Thomas' Calculus, Alternate Edition / Edition 9 available in Hardcover
- Pub. Date:
- Addison Wesley
|Product dimensions:||8.75(w) x 10.25(h) x 1.87(d)|
Table of Contents(NOTE: Every chapter ends with Questions to Guide Your Review, Practice Exercises, and Additional Exercises.)
Real Numbers and the Real Line.
Coordinates, Lines, and Increments.
1. Limits and Continuity.
Rates of Change and Limits.
Rules for Finding Limits.
Target Values and Formal Definitions of Limits.
Extensions of the Limit Concept.
The Derivative of a Function.
Rates of Change.
Derivatives of Trigonometric Functions.
The Chain Rule.
Implicit Differentiation and Rational Exponents.
Related Rates of Change.
3. Applications of Derivatives.
Extreme Values of Functions.
The Mean Value Theorem.
The First Derivative Test for Local Extreme Values.
Graphing with y é and y Æ.
Limits as x
Optimization. Linearization and Differentials.
Differential Equations, Initial Value Problems, and Mathematical Modeling.
Integration by Substitution--Running the Chain Rule Backward.
Estimating with Finite Sums.
Riemann Sums and Definite Integrals.
Properties, Area, and the Mean Value Theorem.
Substitution in Definite Integrals.
5. Applications of Integrals.
Areas Between Curves.
Finding Volumes by Slicing.
Volumes of Solids of Revolution--Disks and Washers.
Cylindrical Shells. Lengths of Plan Curves.
Areas of Surfaces of Revolution.
Moments andCenters of Mass.
Fluid Pressures and Forces.
The Basic Pattern and Other Modeling Applications.
6. Transcendental Functions.
Inverse Functions and Their Derivatives.
The Exponential Function.
Growth and Decay.
Relative Rates of Growth.
Inverse Trigonomic Functions.
Derivatives of Inverse Trigonometric Functions; Integrals.
First Order Differential Equations.
Euler's Numerical Method; Slope Fields.
7. Techniques of Integration.
Basic Integration Formulas.
Integration by Parts.
Integral Tables and CAS.
8. Infinite Series.
Limits of Sequences of Numbers.
Theorems for Calculating Limits of Sequences.
The Integral Test for Series of Nonnegative Terms.
Comparison Tests for Series of Nonnegative Terms.
The Ratio and Root Tests for Series of Nonnegative Terms.
Alternating Series, Absolute and Conditional Convergence.
Taylor and Maclaurin Series.
Convergence of Taylor Series; Error Estimates.
Applications of Power Series.
9. Conic Sections, Parametrized Curves, and Polar Coordinates.
Conic Sections and Quadratic Equations.
Classifying Conic Sections by Eccentricity.
Quadratic Equations and Rotations.
Parametrizations of Plan Curves.
Calculus with Parametrized Curves.
Graphing in Polar Coordinates.
Polar Equations for Conic Sections.
Integration in Polar Coordinates.
10. Vectors and Analytic Geometry in Space.
Vectors in the Plane.
Cartesian (Rectangular) Coordinates and Vectors in Space.
Lines and Planes in Space.
Cylinders and Quadric Surfaces.
Cylindrical and Spherical Coordinates.
11. Vector-Valued Functions and Motion in Space.
Vector-Valued Functions and Space Curves.
Modeling Projectile Motion.
Arc Length and the Unit Tangent Vector T.
Curvature, Torison, and the TNB Frame.
Planetary Motion and Satellites.
12. Multivariable Functions and Partial Derivatives.
Functions of Several Variables.
Limits and Continuity.
Differentiability, Linearization, and Differentials.
The Chain Rule.
Partial Derivatives with Constrained Variables.
Directional Derivatives, Gradient Vectors, and Tangent Planes.
Extreme Values and Saddle Points.
13. Multiple Integrals.
Areas, Moments, and Centers of Mass.
Double Integrals in Polar Form.
Triple Integrals in Rectangular Coordinates.
Masses and Moments in Three Dimensions.
Triple Integrals in Cylindrical and Spherical Coordinates.
Substitutions in Multiple Integrals.
14. Integration in Vector Fields.
Vector Fields, Work, Circulation, and Flux.
Path Independence, Potential Functions, and Conservative Fields.
Green's Theorem in the Plane.
Surface Area and Surface Integrals.
The Divergence Theorem and a Unified Theory.
Proofs of Limit Theorems in Section 1.2.
Simpson's One-Third Rule.
Cauchy's Mean Value Theorem and the Stronger Form of L'Hôpital's Rule.
Limits that Arise Frequently.
The Distributive Law for Vector Cross Products.
Determinants and Cramer's Rule.
Euler's Theorem and the Increment Theorem.