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 Cengage Learning *agena
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 1 Functions and Limits 1.1 Functions and Their Representations 1.2 A Catalog of Essential Functions 1.3 The Limit of a Function 1.4 Calculating Limits 1.5 Continuity 1.6 Limits Involving Infinity 2 Derivatives 2.1 Derivatives and Rates of Change 2.2 The Derivative as a Function 2.3 Basic Differentiation Formulas 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Implicit Differentiation 2.7 Related Rates 2.8 Linear Approximations and Differentials 3 Applications of Differentiation 3.1 Maximum and Minimum Values 3.2 The Mean Value Theorem 3.3 Derivatives and the Shapes of Graphs 3.4 Curve Sketching 3.5 Optimization Problems 3.6 Newton's Method 3.7 Antiderivatives 4 Integrals 4.1 Areas and Distances 4.2 The Definite Integral 4.3 Evaluating Definite Integrals 4.4 The Fundamental Theorem of Calculus 4.5 The Substitution Rule 5 Inverse Functions 5.1 Inverse Functions 5.2 The Natural Logarithmic Function 5.3 The Natural Exponential Function 5.4 General Logarithmic and Exponential Functions 5.5 Exponential Growth and Decay 5.6 Inverse Trigonometric Functions 5.7 Hyperbolic Functions 5.8 Indeterminate Forms and l'Hospital's Rule 6 Techniques of Integration 6.1 Integration by Parts 6.2 Trigonometric Integrals and Substitutions 6.3 Partial Fractions 6.4 Integration with Tables and Computer Algebra Systems 6.5 Approximate Integration 6.6 Improper Integrals 7 Applications of Integration 7.1 Areas between Curves 7.2 Volumes 7.3 Volumes by Cylindrical Shells 7.4 Arc Length 7.5 Applications to Physics and Engineering 7.6 Differential Equations 8 Series 8.1 Sequences 8.2 Series 8.3 The Integral and Comparison Tests 8.4 Other Convergence Tests 8.5 Power Series 8.6 Representing Functions as Power Series 8.7 Taylor and Maclaurin Series 8.8 Applications of Taylor Polynomials 9 Parametric Equations and Polar Coordinates 9.1 Parametric Curves 9.2 Calculus with Parametric Curves 9.3 Polar Coordinates 9.4 Areas and Lengths in Polar Coordinates 9.5 Conic Sections in Polar Coordinates 10 Vectors and the Geometry of Space 10.1 Three-Dimensional Coordinate Systems 10.2 Vectors 10.3 The Dot Product 10.4 The Cross Product 10.5 Equations of Lines and Planes 10.6 Cylinders and Quadric Surfaces 10.7 Vector Functions and Space Curves 10.8 Arc Length and Curvature 10.9 Motion in Space: Velocity and Acceleration 11 Partial Derivatives 11.1 Functions of Several Variables 11.2 Limits and Continuity 11.3 Partial Derivatives 11.4 Tangent Planes and Linear Approximations 11.5 The Chain Rule 11.6 Directional Derivatives and the Gradient Vector 11.7 Maximum and Minimum Values 11.8 Lagrange Multipliers 12 Multiple Integrals 12.1 Double Integrals over Rectangles 12.2 Double Integrals over General Regions 12.3 Double Integrals in Polar Coordinates 12.4 Applications of Double Integrals 12.5 Triple Integrals 12.6 Triple Integrals in Cylindrical Coordinates 12.7 Triple Integrals in Spherical Coordinates 12.8 Change of Variables in Multiple Integrals 13 Vector Calculus 13.1 Vector Fields 13.2 Line Integrals 13.3 The Fundamental Theorem for Line Integrals 13.4 Green's Theorem 13.5 Curl and Divergence 13.6 Parametric Surfaces and Their Areas 13.7 Surface Integrals 13.8 Stokes' Theorem 13.9 The Divergence Theorem