Essential Calculus Early Transcendentals

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 3/1/2006
  • Publisher: Brooks Cole
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This book is a response to those instructors who feel that calculus textbooks are too big. In writing the book James Stewart asked himself:What is essential for a three-semester calculus course for scientists and engineers? Stewart's ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS offers a concise approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS is only 850 pages-two-thirds the size of Stewart's other calculus texts (CALCULUS, Fifth Edition and CALCULUS, EARLY TRANSCENDENTALS, Fifth Edition)-yet it contains almost all of the same topics. The author achieved this relative brevity mainly by condensing the exposition and by putting some of the features on the website www.StewartCalculus.com. Despite the reduced size of the book, there is still a modern flavor: Conceptual understanding and technology are not neglected, though they are not as prominent as in Stewart's other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS has been written with the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world.

Table of Contents

Functions And Limits
Functions and Their Representations
A Catalog of Essential Functions
The Limit of a Function
Calculating Limits
Limits Involving Infinity
Derivatives and Rates of Change
The Derivative as a Function
Basic Differentiation Formulas
The Product and Quotient Rules
The Chain Rule
Implicit Differentiation
Related Rates
Linear Approximations and Differentials
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Exponential Functions
Inverse Functions and Logarithms
Derivatives of Logarithmic and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Hyperbolic Functions
Indeterminate Forms and l'Hospital's Rule
Applications of Differentiation
Maximum and Minimum Values
The Mean Value Theorem
Derivatives and the Shapes of Graphs
Curve Sketching
Optimization Problems
Newton's Method
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
The Fundamental Theorem of Calculus
The Substitution Rule
Techniques of Integration
Integration by Parts
Trigonometric Integrals and Substitutions
Partial Fractions
Integration with Tables and Computer Algebra Systems
Approximate Integration
Improper Integrals
Applications of Integration
Areas between Curves
Volumes by Cylindrical Shells
Arc Length
Applications to Physics and Engineering
Differential Equations
The Integral and Comparison Tests
Other Convergence Tests
Power Series
Representing Functions as Power Series
Taylor and Maclaurin Series
Applications of Taylor Polynomials
Parametric Equations and Polar Coordinates
Parametric Curves
Calculus with Parametric Curves
Polar Coordinates
Areas and Lengths in Polar Coordinates
Conic Sections in Polar Coordinates
Vectors and the Geometry of Space
Three-Dimensional Coordinate Systems
The Dot Product
The Cross Product
Equations of Lines and Planes
Cylinders and Quadric Surfaces
Vector Functions and Space Curves
Arc Length and Curvature
Motion in Space: Velocity and Acceleration
Partial Derivatives
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers
Multiple Integrals
Double Integrals over Rectangles
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Triple Integrals
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Change of Variables in Multiple Integrals
Vector Calculus
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Parametric Surfaces and Their Areas
Surface Integrals
Stokes' Theorem
The Divergence Theorem
Sigma Notation
The Logarithm Defined as an Integral.
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