Calculus: Early Transcendentals

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Calculus: Early Transcendentals

Format:  Hardcover,

115 pages

Publisher: Macmillan Higher Education

Publish Date: Mar 2011

ISBN-13: 9781429208383

ISBN-10: 1429208384

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Book Information

The following content was provided by the publisher.
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching--supported by Rogawski's "Calculus Second Edition"--the most successful new calculus text in 25 years Widely adopted in its first edition, Rogawski's "Calculus" worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus. Now Rogawski's "Calculus" success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.

Specifications

Publisher: Macmillan Higher Education
Publish Date: Mar 2011
ISBN-13: 9781429208383
ISBN-10: 1429208384
Format: Hardcover
Number of Pages: 115
Shipping Weight (in pounds): 5.0
Product in Inches (L x W x H): 8.75 x 10.25 x 1.5
Walmart No.: 9781429208383

Chapter outline

Precalculus Review
Real Numbers, Functions, and Graphs
Linear and Quadratic Functions
The Basic Classes of Functions
Trigonometric Functions
Inverse Functions
Exponential and Logarithmic Functions
Technology Calculators and Computers
Limits
Limits, Rates of Change, and Tangent Lines
Limits: A Numerical and Graphical Approach2.3 Basic Limit Laws
Limits and Continuity
Evaluating Limits Algebraically
Trigonometric Limits
Limits at Infinity
Intermediate Value Theorem
The Formal Definition of a Limit
Differentiation
Definition of the Derivative
The Derivative as a Function
Product and Quotient Rules
Rates of Change
Higher Derivatives
Trigonometric Functions
The Chain Rule
Derivatives of Inverse Functions
Derivatives of General Exponential and Logarithmic Functions
Implicit Differentiation
Related Rates
Applications of the Derivative
Linear Approximation and Applications
Extreme Values
The Mean Value Theorem and Monotonicity
The Shape of a Graph
L'Hopital's Rule
Graph Sketching and Asymptotes
Applied Optimization
Newton's Method
Antiderivatives
The Integral
Approximating and Computing Area
The Definite Integral
The Fundamental Theorem of Calculus, Part I
The Fundamental Theorem of Calculus, Part II
Net Change as the Integral of a Rate
Substitution Method
Further Transcendental Functions
Exponential Growth and Decay
Applications of the Integral
Area Between Two Curves
Setting Up Integrals: Volume, Density, Average Value
Volumes of Revolution
The Method of Cylindrical Shells
Work and Energy
Techniques of Integration
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
The Method of Partial Fractions
Improper Integrals
Probability and Integration
Numerical Integration
Further Applications of the Integral and Taylor Polynomials
Arc Length and Surface Area
Fluid Pressure and Force
Center of Mass
Taylor Polynomials
Introduction to Differential Equations
Solving Differential Equations
Models Involving y' = k (y-b)
Graphical and Numerical Methods
The Logistic Equation
First-Order Linear Equations
Infinite Series
Sequences
Summing an Infinite Series
Convergence of Series with Positive Terms
Absolute and Conditional Convergence
The Ratio and Root Tests
Power Series
Taylor Series
Parametric Equations, Polar Coordinates, and Conic Sections
Parametric Equations
Arc Length and Speed
Polar Coordinates
Area and Arc Length in Polar Coordinates
Conic Sections
Vector Geometry
Vectors in the Plane
Vectors in Three Dimensions
Dot Product and the Angle Between Two Vectors
The Cross Product
Planes in Three-Space
A Survey of Quadric Surfaces
Cylindrical and Spherical Coordinates
Calculus of Vector-Valued Functions
Vector-Valued Functions
Calculus of Vector-Valued Functions
Arc Length and Speed
Curvature
Motion in Three-Space
Planetary Motion According to Kepler and Newton
Differentiation in Several Variables
Functions of Two or More Variables
Limits and Continuity in Several Variables
Partial Derivatives
Differentiability and Tangent Planes
The Gradient and Directional Derivatives
The Chain Rule
Optimization in Several Variables
Lagrange Multipliers: Optimizing with a Constraint
Multiple Integration
Integration in Variables
Double Integrals over More General Regions
Triple Integrals
Integration in Polar, Cylindrical, and Spherical Coordinates
Applications of Multiplying Integrals
Change of Variables
Line and Surface Integrals
Vector Fields
Line Integrals
Conservative Vector Fields
Parametrized Surfaces and Surface Integrals
Surface Integrals of Vector Fields
Fundamental Theorems of Vector Analysis
Green's Theorem
Stokes' Theorem
Divergence Theorem
Appendices
The Language of Mathematics
Properties of Real Numbers
Mathematical Induction and the Binomial Theorem
Additional Proofs of Theorems
Taylor Polynomials
Answers to Odd-Numbered Exercises
References
Photo Credits
Index

Book description

What’s the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching—supported by Rogawski’s Calculus Second Edition—the most successful new calculus text in 25 years!
Widely adopted in its first edition, Rogawski’s Calculus worked for instructors and students by balancing formal precision with a guiding conceptual focus.

Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.

Now Rogawski’s Calculus success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.

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