目录 Preface xiTo the Student xxiiiDiagnostic Tests xxivA PREVIEW OF CALCULUS Functions and Models1.1 Four Ways to Represent a Function1.2 Mathematical Models: A Catalog of Essential Functions1.3 New Functions from Old Functions1.4 Graphing Calculators and Computers1.5 Exponential Functions1.6 Inverse Functions and Logarithms ReviewPrinciples of Problem SolvingLimits and Derivatives2.1 The Tangent and Velocity Problems2.2 The Limit of a Function2.3 Calculating Limits Using the Limit Laws2.4 The Precise Definition of a Limit2.5 Continuity2.6 Limits at Infinity; Horizontal Asymptotes2.7 Derivatives and Rates of Change 143 Writing Project - Early Methods for Finding Tangents2.8 The Derivative as a FunctionReview Problems Plus3 Differentiation Rules4 Applications of Differentiation5 Integrals6 Applications of Integration7 Techniques of Integration8 Further Applications of Integration9 Differential Equations10 Parametric Equations and Polar Coordinates11 Infinite Sequences and Series12 Vectors and the Geometry of Space13 Vector Functions14 Partial Derivatives15 Multiple Integrals16 Vector Calculus17 Second-Order Differential EquationsAppendixesIndex
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