Description: 0. Before Calculus 0.1 Functions 0.2New Functions from Old 0.3Families of Functions 0.4Inverse Functions1. Limits and Continuity 1.1Limits (An Intuitive Approach) 1.2Computing Limits 1.3Limits at Infinity; End Behavior of a Function 1.4Limits (Discussed More Rigorously) 1.5Continuity 1.6Continuity of Trigonometric Functions2. The Derivative 2.1Tangent Lines and Rates of Change 2.2The Derivative Function 2.3Introduction to Techniques of Differentiation 2.4The Product and Quotient Rules 2.5Derivatives of Trigonometric Functions 2.6The Chain Rule 2.7Implicit Differentiation 2.8Related Rates 2.9Local Linear Approximation; Differentials3. The Derivative in Graphing and Applications 3.1Analysis of Functions I: Increase, Decrease, and Concavity 3.2Analysis of Functions II: Relative Extrema; Graphing Polynomials 3.3Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents 3.4Absolute Maxima and Minima 3.5Applied Maximum and Minimum Problems 3.6Rectilinear Motion 3.7Newton's Method 3.8Rolle's Theorem; Mean-Value Theorem4. Integration 4.1An Overview of the Area Problem 4.2The Indefinite Integral 4.3Integration by Substitution 4.4 The Definition of Area as a Limit; Sigma Notation 4.5The Definite Integral 4.6The Fundamental Theorem of Calculus 4.7Rectilinear Motion Revisited: Using Integration 4.8Average Value of a Function and Its Applications 4.9Evaluating Definite Integrals by Substitution5. Applications of the Definite Integral in Geometry, Science and Engineering 5.1Area Between Two Curves 5.2Volumes by Slicing; Disks and Washers 5.3Volumes by Cylindrical Shells 5.4Length of a Plane Curve 5.5Area of a Surface Revolution 5.6Work 5.7Moments, Centers of Gravity, and Centroids 5.8Fluid Pressure and Force6. Exponential, Logarithmic, and Inverse Trigonometric Functions 6.1Exponential and Logarithmic Functions 6.2Derivatives and Integrals Involving Logarithmic Functions 6.3Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions 6.4Graphs and Applications Involving Logarithmic and Exponential Functions 6.5L'Hopital's Rule; Indeterminate Forms 6.6Logarithmic and Other Functions Defined by Integrals 6.7Derivatives and Integrals Involving Inverse Trigonometric Functions 6.8Hyperbolic Functions and Hanging CubesCh 7 Principles of Integral Evaluation 7.1 An Overview of Integration Methods 7.2 Integration by Parts 7.3 Integrating Trigonometric Functions 7.4 Trigonometric Substitutions 7.5 Integrating Rational Functions by Partial Fractions 7.6 Using Computer Algebra Systems and Tables of Integrals 7.7 Numerical Integration; Simpson's Rule 7.8 Improper IntegralsCh 8 Mathematical Modeling with Differential Equations 8.1 Modeling with Differential Equations 8,2 Separation of Variables 8.3 Slope Fields; Euler's Method 8.4 First-Order Differential Equations and ApplicationsCh 9 Infinite Series 9.1 Sequences 9.2 Monotone Sequences 9.3 Infinite Series 9.4 Convergence Tests 9.5 The Comparison, Ratio, and Root Tests 9.6 Alternating Series; Absolute and Conditional Convergence 9.7 Mac

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