Sunday, February 3, 2019

Thomas' Calculus Early Transcendentals Part One (Single Variable, Chs. 1-11) Paperback Version, 11th Edition

Thomas' Calculus Early Transcendentals Part One (Single Variable, Chs. 1-11) Paperback Version, 11th Edition

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Category : Higher Education

Table of Contents

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)

 

1. Functions

Functions and Their Graphs

Identifying Functions; Mathematical Models

Combining Functions; Shifting and Scaling Graphs

Graphing with Calculators and Computers

Exponential Functions

Inverse Functions and Logarithms

 

2. Limits and Continuity

Rates of Change and Limits

Calculating Limits Using the Limit Laws

Precise Definition of a Limit

One-Sided Limits and Limits at Infinity

Infinite Limits and Vertical Asymptotes

Continuity

Tangents and Derivatives

 

3. Differentiation

The Derivative as a Function

Differentiation Rules for Polynomials, Exponentials, Products and Quotients

The Derivative as a Rate of Change

Derivatives of Trigonometric Functions

The Chain Rule and Parametric Equations

Implicit Differentiation

Derivatives of Inverse Functions and Logarithms

Inverse Trigonometric Functions

Related Rates

Linearization and Differentials

 

4. Applications of Derivatives

Extreme Values of Functions

The Mean Value Theorem

Monotonic Functions and the First Derivative Test

Concavity and Curve Sketching

Applied Optimization Problems

Indeterminate Forms and L’Hopital’s Rule

Newton’s Method

Antiderivatives

 

5. Integration

Estimating with Finite Sums

Sigma Notation and Limits of Finite Sums

The Definite Integral

The Fundamental Theorem of Calculus

Indefinite Integrals and the Substitution Rule

Substitution and Area Between Curves

 

6. Applications of Definite Integrals

Volumes by Slicing and Rotation About an Axis

Volumes by Cylindrical Shells

Lengths of Plane Curves

Moments and Centers of Mass

Areas of Surfaces of Revolution and The Theorems of Pappus

Work

Fluid Pressures and Forces

 

7. Integrals and Transcendental Functions

The Logarithm Defined as an Integral

Exponential Growth and Decay

Relative Rates of Growth

Hyperbolic Functions

 

8. Techniques of Integration

Basic Integration Formulas

Integration by Parts

Integration of Rational Functions by Partial Fractions

Trigonometric Integrals

Trigonometric Substitutions

Integral Tables and Computer Algebra Systems

Numerical Integration

Improper Integrals

 

9. Further Applications of Integration

Slope Fields and Separable Differential Equations

First-Order Linear Differential Equations

Euler’s Method

Graphical Solutions of Autonomous Equations

Applications of First-Order Differential Equations

 

10. Conic Sections and Polar Coordinates

Conic Sections and Quadratic Equations

Classifying Conic Sections by Eccentricity

Quadratic Equations and Rotations

Conics and Parametric Equations; The Cycloid

Polar Coordinates

Graphing in Polar Coordinates

Area and Lengths in Polar Coordinates

Conic Sections in Polar Coordinates

 

11. Infinite Sequences and Series

Sequences

Infinite Series

The Integral Test

Comparison Tests

The Ratio and Root Tests

Alternating Series, Absolute and Conditional Convergence

Power Series

Taylor and Maclaurin Series

Convergence of Taylor Series; Error Estimates

Applications of Power Series

Fourier Series

 

Appendices.

Mathematical Induction

Proofs of Limit Theorems

Commonly Occurring Limits

Theory of the Real Numbers

Complex Numbers

The Distributive Law for Vector Cross Products

Determinants and Cramer’s Rule

The Mixed Derivative Theorem and the Increment Theorem

The Area of a Parallelogram’s Projection on a Plane

Instalant Download Thomas' Calculus Early Transcendentals Part One (Single Variable, Chs. 1-11) Paperback Version, 11th Edition by George B. Thomas, Jr., Massachusetts Institute of Technology Maurice D. Weir, Naval Postgraduate School Joel R. Hass, University of California, Davis Frank R. Giordano, Naval Postgraduate School ZIP OR PDF

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