Calculus: Special Edition Chapters 5-8, 11, 12, 14
Edition: 7
Copyright: 2018
Edition: 7
Copyright: 2018
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Special Edition for Rutgers University
The NEW 7th edition of Calculus blends the best aspects of calculus reform along with the goals and methodology of traditional calculus. The format of this text is enhanced, but is not dominated by new technology. Its innovative presentation includes:
- Conceptual Understanding through Verbalization
- Mathematical Communication
- Cooperative Learning Group Research Projects
- Integration of Technology
- Greater Text Visualization
- Supplementary Materials
- Interactive art - Many pieces of art in the book link online to dynamic art to illustrate such topics as limits, slopes, areas, and direction fields
Calculus features:
- An early presentation of transcendental functions: Logarithms, exponential functions, and trigonometric functions
- Differential equations in a natural and reasonable way
- Utilization of the humanness of mathematics
- Precalculus mathematics being taught at most colleges and universities correctly reflected
- A student solutions manual, instructor’s manual, and accompanying website
It’s all about Problems, problems, problems, and even more problems:
- Modeling Problems require the reader to make assumptions about the real world.
- Think Tank Problems prove the proposition true or to find a counterexample to disprove the proposition.
- Exploration Problems go beyond the category of counterexample problem to provide opportunities for innovative thinking.
- Historical Quest Problems invite the students to participate in the historical development of mathematics. History becomes active rather than passive.
- Journal Problems have been reprinted from leading mathematics journals in an effort to show that “mathematicians work problems too.”
- Putnam Examination Problems have been included to challenge not only the “best of the best” but to offer stimulating content for everybody.
- Uniform Problem Sets 60 in every set allow for easy and consistent problem assignment.
- Cumulative Problem Sets for Chapters 6-8 and 11-13.
- Huge Chapter Supplementary Problem Set of 99 miscellaneous problems in each chapter.
- Proficiency Examination Problem Sets consisting of both concept and practice problems.
Preface
5 Integration
5.1 Antidifferentiation
5.2 Area as the Limit of a Sum
5.3 Riemann Sums and the Definite Integral
5.4 The Fundamental Theorems of Calculus
5.5 Integration by Substitution
5.6 Introduction to Differential Equations
5.7 The Mean Value Theorem for Integrals; Average Value
5.8 Numerical Integration: The Trapezoidal Rule and Simpson’s Rule
5.9 An Alternative Approach: The Logarithm as an Integral
Chapter 5 Review
Chapter 5 Group Research Project
6 Additional Applications of the Integral
6.1 Area Between Two Curves
6.2 Volume
6.3 Polar Forms and Area
6.4 Arc Length and Surface Area
6.5 Physical Applications: Work, Liquid Force, and Centroids
6.6 Applications to Business, Economics, and Life Sciences
Chapter 6 Review
Book Report To Infinity and Beyond, A Cultural History of the Infinite, by Eli Maor
Chapter 6 Group Research Project
7 Methods of Integration
7.1 Review of Substitution and Integration by Table
7.2 Integration By Parts
7.3 Trigonometric Methods
7.4 Method of Partial Fractions
7.5 Summary of Integration Techniques
7.6 First-Order Differential Equations
7.7 Improper Integrals
7.8 Hyperbolic and Inverse Hyperbolic Functions
Chapter 7 Review
Chapter 7 Group Research Project
8 Infinite Series
8.1 Sequences and Their Limits
8.2 Introduction to Infinite Series; Geometric Series
8.3 The Integral Test; p-series
8.4 Comparison Tests
8.5 The Ratio Test and the Root Test
8.6 Alternating Series; Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
Chapter 8 Review
Chapter 8 Group Research Project
Cumulative Review Problems—Chapters 6–8
11 Partial Differentiation
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
11.4 Tangent Planes, Approximations, and Differentiability
11.5 Chain Rules
11.6 Directional Derivatives and the Gradient
11.7 Extrema of Functions of Two Variables
11.8 Lagrange Multipliers
Chapter 11 Review
Book Report Hypatia’s Heritage by Margaret Alic
Chapter 11 Group Research Project
12 Multiple Integration
12.1 Double Integration over Rectangular Regions
12.2 Double Integration over Nonrectangular Regions
12.3 Double Integrals in Polar Coordinates
12.4 Surface Area
12.5 Triple Integrals
12.6 Mass, Moments, and Probability Density Functions
12.7 Cylindrical and Spherical Coordinates
12.8 Jacobians: Change of Variables
Chapter 12 Review
Chapter 12 Group Research Project
14 Introduction to Differential Equations
14.1 First-Order Differential Equations
14.2 Second-Order Homogeneous Linear Differential Equations
14.3 Second-Order Nonhomogeneous Linear Differential Equations
Chapter 14 Review
Book Report Mathematical Experience by Philip J. Davis and Reuben Hersh
Chapter 14 Group Research Project
Appendices
A: Introduction to the Theory of Limits
B: Selected Proofs
C: Significant Digits
D: Short Table of Integrals
E: Trigonometry
F: Parabolas
G: Ellipses
H: Hyperbolas
I: Determinants
J: Answers to Selected Problems
Index
Monty Strauss has been on the mathematics faculty at Texas Tech University for almost forty years. He has a Ph.D. from the Courant Institute of Mathematical Sciences at New York University and has taught all levels of mathematics at Texas Tech, from precollege mathematics to doctoral level. He particularly has enjoyed working with honors students and with mathematics and engineering majors. Among his administrative assignments have been departmental undergraduate programs chair and departmental associate chair.
Karl J. Smith received his B.A. and M.A. degrees in mathematics from UCLA. In 1968, he moved to northern California to teach mathematics at Santa Rosa Junior College, where he taught until his retirement in 1993. Along the way, he served as department chair, and he received a Ph.D. in 1979 in mathematics education at Southeastern University. A past president of the American Mathematical Association of Two-Year Colleges, Professor Smith is active nationally in mathematics education. He was the founding editor of the Western AMATYC News, a chairperson of the Committee on Mathematics Excellence, and an NSF grant reviewer. In 1979 he received an Outstanding Young Men of America Award, in 1980 an Outstanding Educator Award, and in 1989 an Outstanding Teacher Award. Professor Smith is the author of over 60 successful textbooks. Over two million students have learned mathematics from his textbooks.
Magdalena Toda holds a PhD in Mathematics from University of Kansas and a PhD in Applied Mathematics from University Politehnica Bucharest. She is employed as a Professor of Mathematics at Texas Tech University, in Lubbock, TX, where she has served as interim chairperson between 2015-2016, and as department chairperson since 2016.
She has authored and co-authored 35 refereed articles, in the areas of differential geometry and geometric PDEs, and has served as an editor for a research monograph that appeared in 2017. She has extensive experience in teaching Calculus, in both the traditional, face-to-face format (since 1995), and online (since 2011). She is a recipient of 6 teaching awards (2 at University of Kansas and 4 at Texas Tech University - including the President's Award for Excellence in Teaching, 2008).
Special Edition for Rutgers University
The NEW 7th edition of Calculus blends the best aspects of calculus reform along with the goals and methodology of traditional calculus. The format of this text is enhanced, but is not dominated by new technology. Its innovative presentation includes:
- Conceptual Understanding through Verbalization
- Mathematical Communication
- Cooperative Learning Group Research Projects
- Integration of Technology
- Greater Text Visualization
- Supplementary Materials
- Interactive art - Many pieces of art in the book link online to dynamic art to illustrate such topics as limits, slopes, areas, and direction fields
Calculus features:
- An early presentation of transcendental functions: Logarithms, exponential functions, and trigonometric functions
- Differential equations in a natural and reasonable way
- Utilization of the humanness of mathematics
- Precalculus mathematics being taught at most colleges and universities correctly reflected
- A student solutions manual, instructor’s manual, and accompanying website
It’s all about Problems, problems, problems, and even more problems:
- Modeling Problems require the reader to make assumptions about the real world.
- Think Tank Problems prove the proposition true or to find a counterexample to disprove the proposition.
- Exploration Problems go beyond the category of counterexample problem to provide opportunities for innovative thinking.
- Historical Quest Problems invite the students to participate in the historical development of mathematics. History becomes active rather than passive.
- Journal Problems have been reprinted from leading mathematics journals in an effort to show that “mathematicians work problems too.”
- Putnam Examination Problems have been included to challenge not only the “best of the best” but to offer stimulating content for everybody.
- Uniform Problem Sets 60 in every set allow for easy and consistent problem assignment.
- Cumulative Problem Sets for Chapters 6-8 and 11-13.
- Huge Chapter Supplementary Problem Set of 99 miscellaneous problems in each chapter.
- Proficiency Examination Problem Sets consisting of both concept and practice problems.
Preface
5 Integration
5.1 Antidifferentiation
5.2 Area as the Limit of a Sum
5.3 Riemann Sums and the Definite Integral
5.4 The Fundamental Theorems of Calculus
5.5 Integration by Substitution
5.6 Introduction to Differential Equations
5.7 The Mean Value Theorem for Integrals; Average Value
5.8 Numerical Integration: The Trapezoidal Rule and Simpson’s Rule
5.9 An Alternative Approach: The Logarithm as an Integral
Chapter 5 Review
Chapter 5 Group Research Project
6 Additional Applications of the Integral
6.1 Area Between Two Curves
6.2 Volume
6.3 Polar Forms and Area
6.4 Arc Length and Surface Area
6.5 Physical Applications: Work, Liquid Force, and Centroids
6.6 Applications to Business, Economics, and Life Sciences
Chapter 6 Review
Book Report To Infinity and Beyond, A Cultural History of the Infinite, by Eli Maor
Chapter 6 Group Research Project
7 Methods of Integration
7.1 Review of Substitution and Integration by Table
7.2 Integration By Parts
7.3 Trigonometric Methods
7.4 Method of Partial Fractions
7.5 Summary of Integration Techniques
7.6 First-Order Differential Equations
7.7 Improper Integrals
7.8 Hyperbolic and Inverse Hyperbolic Functions
Chapter 7 Review
Chapter 7 Group Research Project
8 Infinite Series
8.1 Sequences and Their Limits
8.2 Introduction to Infinite Series; Geometric Series
8.3 The Integral Test; p-series
8.4 Comparison Tests
8.5 The Ratio Test and the Root Test
8.6 Alternating Series; Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
Chapter 8 Review
Chapter 8 Group Research Project
Cumulative Review Problems—Chapters 6–8
11 Partial Differentiation
11.1 Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
11.4 Tangent Planes, Approximations, and Differentiability
11.5 Chain Rules
11.6 Directional Derivatives and the Gradient
11.7 Extrema of Functions of Two Variables
11.8 Lagrange Multipliers
Chapter 11 Review
Book Report Hypatia’s Heritage by Margaret Alic
Chapter 11 Group Research Project
12 Multiple Integration
12.1 Double Integration over Rectangular Regions
12.2 Double Integration over Nonrectangular Regions
12.3 Double Integrals in Polar Coordinates
12.4 Surface Area
12.5 Triple Integrals
12.6 Mass, Moments, and Probability Density Functions
12.7 Cylindrical and Spherical Coordinates
12.8 Jacobians: Change of Variables
Chapter 12 Review
Chapter 12 Group Research Project
14 Introduction to Differential Equations
14.1 First-Order Differential Equations
14.2 Second-Order Homogeneous Linear Differential Equations
14.3 Second-Order Nonhomogeneous Linear Differential Equations
Chapter 14 Review
Book Report Mathematical Experience by Philip J. Davis and Reuben Hersh
Chapter 14 Group Research Project
Appendices
A: Introduction to the Theory of Limits
B: Selected Proofs
C: Significant Digits
D: Short Table of Integrals
E: Trigonometry
F: Parabolas
G: Ellipses
H: Hyperbolas
I: Determinants
J: Answers to Selected Problems
Index
Monty Strauss has been on the mathematics faculty at Texas Tech University for almost forty years. He has a Ph.D. from the Courant Institute of Mathematical Sciences at New York University and has taught all levels of mathematics at Texas Tech, from precollege mathematics to doctoral level. He particularly has enjoyed working with honors students and with mathematics and engineering majors. Among his administrative assignments have been departmental undergraduate programs chair and departmental associate chair.
Karl J. Smith received his B.A. and M.A. degrees in mathematics from UCLA. In 1968, he moved to northern California to teach mathematics at Santa Rosa Junior College, where he taught until his retirement in 1993. Along the way, he served as department chair, and he received a Ph.D. in 1979 in mathematics education at Southeastern University. A past president of the American Mathematical Association of Two-Year Colleges, Professor Smith is active nationally in mathematics education. He was the founding editor of the Western AMATYC News, a chairperson of the Committee on Mathematics Excellence, and an NSF grant reviewer. In 1979 he received an Outstanding Young Men of America Award, in 1980 an Outstanding Educator Award, and in 1989 an Outstanding Teacher Award. Professor Smith is the author of over 60 successful textbooks. Over two million students have learned mathematics from his textbooks.
Magdalena Toda holds a PhD in Mathematics from University of Kansas and a PhD in Applied Mathematics from University Politehnica Bucharest. She is employed as a Professor of Mathematics at Texas Tech University, in Lubbock, TX, where she has served as interim chairperson between 2015-2016, and as department chairperson since 2016.
She has authored and co-authored 35 refereed articles, in the areas of differential geometry and geometric PDEs, and has served as an editor for a research monograph that appeared in 2017. She has extensive experience in teaching Calculus, in both the traditional, face-to-face format (since 1995), and online (since 2011). She is a recipient of 6 teaching awards (2 at University of Kansas and 4 at Texas Tech University - including the President's Award for Excellence in Teaching, 2008).