Preface xi
To the Student
Diagnostic Tests xxiv
A PREVIEW OF CALCULUS
1 Functions and Models
1.1 Four Ways to Represent a Function
1.2 Mathematical Models:A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Graphing Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
Principles of Problem Solving
2 Limits and Derivatives
2.1 The Tangent and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity;Horizontal Asymptotes
2.7 Derivatives and Rates of Change Writing Project Early Methods for Finding Tangents
2.8 The Derivative as a Function
Review
Problems PlUS
3 Differentiation Rules
4 Aookucatuibs if Dufferebtuatuib
5 Integrals
6 Applications of Integration
7 Techniques of Integration
8 Further Applications of Integration
9 Differential Equations
10 Parametric Equations and Polar Coordinates
11 Infinite Sequences and Series
12 Vectors and the Geometry of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
17 Second-Order Differential Equations
Appendixes
Index
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