Calculus I with Integrated Precalculus
First Edition ©2014 Laura Taalman Formats: Achieve, E-book, Print
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Authors
-
Laura Taalman
Laura Taalman and Peter Kohn are professors of mathematics at James Madison University, where they have taught calculus for a combined total of over 30 years.Laura Taalman received her undergraduate degree from the University of Chicago
and master’s and Ph.D. degrees in mathematics from Duke University. Her research includes singular algebraic geometry, knot theory, and the mathematics of games and puzzles. She is a recipient of both the Alder Award and the Trevor Evans award from the Mathematical Association of America, and the author of five books on Sudoku and the mathematics of Sudoku. In her spare time, she enjoys being a geek.Peter Kohn received his undergraduate degree from Antioch College, a master’s
degree from San Francisco State University, and a Ph.D. in mathematics from the University of Texas at Austin. His main areas of research are low-dimensional topology and knot theory. He has been a national judge for MathCounts since 2001. In his spare time, he enjoys hiking and riding his bicycle in the beautiful Shenandoah Valley.
Table of Contents
I Differential Calculus
0 Functions and Precalculus
0.1 Numbers and Sets
0.2 Equations
0.3 Inequalities
0.4 Functions and Graphs
0.5 A Basic Library of Functions
0.6 Operations, Transformations, and Inverses
0.7 Logic and Mathematical Thinking*
Chapter Review, Self-Test, and Capstones
1 Limits
1.1 An Intuitive Introduction to Limits
1.2 Formal Definition of a Limit
1.3 Delta-Epsilon Proofs*
1.4 Continuity and Its Consequences
1.5 Limit Rules and Calculating Basic Limits
1.6 Infinite Limits and Indeterminate Forms
Chapter Review, Self-Test, and Capstones
2 Derivatives
2.1 An Intuitive Introduction to Derivatives
2.2 Formal Definition of the Derivative
2.3 Rules for Calculating Basic Derivatives
2.4 The Chain Rule and Implicit Differentiation
Chapter Review, Self-Test, and Capstones
3 Applications of the Derivative
3.1 The Mean Value Theorem
3.2 The First Derivative and Curve Sketching
3.3 The Second Derivative and Curve Sketching
3.4 Optimization
3.5 Related Rates
Chapter Review, Self-Test, and Capstones
II Exploring Functions with Calculus
4 Calculus with Power, Polynomial, and Rational Functions
4.1 Advanced Algebraic Techniques
4.2 Power Functions
4.3 Polynomial Functions
4.4 Rational Functions
Chapter Review, Self-Test, and Capstones
5 Calculus with Exponential and Logarithmic Functions
5.1 Defining Exponential and Logarithmic Functions
5.2 Limits of Exponential and Logarithmic Functions
5.3 Derivatives of Exponential and Logarithmic Functions
5.4 Applications of Exponential Functions
5.5 L’Hopital’s Rule
Chapter Review, Self-Test, and Capstones
6 Calculus with Trignometric and Inverse Trigonometric Functions
6.1 Defining the Trigonometric Functions
6.2 Trigonometric Identities
6.3 Limits and Derivatives of Trigonometric Functions
6.4 Inverse Trigonometric Functions
Chapter Review, Self-Test, and Capstones
III Integral Calculus
7 Definite Integrals
7.1 Addition and Accumulation
7.2 Riemann Sums
7.3 Definite Integrals
7.4 Indefinite Integrals
7.5 The Fundamental Theorem of Calculus
7.6 Areas and Average Values
7.7 Functions Defined by Integrals
Chapter Review, Self-Test, and Capstones
8 Techniques of Integration
8.1 Integration by Substitution
8.2 Integration by Parts
8.3 Partial Fractions and Other Algebraic Techniques
8.4 Trigonometric Integrals
8.5 Trigonometric Substitution
8.6 Improper Integrals
8.7 Numerical Integration*
Chapter Review, Self-Test, and Capstones
9 Applications of Integration
9.1 Volumes by Slicing
9.2 Volumes by Shells
9.3 Arc Length and Surface Area
9.4 Real-World Applications of Integration
9.5 Differential Equations*
Chapter Review, Self-Test, and Capstones
Answers to Odd Problems
Index
Product Updates
Authors
-
Laura Taalman
Laura Taalman and Peter Kohn are professors of mathematics at James Madison University, where they have taught calculus for a combined total of over 30 years.Laura Taalman received her undergraduate degree from the University of Chicago
and master’s and Ph.D. degrees in mathematics from Duke University. Her research includes singular algebraic geometry, knot theory, and the mathematics of games and puzzles. She is a recipient of both the Alder Award and the Trevor Evans award from the Mathematical Association of America, and the author of five books on Sudoku and the mathematics of Sudoku. In her spare time, she enjoys being a geek.Peter Kohn received his undergraduate degree from Antioch College, a master’s
degree from San Francisco State University, and a Ph.D. in mathematics from the University of Texas at Austin. His main areas of research are low-dimensional topology and knot theory. He has been a national judge for MathCounts since 2001. In his spare time, he enjoys hiking and riding his bicycle in the beautiful Shenandoah Valley.
Table of Contents
I Differential Calculus
0 Functions and Precalculus
0.1 Numbers and Sets
0.2 Equations
0.3 Inequalities
0.4 Functions and Graphs
0.5 A Basic Library of Functions
0.6 Operations, Transformations, and Inverses
0.7 Logic and Mathematical Thinking*
Chapter Review, Self-Test, and Capstones
1 Limits
1.1 An Intuitive Introduction to Limits
1.2 Formal Definition of a Limit
1.3 Delta-Epsilon Proofs*
1.4 Continuity and Its Consequences
1.5 Limit Rules and Calculating Basic Limits
1.6 Infinite Limits and Indeterminate Forms
Chapter Review, Self-Test, and Capstones
2 Derivatives
2.1 An Intuitive Introduction to Derivatives
2.2 Formal Definition of the Derivative
2.3 Rules for Calculating Basic Derivatives
2.4 The Chain Rule and Implicit Differentiation
Chapter Review, Self-Test, and Capstones
3 Applications of the Derivative
3.1 The Mean Value Theorem
3.2 The First Derivative and Curve Sketching
3.3 The Second Derivative and Curve Sketching
3.4 Optimization
3.5 Related Rates
Chapter Review, Self-Test, and Capstones
II Exploring Functions with Calculus
4 Calculus with Power, Polynomial, and Rational Functions
4.1 Advanced Algebraic Techniques
4.2 Power Functions
4.3 Polynomial Functions
4.4 Rational Functions
Chapter Review, Self-Test, and Capstones
5 Calculus with Exponential and Logarithmic Functions
5.1 Defining Exponential and Logarithmic Functions
5.2 Limits of Exponential and Logarithmic Functions
5.3 Derivatives of Exponential and Logarithmic Functions
5.4 Applications of Exponential Functions
5.5 L’Hopital’s Rule
Chapter Review, Self-Test, and Capstones
6 Calculus with Trignometric and Inverse Trigonometric Functions
6.1 Defining the Trigonometric Functions
6.2 Trigonometric Identities
6.3 Limits and Derivatives of Trigonometric Functions
6.4 Inverse Trigonometric Functions
Chapter Review, Self-Test, and Capstones
III Integral Calculus
7 Definite Integrals
7.1 Addition and Accumulation
7.2 Riemann Sums
7.3 Definite Integrals
7.4 Indefinite Integrals
7.5 The Fundamental Theorem of Calculus
7.6 Areas and Average Values
7.7 Functions Defined by Integrals
Chapter Review, Self-Test, and Capstones
8 Techniques of Integration
8.1 Integration by Substitution
8.2 Integration by Parts
8.3 Partial Fractions and Other Algebraic Techniques
8.4 Trigonometric Integrals
8.5 Trigonometric Substitution
8.6 Improper Integrals
8.7 Numerical Integration*
Chapter Review, Self-Test, and Capstones
9 Applications of Integration
9.1 Volumes by Slicing
9.2 Volumes by Shells
9.3 Arc Length and Surface Area
9.4 Real-World Applications of Integration
9.5 Differential Equations*
Chapter Review, Self-Test, and Capstones
Answers to Odd Problems
Index
Product Updates
Taalman’s Calculus I with Integrated Precalculus helps students with weak mathematical backgrounds be successful in the calculus sequence, without retaking a precalculus course.
Taalman’s innovative text is the only book to interweave calculus with precalculus and algebra in a manner suitable for math and science majors— not a rehashing or just-in-time review of precalculus and algebra, but rather a new approach that uses a calculus-level toolbox to examine the structure and behavior of algebraic and transcendental functions.
This book was written specifically to tie in with the material covered in Taalman/Kohn Calculus. Students who begin their calculus sequence with Calculus I with Integrated Precalculus can easily continue on to Calculus II using the Taalman/Kohn text.
Maximize Teaching and Learning with WebAssign Premium
Macmillan Learning and WebAssign have partnered to deliver WebAssign Premium – a comprehensive and flexible suite of resources for your calculus course. Combining the most widely used online homework platform with authoritative textbook content and Macmillan’s esteemed Calctools, WebAssign Premium extends and enhances the classroom experience for instructors and students. Preview course content and sample assignments at www.webassign.net/whfreeman.
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If you’re a verified instructor, you can request a free sample of our courseware, e-book, or print textbook to consider for use in your courses. Only registered and verified instructors can receive free print and digital samples, and they should not be sold to bookstores or book resellers. If you don't yet have an existing account with Macmillan Learning, it can take up to two business days to verify your status as an instructor. You can request a free sample from the right side of this product page by clicking on the "Request Instructor Sample" button or by contacting your rep. Learn more.
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Sometimes also referred to as a spiral-bound or binder-ready textbook, loose-leaf textbooks are available to purchase. This three-hole punched, unbound version of the book costs less than a hardcover or paperback book.
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Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Most Achieve Essentials courses do not include our e-books and adaptive quizzing.
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Achieve (full course) includes our complete e-book, as well as online quizzing tools, multimedia assets, and iClicker active classroom manager.
Achieve Read & Practice only includes our e-book and adaptive quizzing, and does not include instructor resources and assignable assessments. Read & Practice does integrate with LMS.
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Calculus I with Integrated Precalculus
Taalman’s Calculus I with Integrated Precalculus helps students with weak mathematical backgrounds be successful in the calculus sequence, without retaking a precalculus course.
Taalman’s innovative text is the only book to interweave calculus with precalculus and algebra in a manner suitable for math and science majors— not a rehashing or just-in-time review of precalculus and algebra, but rather a new approach that uses a calculus-level toolbox to examine the structure and behavior of algebraic and transcendental functions.
This book was written specifically to tie in with the material covered in Taalman/Kohn Calculus. Students who begin their calculus sequence with Calculus I with Integrated Precalculus can easily continue on to Calculus II using the Taalman/Kohn text.
Maximize Teaching and Learning with WebAssign Premium
Macmillan Learning and WebAssign have partnered to deliver WebAssign Premium – a comprehensive and flexible suite of resources for your calculus course. Combining the most widely used online homework platform with authoritative textbook content and Macmillan’s esteemed Calctools, WebAssign Premium extends and enhances the classroom experience for instructors and students. Preview course content and sample assignments at www.webassign.net/whfreeman.
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