TY - BOOK AU - Stewart,James TI - Single variable calculus: early transcendentals SN - 0534355633 U1 - 515 21 PY - 1999/// CY - Pacific Grove, Calif. PB - Brooks/Cole KW - Calculus N1 - Contents 1. FUNCTIONS AND MODELS Four Ways to Represent a Function Mathematical Models New Functions from Old Functions Graphing Calculators and Computers Exponential Functions Inverse Functions and Logarithms Review Problems Plus 2. LIMITS AND DERIVATIVES The Tangent and Velocity Problems The Limit of a Function Calculating Limits Using Limit Laws The Precise Definition of a Limit Continuity Limits at Infinity; Horizontal Asymptotes Tangents, Velocities, and Other Rates of Change Derivatives Writing Project: Early Methods for Finding Tangents The Derivative as a Function Review Problems Plus 3. DIFFERENTIATION RULES Derivatives of Polynomials and Exponential Functions The Product and Quotient Rules Rates of Change in the Natural and Social Sciences Derivatives of Trigonometric Functions The Chain Rule Implicit Differentiation Higher Derivatives Applied Project: Where Should a Pilot Start Descent? Derivatives of Logarithmic Functions Hyperbolic Functions Related Rates Linear Approximations and Differentials Laboratory Project: Taylor Polynomials Review Problems Plus 4. APPLICATIONS OF DIFFERENTIATION Maximum and Minimum Values Applied Project: The Calculus of Rainbows The Mean Value Theorem How Derivatives Affect the Shape of a Graph Intermediate Forms and L''''Hospital''''s Rule Writing Project: The Origins of L''''Hospital''''s Rule Summary of Curve Sketching Graphing with Calculus and Calculators Optimization Problems Applied Project: The Shape of a Can Applications to Economics Newton''''s Method Antiderivatives Review Problems Plus 5. INTEGRALS Areas and Distances The Definite Integral Discovery Project: Area Functions The Fundamental Theorem of Calculus Indefinite Integrals and the Total Change Theorem Writing Project: Newton, Leibniz, and the Invention of Calculus The Substitution Rule The Logarithm Defined as an Integral Review Problems Plus 6. APPLICATIONS OF INTEGRATION Areas between Curves Volume Volumes by Cylindrical Shells Work Average Value of a Function Applied Project: Where to Sit at the Movies Review Problems Plus 7. TECHNIQUES OF INTEGRATION Integration by Parts Trigonometric Integrals Trigonometric Substitution Integration of Rational Functions by Partial Fractions Strategy for Integration Integration Using Tables and Computer Algebra Systems Discovery Project: Patterns in Integrals Approximate Integration Improper Integrals Review Problems Plus 8. FURTHER APPLICATIONS OF INTEGRATION Arc Length Area of a Surface of Revolution Discovery Project: Rotating on a Slant Applications to Physics and Engineering Applications to Economics and Biology Probability Review Problems Plus 9. DIFFERENTIAL EQUATIONS Modeling with Differential Equations Direction Fields and Euler''''s Method Separable Equations Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay Applied Project: Calculus and Baseball The Logistic Equation Linear Equations Predator-Prey Systems Review Problems Plus 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES Curves Defined by Parametric Equations Laboratory Project: Families of Hypocycloids Tangents and Areas Laboratory Project: Bezier Curves Arc Length and Surface Area Polar Coordinates Areas and Lengths in Polar Coordinates Conic Sections Conic Sections in Polar Coordinates Applied Project: Transfer Orbits Review Problems Plus 11. INFINITE SEQUENCES AND SERIES Sequences Laboratory Project: Logistic Sequences Series The Integral Test and Estimates of Sums The Comparison Tests Alternating Series Absolute Convergence and the Ratio and Root Tests Strategy for Testing Series Power Series Representation of Functions as a Power Series Taylor and Maclaurin Series The Binomial Series Writing Project: How Newton Discovered the Binomial Series Applications of Taylor Polynomials Applied Project: Radiation from the Stars ; Includes index : p. A107-A115 UR - http://www.loc.gov/catdir/enhancements/fy1515/98049805-b.html UR - http://www.loc.gov/catdir/enhancements/fy1515/98049805-d.html UR - http://www.loc.gov/catdir/enhancements/fy1515/98049805-t.html ER -