Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog
of Essential Functions. New Functions from Old Functions. Graphing
Calculators and Computers. Exponential Functions. Inverse Functions
and Logarithms. Parametric Curves. Laboratory Project: Running
Circles around Circles. Review. Principles of Problem Solving.
2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function.
Calculating Limits Using the Limit Laws. Continuity. Limits
Involving Infinity. Derivatives and Rates of Change. Writing
Project: Early Methods for Finding Tangents. The Derivative as a
Function. What Does f? ? Say about f ? Review. Focus on Problem
Solving.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied
Project: Building a Better Roller Coaster. The Product and Quotient
Rules. Derivatives of Trigonometric Functions. The Chain Rule.
Laboratory Project: Bézier Curves. Applied Project: Where Should a
Pilot Start Descent? Implicit Differentiation. Inverse
Trigonometric Functions and their Derivatives. Derivatives of
Logarithmic Functions. Discovery Project: Hyperbolic Functions.
Rates of Change in the Natural and Social Sciences. Linear
Approximations and Differentials. Laboratory Project: Taylor
Polynomials. Review. Focus on Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values. Applied Project: The
Calculus of Rainbows. Derivatives and the Shapes of Curves.
Graphing with Calculus and Calculators. Indeterminate Forms and
l'Hospital's Rule. Writing Project: The Origins of l'Hospital's
Rule. Optimization Problems. Applied Project: The Shape of a Can.
Newton's Method. Antiderivatives. Review. Focus on Problem
Solving.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite
Integrals. Discovery Project: Area Functions. The Fundamental
Theorem of Calculus. Writing Project: Newton, Leibniz, and the
Invention of Calculus. The Substitution Rule. Integration by Parts.
Additional Techniques of Integration. Integration Using Tables and
Computer Algebra Systems. Discovery Project: Patterns in Integrals.
Approximate Integration. Improper Integrals. Review. Focus on
Problem Solving.
6. APPLICATIONS OF INTEGRATION.
More about Areas. Volumes. Discovery Project: Rotating on a Slant.
Volumes by Cylindrical Shells. Arc Length. Discovery Project: Arc
Length Contest. Average Value of a Function. Applied Project: Where
To Sit at the Movies. Applications to Physics and Engineering.
Discovery Project: Complementary Coffee Cups. Applications to
Economics and Biology. Probability. Review. Focus on Problem
Solving.
7. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields and Euler's
Method. Separable Equations. Applied Project: How Fast Does a Tank
Drain? Applied Project: Which Is Faster, Going Up or Coming Down?
Exponential Growth and Decay. Applied Project: Calculus and
Baseball. The Logistic Equation. Predator-Prey Systems. Review.
Focus on Problem Solving.
8. INFINTE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences. Series. The
Integral and Comparison Tests; Estimating Sums. Other Convergence
Tests. Power Series. Representations of Functions as Power Series.
Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit.
Writing Project: How Newton Discovered the Binomial Series.
Applications of Taylor Polynomials. Applied Project: Radiation from
the Stars. Review. Focus on Problem Solving.
APPENDIXES.
A. Intervals, Inequalities, and Absolute Values.
B. Coordinate Geometry.
C. Trigonometry.
D. Precise Definitions of Limits.
E. A Few Proofs.
F. Sigma Notation.
G. Integration of Rational Functions by Partial Fractions.
H. Polar Coordinates.
I. Complex Numbers.
J. Answers to Odd-Numbered Exercises.
The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
Ask a Question About this Product More... |