| A Preview of Calculus 1 Functions and Models 1.1 Four Ways to Represent a Function 1.2 Mathematical Models 1.3 New Functions from Old Functions 1.4 Graphing Calculators and Computers 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 1.7 Parametric Curves Laboratory Project Running Circles around Circles Review 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 Continuity 2.5 Limits Involving Infinity 2.6 Tangents, Velocities, and Other Rates of Change 2.7 Derivatives Writing Project: Early Methods for Finding Tangents 2.8 The Derivative as a Function 2.9 Linear Approximations 2.10 What Does f1 Say about f? Review Focus on Problem Solving 3 Differentiation Rules 4 Applications of Differentiation 5 Integrals 6 Applications of Integration 7 Differential Equations 8 Infinite Sequences and Series 9 Vectors and the Geometry of Space 10 Vector Functions 11 Partial Derivatives 12 Multiple Integrals 13 Vector Calculus Appendixes Index |
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