Thomas' Calculus in SI Units

Series
Pearson
Author
George B. Thomas / Maurice D. Weir / Joel R. Hass  
Publisher
Pearson
Cover
Softcover
Edition
13
Language
English
Total pages
1200
Pub.-date
May 2016
ISBN13
9781292089799
ISBN
1292089792
Related Titles


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Thomas' Calculus in SI Units
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Thomas' Calculus in SI Units
14 May 2019 88.90

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Were you looking for the book with access to Pearson MyLab Mathematics Global? This product is the book alone and does NOT come with access to Pearson MyLab Mathematics Global. Buy Thomas’ Calculus, Thirteenth Edition with Pearson MyLab Mathematics Global access card (ISBN 9781292089942) if you need access to Pearson MyLab Mathematics Global as well, and save money on this resource. You will also need a course ID from your instructor to access Pearson MyLab Mathematics Global.

 

This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).

 

Thomas’ Calculus, Thirteenth Edition, introduces students to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded—always with the goal of developing technical competence while furthering students’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's students.

 

The text is available with a robust Pearson MyLab Mathematics® course–an online homework, tutorial, and study solution. In addition to interactive multimedia features like lecture videos and eBook, nearly 9,000 algorithmic exercises are available for students to get the practice they need.

 

Pearson MyLab Mathematics is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts.

Features

Features

This title is a Pearson Global Edition. The Editorial team at Pearson has worked closely with educators around the world to include content which is especially relevant to students outside the United States.

  • Strong exercise sets feature a great breadth of problems–progressing from skills problems to applied and theoretical problems–to encourage students to think about and practice the concepts until they achieve mastery.
  • Figures are conceived and rendered to provide insight for students and support conceptual reasoning.
  • The flexible table of contents divides topics into manageable sections, allowing instructors to tailor their course to meet the specific needs of their students.
  • Complete and precise multivariable coverage enhances the connections of multivariable ideas with their single-variable analogs studied earlier in the book.

 

Pearson MyLab Mathematics not included. Students, if Pearson MyLab Mathematics is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. Pearson MyLab Mathematics should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

  • A robust Pearson MyLab Mathematics course contains nearly 9,000 assignable exercises, a complete eBook, and built-in tutorials so students can get help whenever they need it.

Short Retail DescriptionThis text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).

Thomas’ Calculus, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded—always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.

 

KEY TOPICS: Functions, Limits and Continuity, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, First-Order Differential Equations, Infinite Sequences and Series, Parametric Equations and Polar Coordinates, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integrals and Vector Fields, Second-Order Differential Equations

 

MARKET: For all readers interested in calculus.

New to this Edition

 

  • Two new sections:
    • Section 8.1 reviews basic integration formulas and the Substitution Rules combined with algebraic methods and trigonometric identities
    • Section 8.10 on probability as an application of improper integrals to making predictions for probabilistic models, with a wide range of applications in business and sciences
  • Presentation of absolute convergence before considering the Ratio and Root Tests for convergence of a series, which allows the tests to be stated in their stronger forms (Theorems 13 and 14, Section 10.5)
  • Updated and new art, and additional tables, supporting examples and exercises throughout
  • Material has been rewritten or enhanced, for greater clarity or improved motivation. Here are some examples:  
    • Definition of continuous at x = c
    • Geometric insight into L’Hôpital’s Rule
    • Discussion of cycloid curve
    • Introduction to differentiability for functions of several variables
    • Chain Rule for paths
    • Most chapter introductory overviews
  • A variety of new examples throughout, including:
    • Predicting the rise in college tuition costs
    • Predicting the decline in tuberculosis death rates
    • Minimizing production costs
    • Integration by parts
    • Log formula for the inverse hyperbolic sine function
    • Using the Integral Test
    • Finding the perimeter of an ellipse
    • Testing multivariable critical points in an exponential function
  • Updated and new exercises, including:
    • Using regression analysis to predict Federal minimum wage, median home and energy prices, and global warming
    • More limits involving rational functions
    • Interpreting derivatives from graphs
    • Growth in the Gross National Product
    • Vehicular stopping distance
    • Spread of an oil spill in gulf waters
    • Estimating concentration of a drug
    • Considering endangered species
    • Prescribing drug dosage
    • Summing infinitely many areas
    • Representing functions by a geometric series
    • Unusual polar graphs
    • Finding the distance between skew lines in space
    • Finding mass and distances in our solar system

 

Pearson MyLab Mathematics not included. Students, if Pearson MyLab Mathematics is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN and course ID. Pearson MyLab Mathematics should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

Pearson MyLab Mathematics now has hundreds of additional assignable exercises, including 670 that address prerequisite skills, giving you the selection you need to create the right homework assignments and assessments.

Web Online CopyThis text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors).

Thomas’ Calculus, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded–always with the goal of developing technical competence while furthering readers’ appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.

 

 

Table of Contents

1 Functions

1.1 Functions and Their Graphs

1.2 Combining Functions; Shifting and Scaling Graphs

1.3 Trigonometric Functions

1.4 Graphing with Software

 

2 Limits and Continuity

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 The Precise Definition of a Limit

2.4 One-Sided Limits

2.5 Continuity

2.6 Limits Involving Infinity; Asymptotes of Graphs

 

3 Derivatives
3.1 Tangents and the Derivative at a Point

3.2 The Derivative as a Function

3.3 Differentiation Rules

3.4 The Derivative as a Rate of Change

3.5 Derivatives of Trigonometric Functions

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Related Rates

3.9 Linearization and Differentials

 

4 Applications of Derivatives

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 Monotonic Functions and the First Derivative Test

4.4 Concavity and Curve Sketching
4.5 Applied Optimization

4.6 Newton’s Method

4.7 Antiderivatives

 

5 Integrals

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Method

5.6 Definite Integral Substitutions and the Area Between Curves

 

6 Applications of Definite Integrals

6.1 Volumes Using Cross-Sections

6.2 Volumes Using Cylindrical Shells

6.3 Arc Length

6.4 Areas of Surfaces of Revolution

6.5 Work and Fluid Forces

6.6 Moments and Centers of Mass

 

7 Transcendental Functions

7.1 Inverse Functions and Their Derivatives

7.2 Natural Logarithms

7.3 Exponential Functions

7.4 Exponential Change and Separable Differential Equations

7.5 Indeterminate Forms and L’Hôpital’s Rule

7.6 Inverse Trigonometric Functions

7.7 Hyperbolic Functions

7.8 Relative Rates of Growth

 

8 Techniques of Integration

8.1 Using Basic Integration Formulas

8.2 Integration by Parts
8.3 Trigonometric Integrals

8.4 Trigonometric Substitutions

8.5 Integration of Rational Functions by Partial Fractions

8.6 Integral Tables and Computer Algebra Systems

8.7 Numerical Integration

8.8 Improper Integrals

8.9 Probability

 

9 First-Order Differential Equations

9.1 Solutions, Slope Fields, and Euler’s Method

9.2 First-Order Linear Equations

9.3 Applications

9.4 Graphical Solutions of Autonomous Equations

9.5 Systems of Equations and Phase Planes

 

10 Infinite Sequences and Series

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 Absolute Convergence; The Ratio and Root Tests

10.6 Alternating Series and Conditional Convergence

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Convergence of Taylor Series

10.10 The Binomial Series and Applications of Taylor Series

 

11 Parametric Equations and Polar Coordinates

11.1 Parametrizations of Plane Curves

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Graphing Polar Coordinate Equations

11.5 Areas and Lengths in Polar Coordinates

11.6 Conic Sections

11.7 Conics in Polar Coordinates


12 Vectors and the Geometry of Space

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

 

13 Vector-Valued Functions and Motion in Space

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

13.6 Velocity and Acceleration in Polar Coordinates

 

14 Partial Derivatives

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Taylor’s Formula for Two Variables

14.10 Partial Derivatives with Constrained Variables

 

15 Multiple Integrals

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Moments and Centers of Mass

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

15.8 Substitutions in Multiple Integrals

 

16 Integrals and Vector Fields

16.1 Line Integrals

16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux

16.3 Path Independence, Conservative Fields, and Potential Functions

16.4 Green’s Theorem in the Plane

16.5 Surfaces and Area

16.6 Surface Integrals

16.7 Stokes’ Theorem

16.8 The Divergence Theorem and a Unified Theory

 

17 Second-Order Differential Equations online

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power Series Solutions

 

Appendices

A.1 Real Numbers and the Real Line

A.2 Mathematical Induction

A.3 Lines, Circles, and Parabolas

A.4 Proofs of Limit Theorems

A.5 Commonly Occurring Limits

A.6 Theory of the Real Numbers

A.7 Complex Numbers

A.8 The Distributive Law for Vector Cross Products

A.9 The Mixed Derivative Theorem and the Increment Theorem