Coverart for item
The Resource Calculus : early transcendentals, James Stewart, McMaster University and University of Toronto

Calculus : early transcendentals, James Stewart, McMaster University and University of Toronto

Label
Calculus : early transcendentals
Title
Calculus
Title remainder
early transcendentals
Statement of responsibility
James Stewart, McMaster University and University of Toronto
Creator
Author
Subject
Genre
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1941-
http://library.link/vocab/creatorName
Stewart, James
Illustrations
illustrations
Index
index present
LC call number
QA303.2
LC item number
.S7315 2016
Literary form
non fiction
http://library.link/vocab/subjectName
  • Calculus
  • Calculus
Label
Calculus : early transcendentals, James Stewart, McMaster University and University of Toronto
Instantiates
Publication
Note
Includes index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- To the student -- Diagnostic tests -- A preview of calculus -- 1. Functions and models -- 1.1. Four ways to represent a function -- 1.2. Mathematical models : a catalog of essential functions -- 1.3. New functions from old functions -- 1.4. Graphing calculators and computers -- 1.5. Exponential functions -- 1.6. Inverse functions and logarithms -- Review -- Principles of problem solving -- 2. Limits and derivatives -- 2.1. The tangent and velocity problems -- 2.2. The limit of a function -- 2.3. Calculating limits using the limit laws -- 2.4. The precise definition of a limit -- 2.5. Continuity -- 2.6. Limits at infinity ; horizontal asymptotes -- 2.7. Derivatives and rates of change -- Writing project : early methods for finding tangents -- 2.8. The derivative as a function -- Review -- Problems plus -- 3. Differentiation rules -- 3.1. Derivatives of polynomials and exponential functions -- Applied project : building a better roller coaster -- 3.2. The product and quotient rules -- 3.3. Derivatives of trigonometric functions -- 3.4. The chain rule -- Applied project : where should a pilot start descent? -- 3.5. Implicit differentiation -- 3.6. Derivatives of logarithmic functions -- 3.7. Rates of change in the natural and social sciences -- 3.8. Exponential growth and decay -- 3.9. Related rates -- 3.10. Linear approximations and differentials -- Laboratory project : Taylor polynomials -- 3.11. Hyperbolic functions -- Review -- Problems plus -- 4. Applications of differentiation -- 4.1. Maximum and minimum values -- Applied project : the calculus of rainbows -- 4.2. The mean value theorem -- 4.3. How derivatives affect the shape of a graph -- 4.4. Indeterminate forms and L'Hospital's rule -- Writing project : the origins of L'Hospital's rule -- 4.5. Summary of curve sketching -- 4.6. Graphing with calculus and calculators -- 4.7. Optimization problems -- Applied project : the shape of a can -- Applied project : Planes and birds: Minimizing energy -- 4.8. Newton's method -- 4.9. Antiderivatives -- Review -- Problems plus -- 5. Integrals -- 5.1. Areas and distances -- 5.2. The definite integral -- Discovery project : area functions -- 5.3. The fundamental theorem of calculus -- 5.4. Indefinite integrals and the net change theorem -- Writing project : Newton, Leibniz, and the invention of calculus -- 5.5. The substitution rule -- Review -- Problems plus -- 6. Application of integration -- 6.1. Areas between curves -- Applied project : the gini index -- 6.2. Volumes -- 6.3. Volumes by cylindrical shells -- 6.4. Work -- 6.5. Average value of a function -- Applied projects : calculus and baseball -- Applied projects : where to sit at the movies -- Review -- Problems plus -- 7. Techniques of integration -- 7.1. Integration by parts -- 7.2. Trigonometric integrals -- 7.3. Trigonometric substitution -- 7.4. Integration of rational functions by partial fractions -- 7.5. Strategy for integration -- 7.6. Integration using tables and computer algebra systems -- Discovery project : patterns in integrals -- 7.7. Approximate integration -- 7.8. Improper integrals -- Review -- Problems plus -- 8. Further applications of integration -- 8.1. Arc length -- Discovery project : arc length contest -- 8.2. Area of a surface of revolution -- Discovery project : rotating on a slant -- 8.3. Applications to physics and engineering -- Discovery project : complementary coffee cups -- 8.4. Applications to economics and biology -- 8.5. Probability -- Review -- Problems plus -- 9. Differential equations -- 9.1. Modeling with differential equations -- 9.2. Direction fields and Euler's method -- 9.3. Separable equations -- Applied project : how fast does a tank drain? -- Applied project : which is faster, going up or coming down? -- 9.4. Models for population growth -- 9.5. Linear equations -- 9.6. Predator-prey systems -- Review -- Problems plus -- 10. Parametric equations and polar coordinates -- 10.1. Curves defined by parametric equations -- Laboratory project : running circles around circles -- 10.2. Calculus with parametric curves -- Laboratory project : Bézier curves -- 10.3. Polar coordinates -- Laboratory project : Families of polar curves 10.4. Areas and lengths in polar coordinates -- 10.5. Conic sections -- 10.6. Conic sections in polar coordinates -- Review -- Problems plus -- 11. Infinite sequences and series -- 11.1. Sequences -- Laboratory project : logistic sequences -- 11.2. Series -- 11.3. The integral test and estimates of sums -- 11.4. The comparison tests -- 11.5. Alternating series -- 11.6. Absolute convergence and the ratio and root tests -- 11.7. Strategy for testing series -- 11.8. Power series -- 11.9. Representations of functions as power series -- 11.10. Taylor and Maclaurin series -- Laboratory project : an elusive limit -- Writing project : how Newton discovered the binomial series -- 11.11. Applications of Taylor polynomials -- Applied project : radiation from the stars -- Review -- Problems plus -- 12. Vectors and geometry of space -- 12.1. Three-dimensional coordinate systems -- 12.2. Vectors -- 12.3. The dot product -- 12.4. The cross product -- Discovery project : the geometry of a tetrahedrom -- 12.5. Equations of lines and planes -- Laboratory project : putting 3D in perspective -- 12.6. Cylinders and quadric surfaces -- Review -- Problems plus -- 13. Vector functions -- 13.1. Vector functions and space curves -- 13.2. Derivatives and integrals of vector functions -- 13.3. Arc length and curvature -- 13.4. Motion in space : velocity and acceleration -- Applied project : Kepler's laws -- Review -- Problems plus -- 14. Partial derivatives -- 14.1. Functions of several variables -- 14.2. Limits and continuity -- 14.3. Partial derivatives -- 14.4. Tangent planes and linear approximations -- Applied project ; the speedo LZR racer -- 14.5. The chain rule -- 14.6. Directional derivatives and the gradient vector -- 14.7. Maximum and minimum values -- Applied project : designing a dumpster -- Discovery project : quadratic approximation and critical points -- 14.8. Lagrange multipliers -- Applied project : rocket science -- Applied project : hydro-turbine optimization -- Review -- Problems plus -- 15. Multiple integrals -- 15.1. Double integrals over rectangles -- 15.2. Double integrals over general regions -- 15.3. Double integrals in polar coordinates -- 15.4. Applications of double integrals -- 15.5. Surface area -- 15.6. Triple integrals -- Discovery project : volumes of hyperspheres -- 15.7. Triple integrals in cylindrical coordinates -- Discovery project : the intersection of three cylinders -- 15.8. Triple integrals in spherical coordinates -- Applied project : roller derby -- 15.9. Change of variables in multiple integrals -- Review -- Problems plus -- 16. Vector calculus -- 16.1. Vector fields -- 16.2. Line integrals -- 16.3. The fundamental theorem for line integrals -- 16.4. Green's theorem -- 16.5. Curl and divergence -- 16.6. Parametric surfaces and their areas -- 16.7. Surface integrals -- 16.8. Stokes' theorem -- Writing project : three men and two theorems -- 16.9. The divergence theorem -- 16.10. Summary -- Review -- Problems plus -- 17. Second-order differential equations -- 17.1. Second-order linear equations -- 17.2. Nonhomogeneous linear equations -- 17.3. Applications of second-order differential equations -- 17.4. Series solutions -- Review -- Appendixes -- A. Numbers, inequalities, and absolute values -- B. Coordinate geometry and lines -- C. Graphs of second-degree equations -- D. Trigonometry -- E. Sigma notation -- F. Proofs of theorems -- G. The logarithm defined as an integral -- H. Complex numbers -- I. Answers to odd-numbered exercises -- Index
Control code
884617308
Dimensions
27 cm
Edition
Eighth edition
Extent
1 volume (various pagings)
Isbn
9781285741550
Lccn
2014951195
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Note
ASSOCIATED STUDENT GOVERNMENT TEXTBOOKS RESERVES IN COPLEY LIBRARY DO NOT CONTAIN TEXTBOOK ACCESS CODES
Other physical details
color illustrations
System control number
(OCoLC)884617308
Label
Calculus : early transcendentals, James Stewart, McMaster University and University of Toronto
Publication
Note
Includes index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Preface -- To the student -- Diagnostic tests -- A preview of calculus -- 1. Functions and models -- 1.1. Four ways to represent a function -- 1.2. Mathematical models : a catalog of essential functions -- 1.3. New functions from old functions -- 1.4. Graphing calculators and computers -- 1.5. Exponential functions -- 1.6. Inverse functions and logarithms -- Review -- Principles of problem solving -- 2. Limits and derivatives -- 2.1. The tangent and velocity problems -- 2.2. The limit of a function -- 2.3. Calculating limits using the limit laws -- 2.4. The precise definition of a limit -- 2.5. Continuity -- 2.6. Limits at infinity ; horizontal asymptotes -- 2.7. Derivatives and rates of change -- Writing project : early methods for finding tangents -- 2.8. The derivative as a function -- Review -- Problems plus -- 3. Differentiation rules -- 3.1. Derivatives of polynomials and exponential functions -- Applied project : building a better roller coaster -- 3.2. The product and quotient rules -- 3.3. Derivatives of trigonometric functions -- 3.4. The chain rule -- Applied project : where should a pilot start descent? -- 3.5. Implicit differentiation -- 3.6. Derivatives of logarithmic functions -- 3.7. Rates of change in the natural and social sciences -- 3.8. Exponential growth and decay -- 3.9. Related rates -- 3.10. Linear approximations and differentials -- Laboratory project : Taylor polynomials -- 3.11. Hyperbolic functions -- Review -- Problems plus -- 4. Applications of differentiation -- 4.1. Maximum and minimum values -- Applied project : the calculus of rainbows -- 4.2. The mean value theorem -- 4.3. How derivatives affect the shape of a graph -- 4.4. Indeterminate forms and L'Hospital's rule -- Writing project : the origins of L'Hospital's rule -- 4.5. Summary of curve sketching -- 4.6. Graphing with calculus and calculators -- 4.7. Optimization problems -- Applied project : the shape of a can -- Applied project : Planes and birds: Minimizing energy -- 4.8. Newton's method -- 4.9. Antiderivatives -- Review -- Problems plus -- 5. Integrals -- 5.1. Areas and distances -- 5.2. The definite integral -- Discovery project : area functions -- 5.3. The fundamental theorem of calculus -- 5.4. Indefinite integrals and the net change theorem -- Writing project : Newton, Leibniz, and the invention of calculus -- 5.5. The substitution rule -- Review -- Problems plus -- 6. Application of integration -- 6.1. Areas between curves -- Applied project : the gini index -- 6.2. Volumes -- 6.3. Volumes by cylindrical shells -- 6.4. Work -- 6.5. Average value of a function -- Applied projects : calculus and baseball -- Applied projects : where to sit at the movies -- Review -- Problems plus -- 7. Techniques of integration -- 7.1. Integration by parts -- 7.2. Trigonometric integrals -- 7.3. Trigonometric substitution -- 7.4. Integration of rational functions by partial fractions -- 7.5. Strategy for integration -- 7.6. Integration using tables and computer algebra systems -- Discovery project : patterns in integrals -- 7.7. Approximate integration -- 7.8. Improper integrals -- Review -- Problems plus -- 8. Further applications of integration -- 8.1. Arc length -- Discovery project : arc length contest -- 8.2. Area of a surface of revolution -- Discovery project : rotating on a slant -- 8.3. Applications to physics and engineering -- Discovery project : complementary coffee cups -- 8.4. Applications to economics and biology -- 8.5. Probability -- Review -- Problems plus -- 9. Differential equations -- 9.1. Modeling with differential equations -- 9.2. Direction fields and Euler's method -- 9.3. Separable equations -- Applied project : how fast does a tank drain? -- Applied project : which is faster, going up or coming down? -- 9.4. Models for population growth -- 9.5. Linear equations -- 9.6. Predator-prey systems -- Review -- Problems plus -- 10. Parametric equations and polar coordinates -- 10.1. Curves defined by parametric equations -- Laboratory project : running circles around circles -- 10.2. Calculus with parametric curves -- Laboratory project : Bézier curves -- 10.3. Polar coordinates -- Laboratory project : Families of polar curves 10.4. Areas and lengths in polar coordinates -- 10.5. Conic sections -- 10.6. Conic sections in polar coordinates -- Review -- Problems plus -- 11. Infinite sequences and series -- 11.1. Sequences -- Laboratory project : logistic sequences -- 11.2. Series -- 11.3. The integral test and estimates of sums -- 11.4. The comparison tests -- 11.5. Alternating series -- 11.6. Absolute convergence and the ratio and root tests -- 11.7. Strategy for testing series -- 11.8. Power series -- 11.9. Representations of functions as power series -- 11.10. Taylor and Maclaurin series -- Laboratory project : an elusive limit -- Writing project : how Newton discovered the binomial series -- 11.11. Applications of Taylor polynomials -- Applied project : radiation from the stars -- Review -- Problems plus -- 12. Vectors and geometry of space -- 12.1. Three-dimensional coordinate systems -- 12.2. Vectors -- 12.3. The dot product -- 12.4. The cross product -- Discovery project : the geometry of a tetrahedrom -- 12.5. Equations of lines and planes -- Laboratory project : putting 3D in perspective -- 12.6. Cylinders and quadric surfaces -- Review -- Problems plus -- 13. Vector functions -- 13.1. Vector functions and space curves -- 13.2. Derivatives and integrals of vector functions -- 13.3. Arc length and curvature -- 13.4. Motion in space : velocity and acceleration -- Applied project : Kepler's laws -- Review -- Problems plus -- 14. Partial derivatives -- 14.1. Functions of several variables -- 14.2. Limits and continuity -- 14.3. Partial derivatives -- 14.4. Tangent planes and linear approximations -- Applied project ; the speedo LZR racer -- 14.5. The chain rule -- 14.6. Directional derivatives and the gradient vector -- 14.7. Maximum and minimum values -- Applied project : designing a dumpster -- Discovery project : quadratic approximation and critical points -- 14.8. Lagrange multipliers -- Applied project : rocket science -- Applied project : hydro-turbine optimization -- Review -- Problems plus -- 15. Multiple integrals -- 15.1. Double integrals over rectangles -- 15.2. Double integrals over general regions -- 15.3. Double integrals in polar coordinates -- 15.4. Applications of double integrals -- 15.5. Surface area -- 15.6. Triple integrals -- Discovery project : volumes of hyperspheres -- 15.7. Triple integrals in cylindrical coordinates -- Discovery project : the intersection of three cylinders -- 15.8. Triple integrals in spherical coordinates -- Applied project : roller derby -- 15.9. Change of variables in multiple integrals -- Review -- Problems plus -- 16. Vector calculus -- 16.1. Vector fields -- 16.2. Line integrals -- 16.3. The fundamental theorem for line integrals -- 16.4. Green's theorem -- 16.5. Curl and divergence -- 16.6. Parametric surfaces and their areas -- 16.7. Surface integrals -- 16.8. Stokes' theorem -- Writing project : three men and two theorems -- 16.9. The divergence theorem -- 16.10. Summary -- Review -- Problems plus -- 17. Second-order differential equations -- 17.1. Second-order linear equations -- 17.2. Nonhomogeneous linear equations -- 17.3. Applications of second-order differential equations -- 17.4. Series solutions -- Review -- Appendixes -- A. Numbers, inequalities, and absolute values -- B. Coordinate geometry and lines -- C. Graphs of second-degree equations -- D. Trigonometry -- E. Sigma notation -- F. Proofs of theorems -- G. The logarithm defined as an integral -- H. Complex numbers -- I. Answers to odd-numbered exercises -- Index
Control code
884617308
Dimensions
27 cm
Edition
Eighth edition
Extent
1 volume (various pagings)
Isbn
9781285741550
Lccn
2014951195
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Note
ASSOCIATED STUDENT GOVERNMENT TEXTBOOKS RESERVES IN COPLEY LIBRARY DO NOT CONTAIN TEXTBOOK ACCESS CODES
Other physical details
color illustrations
System control number
(OCoLC)884617308

Library Locations

    • Copley LibraryBorrow it
      5998 Alcalá Park, San Diego, CA, 92110-2492, US
      32.771354 -117.193327
Processing Feedback ...