISES, 573 INDEX, 597

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