Table of contents for Single variable calculus / James Stewart.
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A PREVIEW OF CALCULUS 1. FUNCTIONS AND MODELS Four Ways to Represent a Function / Mathematical Models / New Functions from Old Functions / Graphing Calculators and Computers / Principles of Problem Solving / Review / Problems Plus 2. LIMITS AND RATES OF CHANGE The Tangent and Velocity Problems / The Limit of a Function / Calculating Limits Using the Limit Laws / The Precise Definition of a Limit / Continuity / Tangents, Velocities, and Other Rates of Change / Review / Problems Plus 3. DERIVATIVES Derivatives / Writing Project: Early Methods for Finding Tangents / The Derivative as a Function / Differentiation Formulas / 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? / 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 / Limits at Infinity: Horizontal Asymptotes / 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 / Review / Problems Plus 6. APPLICATIONS OF INTEGRATION Areas Between Curves / Volume / Volumes by Cylindrical Shells / Work / Average Value of a Function / Review / Problems Plus 7. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS Exponential Functions and Their Derivatives / Logarithmic Functions / Derivatives of Logarithmic Functions / The Natural Logarithmic Function / The Natural Exponential Function / General Logarithmic and Exponential Functions / Inverse Trigonometric Functions / Applied Project: Where to Sit at the Movie / Hyperbolic Functions / Indeterminate Forms and L''''Hospital''''s Rule / Writing Project: The Origins of L''''Hospital''''s Rule / Review / Problems Plus 8. 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 9. 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 10. 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 11. 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 12. 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 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 / Review / Problems Plus / APPENDIXES / A. Intervals, Inequalities, and Absolute Values / B. Coordinate Geometry and Lines / C. Graphs of Second-Degree Equations / D. Trigonometry / E. Sigma Notation / F. Proofs of Theorems / G. Complex Numbers / H. Answers to Odd-Numbered Exercises / INDEX
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