Browse Visuals and Modules Browse Homework Hints
 Cengage Learning *agena
Browse Visuals and Modules
Browse Homework Hints
 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 2 Limits and Derivatives 2.1 The Tangent and Velocity Problems 2.2 Limit of a Function 2.3 Calculating Limits Using the Limit Law 2.4 Continuity 2.5 Limits Involving Infinity 2.6 Tangents, Velocities, and Other Rates of Change 2.7 Derivatives 2.8 The Derivative as a Function 2.9 What Does f' Say about f'? 3 Differentiation Rules 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Rates of Change in the Natural and Social Sciences 3.4 Derivatives of Trigonometric Function 3.5 The Chain Rule 3.6 Implicit Differentiation 3.7 Derivatives of Logarithmic Functions 3.8 Linear Approximations and Differentials 4 Applications of Differentiation 4.1 Related Rates 4.2 Maximum and Minimum Values 4.3 Derivatives and the Shapes of Curves 4.4 Graphing with Calculus and Calculators 4.5 Indeterminate Forms and l'Hospital's Rule 4.6 Optimization Problems 4.7 Applications to Business and Economics 4.8 Newton's Method 4.9 Antiderivatives 5 Integrals 5.1 Areas and Distances 5.2 The Definite Integral 5.3 Evaluating Definite Integrals 5.4 The Fundamental Theorem of Calculus 5.5 The Substitution Rule 5.6 Integration by Parts 5.7 Additional Techniques of Integration 5.8 Integration Using Tables and Computer Algebra Systems 5.9 Approximate Integration 5.10 Improper Integrals 6 Applications of Integration 6.1 More about Areas 6.2 Volumes 6.3 Arc Length 6.4 Average Value of a Function 6.5 Applications to Physics and Engineering 6.6 Applications to Economics and Biology 6.7 Probability 7 Differential Equations 7.1 Modeling with Differential Equations 7.2 Direction Fields and Euler's Method 7.3 Separable Equations 7.4 Exponential Growth and Decay 7.5 The Logistic Equation 7.6 Predator-Prey Systems 8 Infinite Sequences and Series 8.1 Sequences 8.2 Series 8.3 The Integral and Comparison Tests; Estimating Sums 8.4 Other Convergence Tests 8.5 Power Series 8.6 Representations of Functions as Power Series 8.7 Taylor and Maclaurin Series 8.8 The Binomial Series 8.9 Applications of Taylor Polynomials 9 Vectors and the Geometry of Space 9.1 Three-Dimensional Coordinate Systems 9.2 Vectors 9.3 The Dot Product 9.4 The Cross Product 9.5 Equations of Lines and Planes 9.6 Functions and Surfaces 9.7 Cylindrical and Spherical Coordinates 10 Vector Functions 10.1 Vector Functions and Space Curves 10.2 Derivatives and Integrals of Vector Functions 10.3 Arc Length and Curvature 10.4 Motion in Space: Velocity and Acceleration 10.5 Parametric Surfaces 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 Iterated Integrals 12.3 Double Integrals over General Regions 12.4 Double Integrals in Polar Coordinates 12.5 Applications of Double Integrals 12.6 Surface Area 12.7 Triple Integrals 12.8 Triple Integrals in Cylindrical and Spherical Coordinates 12.9 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 Surface Integrals 13.7 Stokes' Theorem 13.8 The Divergence Theorem Appendixes Appendix D Precise Definitions of Limits Appendix G Integration of Rational Functions by Partial Fractions Appendix H.1 Polar Coordinates Appendix H.2 Polar Coordinates