Introductory Calculus

Preface to the Second EditionAcknowledgmentsChapter 1 Some Analytic Geometry 1.1 What Is Analytic Geometry? 1.2 Vectors in.the Plane 1.3 The Straight Line 1.4 The Conic SectionsChapter 2 Functions 2.1 Number Machines 2.2 Functions 2.3 Graphs; Getting the Picture 2.4 This Is the Limit 2.5 Composition of Functions; the Inverse 2.6 Well-Behaved Functions 2.7 ApproximationChapter 3 The Derivative 3.1 The Definition 3.2 Notation 3.3 The Speedometer Reading 3.4 Computational Rules 3.5 The Derivative as a Linear TransformationChapter 4 More About the Derivative 4.1 The Mean Value Theorem 4.2 Higher Derivatives 4.3 Taylor's FormulaChapter 5 Applications 5.1 Graphs; Refining the Picture 5.2 Maxima-Minima Problems 5.3 Velocity and Acceleration; Related RatesChapter 6 The Definite Integral 6.1 The Area Under a Curve 6.2 The Integral Defined 6.3 Properties of the Integral 6.4 The Fundamental Theorem 6.5 Improper IntegralsChapter 7 Transcendental Functions 7.1 Trigonometric Functions 7.2 Derivatives of the Trigonometric Functions 7.3 Derivatives of the Inverse Trigonometric Functions 7.4 The Logarithm and Its Inverse 7.5 The Hyperbolic Functions 7.6 A Tool for Finding LimitsChapter 8 Finding Antiderivatives 8.1 A Summary 8.2 Trigonometric Substitutions 8.3 Integration by Parts 8.4 Rational Functions 8.5 Other MethodsChapter 9 Curves in the Plane 9.1 Parametric Equations 9.2 Curves 9.3 Differentiation of Vector-Valued Functions 9.4 Acceleration and Curvature 9.5 Polar CoordinatesChapter 10 Linear Algebra 10.1 Solving Linear Equations 10.2 More About Vectors 10.3 Linear Transformations 10.4 Determinants 10.5 Change of Basis 10.6 Bilinear Transformations and Quadratic Forms 10.7 Symmetric MatricesChapter 11 Functions of Several Variables 11.1 Vectors in R3 11.2 Lines and Planes in R3 11.3 Surfaces in R3 11.4 Functions 11.5 The Approximation ProblemChapter 12 The Derivative of Functions of Several Variables 12.1 The Definition 12.2 Real-Valued Functions of Several Variables 12.3 Higher Derivatives 12.4 More About Extreme Values of FunctionsChapter 13 Integration of Functions of Several Variables 13.1 The Integral on a Rectangle 13.2 The Integral on a Nice Set 13.3 Change of VariablesChapter 14 Infinite Series 14.1 Sequences and Series 14.2 Positive Series 14.3 Series with Some Negative Terms 14.4 Functions Defined by Infinite SeriesChapter 15 Differential Equations 15.1 Problems That Lead to Differential Equations 15.2 Families of Solutions 15.3 Linear Differential Equations with Constant Coefficients 15.4 First-Order Linear Differential Equations 15.5 Other First-Order, First-Degree Differential Equations 15.6 Approximating SolutionsWhat Next?BibliographyTable of AntiderivativesSolutions to ProblemsAnswers to Odd ExercisesIndex