书名：CALCULUS CALCU LUS I

作者：Paul Dawkins

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文件大小：2.86M

页数：574

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目录：Preface .......................................................................................................................................... iii
Outline .......................................................................................................................................... iv
Review............................................................................................................................................ 2 Introduction ............................................................................................................................................. 2 Review : Functions .................................................................................................................................. 4 Review : Inverse Functions .................................................................................................................... 14 Review : Trig Functions ......................................................................................................................... 21 Review : Solving Trig Equations ............................................................................................................ 28 Review : Solving Trig Equations with Calculators, Part I .................................................................... 37 Review : Solving Trig Equations with Calculators, Part II ................................................................... 48 Review : Exponential Functions ............................................................................................................ 53 Review : Logarithm Functions ............................................................................................................... 56 Review : Exponential and Logarithm Equations .................................................................................. 62 Review : Common Graphs ...................................................................................................................... 68
Limits ........................................................................................................................................... 80 Introduction ........................................................................................................................................... 80 Rates of Change and Tangent Lines ...................................................................................................... 82 The Limit ................................................................................................................................................ 91 One‐Sided Limits ..................................................................................................................................101 Limit Properties ....................................................................................................................................107 Computing Limits .................................................................................................................................113 Infinite Limits .......................................................................................................................................121 Limits At Infinity, Part I .........................................................................................................................130 Limits At Infinity, Part II .......................................................................................................................139 Continuity ..............................................................................................................................................148 The Definition of the Limit ....................................................................................................................155
Derivatives ................................................................................................................................. 170 Introduction ..........................................................................................................................................170 The Definition of the Derivative ...........................................................................................................172 Interpretations of the Derivative .........................................................................................................178 Differentiation Formulas ......................................................................................................................183 Product and Quotient Rule ...................................................................................................................191 Derivatives of Trig Functions ...............................................................................................................197 Derivatives of Exponential and Logarithm Functions ........................................................................208 Derivatives of Inverse Trig Functions ..................................................................................................213 Derivatives of Hyperbolic Functions ....................................................................................................219 Chain Rule .............................................................................................................................................221 Implicit Differentiation .........................................................................................................................231 Related Rates ........................................................................................................................................240 Higher Order Derivatives ......................................................................................................................254 Logarithmic Differentiation ..................................................................................................................259
Applications of Derivatives ....................................................................................................... 262 Introduction ..........................................................................................................................................262 Rates of Change.....................................................................................................................................264 Critical Points ........................................................................................................................................267 Minimum and Maximum Values ...........................................................................................................273 Finding Absolute Extrema ....................................................................................................................281 The Shape of a Graph, Part I ..................................................................................................................287 The Shape of a Graph, Part II ................................................................................................................296 The Mean Value Theorem .....................................................................................................................305 Optimization .........................................................................................................................................312 More Optimization Problems ...............................................................................................................326
Calculus I
© 2007 Paul Dawkins ii http://tutorial.math.lamar.edu/terms.aspx
Indeterminate Forms and L’Hospital’s Rule ........................................................................................341 Linear Approximations .........................................................................................................................347 Differentials ..........................................................................................................................................350 Newton’s Method ..................................................................................................................................353 Business Applications ...........................................................................................................................358
Integrals ..................................................................................................................................... 364 Introduction ..........................................................................................................................................364 Indefinite Integrals ...............................................................................................................................365 Computing Indefinite Integrals ............................................................................................................371 Substitution Rule for Indefinite Integrals ............................................................................................381 More Substitution Rule .........................................................................................................................394 Area Problem ........................................................................................................................................407 The Definition of the Definite Integral .................................................................................................417 Computing Definite Integrals ...............................................................................................................427 Substitution Rule for Definite Integrals ...............................................................................................439
Applications of Integrals ........................................................................................................... 450 Introduction ..........................................................................................................................................450 Average Function Value ........................................................................................................................451 Area Between Curves ............................................................................................................................454 Volumes of Solids of Revolution / Method of Rings ............................................................................465 Volumes of Solids of Revolution / Method of Cylinders .....................................................................475 More Volume Problems .........................................................................................................................483 Work ......................................................................................................................................................494
Extras ......................................................................................................................................... 498 Introduction ..........................................................................................................................................498 Proof of Various Limit Properties ........................................................................................................499 Proof of Various Derivative Facts/Formulas/Properties ...................................................................510 Proof of Trig Limits ...............................................................................................................................523 Proofs of Derivative Applications Facts/Formulas .............................................................................528 Proof of Various Integral Facts/Formulas/Properties .......................................................................539 Area and Volume Formulas ..................................................................................................................551 Types of Infinity ....................................................................................................................................555 Summation Notation .............................................................................................................................559 Constants of Integration .......................................................................................................................561

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