Calculus
Fourth Edition ©2019 Jon Rogawski; Colin Adams; Robert Franzosa Formats: Achieve, E-book, Print
As low as C$80.99
As low as C$80.99
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Authors
-
Jon Rogawski
Jon Rogawski received his undergraduate and master’s degrees in mathematics simultaneously from Yale University, and he earned his PhD in mathematics from Princeton University, where he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, where he was a full professor, he held teaching and visiting positions at the Institute for Advanced Study, the University of Bonn, and the University of Paris at Jussieu and Orsay. Jon’s areas of interest were number theory, automorphic forms, and harmonic analysis on semisimple groups. He published numerous research articles in leading mathematics journals, including the research monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton University Press). He was the recipient of a Sloan Fellowship and an editor of the Pacific Journal of Mathematics and the Transactions of the AMS. As a successful teacher for more than 30 years, Jon Rogawski listened and learned much from his own students. These valuable lessons made an impact on his thinking, his writing, and his shaping of a calculus text. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and the important role it plays in students’ understanding of the wider world is the legacy that lives on in each new edition of Calculus.
-
Colin Adams
Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, where he has taught since 1985. Colin received his undergraduate degree from MIT and his PhD from the University of Wisconsin. His research is in the area of knot theory and low-dimensional topology. He has held various grants to support his research, and written numerous research articles. Colin is the author or co-author of The Knot Book, How to Ace Calculus: The Streetwise Guide, How to Ace the Rest of Calculus: The Streetwise Guide, Riot at the Calc Exam and Other Mathematically Bent Stories, Why Knot?, Introduction to Topology: Pure and Applied, and Zombies & Calculus. He co-wrote and appears in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdown.” He is a recipient of the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has two children and one slightly crazy dog, who is great at providing the entertainment.
-
Robert Franzosa
Robert (Bob) Franzosa is a professor of mathematics at the University of Maine where he has been on the faculty since 1983. Bob received a BS in mathematics from MIT in 1977 and a Ph.D. in mathematics from the University of Wisconsin in 1984. His research has been in dynamical systems and in applications of topology in geographic information systems. He has been involved in mathematics education outreach in the state of Maine for most of his career. Bob is a co-author of Introduction to Topology: Pure and Applied and Algebraic Models in Our World. He was awarded the University of Maine’s Presidential Outstanding Teaching award in 2003. Bob is married, has two children, three step-children, and one recently-arrived grandson.
Table of Contents
Chapter 1: Precalculus Review
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology: Calculators and Computers
Chapter 2: Limits
2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines
2.2 Investigating Limits
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Indeterminate Forms
2.6 The Squeeze Theorem and Trigonometric Limits
2.7 Limits at Infinity
2.8 The Intermediate Value Theorem
2.9 The Formal Definition of a Limit
Chapter 3: Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of General Exponential and Logarithmic Functions
3.10 Related Rates
Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Second Derivative and Concavity
4.5 L’Hôpital’s Rule
4.6 Analyzing and Sketching Graphs of Functions
4.7 Applied Optimization
4.8 Newton’s Method
Chapter 5: Integration
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Indefinite Integral
5.4 The Fundamental Theorem of Calculus, Part I
5.5 The Fundamental Theorem of Calculus, Part II
5.6 Net Change as the Integral of a Rate of Change
5.7 The Substitution Method
5.8 Further Integral Formulas
Chapter 6: Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution: Disks and Washers
6.4 Volumes of Revolution: Cylindrical Shells
6.5 Work and Energy
Chapter 7: Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
7.5 The Method of Partial Fractions
7.6 Strategies for Integration
7.7 Improper Integrals
7.8 Numerical Integration
Chapter 8: Further Applications of the Integral
8.1 Probability and Integration
8.2 Arc Length and Surface Area
8.3 Fluid Pressure and Force
8.4 Center of Mass
Chapter 9: Introduction to Differential Equations
9.1 Solving Differential Equations
9.2 Models Involving y=k(y-b)
9.3 Graphical and Numerical Methods
9.4 The Logistic Equation
9.5 First-Order Linear Equations
Chapter 10: Infinite Series
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests and Strategies for Choosing Tests
10.6 Power Series
10.7 Taylor Polynomials
10.8 Taylor Series
Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections
Chapter 12: Vector Geometry
12.1 Vectors in the Plane
12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.5 Planes in 3-Space
12.6 A Survey of Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates
Chapter 13: Calculus of Vector-Valued Functions
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in 3-Space
13.6 Planetary Motion According to Kepler and Newton
Chapter 14: Differentiation in Several Variables
14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives
14.4 Differentiability, Tangent Planes, and Linear Approximation
14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule
14.7 Optimization in Several Variables
14.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter 15: Multiple Integration
15.1 Integration in Two Variables
15.2 Double Integrals Over More General Regions
15.3 Triple Integrals
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 Applications of Multiple Integrals
15.6 Change of Variables
Chapter 16: Line and Surface Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Parametrized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields
Chapter 17: Fundamental Theorems of Vector Analysis
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem
Product Updates
Achieve for Calculus is built in partnership with adopting institutions and educators. Macmillan is responsive to the needs of these courses and provides frequent user-informed updates to support a range of teaching and learning goals.
2025 Update:
New for Math courses, the AI Tutor in Achieve helps students learn mathematics and complete homework successfully without giving away the answers. Using advanced OpenAI models and Macmillan Learning content, the thoroughly-tested and responsibly-developed AI Tutor provides real-time help on everything from prerequisite mathematics content to current concepts and skills students are working to build.
- Built on the Socratic method, the AI Tutor asks questions to encourage deep thinking and individual agency over learning and problem solving.
- Once enabled by the instructor, the AI Tutor is available to provide individualized guidance in all question types, including those with embedded videos and graphs. The AI Tutor is also available in edited or instructor-authored exercises.
- For expression entry, the AI Tutor includes a math palette so students can engage with the Tutor about the question without having to design a shorthand for mathematical symbols or formatting.
- The AI Tutor is available in numerous foreign languages. Being multilingual means a person is thinking in multiple languages, not just speaking. Mathematical tasks are often challenging to understand, particularly word problems and deeper conceptual tasks; however, those tasks offer opportunities to engage authentically with the concepts as they relate to real-world applications.
2024 Update:
Desmos Dynamic Figure Bank
- This bank contains a selection of Dynamic Figures from the book, powered by the Desmos graphing calculator, that you can use for demoing purposes in class. The selected figures represent visualizations for key topics from single and multivariable Calculus. Click on a chapter, navigate to a figure, and interact with it directly on the page. Each Dynamic Figure is labeled with its figure number from the book and a brief description. Each figure is also available in Achieve in the e-book and paired with assessment questions in the Guided Learn and Practice assignment for the relevant section.
Placement Exam
- Achieve for Calculus now features a customizable 20-question placement exam for institutions that require placement or pre-class evaluation.
Interactive Video Activities
- Over 30 new Interactive Video Activities have been added to allow students to review fundamental prerequisite math topics by watching a brief video and answering conceptual and reflection questions at specified timestamps throughout the video. This format allows students to practice key math skills in an interactive, self-paced lesson.
2023 Update:
- Over 100 Desmos-powered Graded Graph exercises, which allow students to manipulate points and functions on an autograded graph, are available in the question bank.
- Video feedback, embedded within the feedback tab of homework exercises, is available for 250 of the most frequently assigned questions, providing brief step-by-step tutorial videos to guide students toward the correct answer.
- A new video index is available in the Resources tab, linking each section of the text to correlated videos from the popular Patrick JMT YouTube channel.
- New “Identify the Error” question types are available in the question library and pre-built assignments. These exercises ask students to think conceptually to recognize the mistaken step or concept. These 100+ new exercises, marked with "(ITE)" in the question bank, provide an opportunity to show mastery of the entire problem, instead of simply finding the final correct answer.
- Chapter-level adaptive quizzes are now available as an end of chapter study tool, in addition to existing section-level adaptive quizzes.
For more information on Achieve platform updates, visit the Achieve What’s New page here.
Hallmark Features of Achieve for Rogawski’s Calculus:
Achieve focuses on engaging students through pre-class and post-class assessment, interactive activities, and a full e-book. Achieve is a complete learning environment with easy course setup, gradebook, and LMS integration.
- Homework: Achieve’s proprietary grading algorithm combines Macmillan’s homegrown parser and the computer algebra system, SymPy, to accept every valid equivalent answer unless clearly declared (e.g. simplified form, factored form). Improper formatting triggers syntax warnings for answers entered incorrectly. Personalized feedback and individualized guidance through the AI Tutor, as well as fully worked solutions, provide in-question guidance for students as they solve. Homework is easy to format for students by using the intuitive Math Palette, and exercises are easy to author and edit for instructors using Macmillan’s built-in question editor.
- Guided Learn and Practice: assignments include interactive content, videos, and instructional feedback to prepare students before they come to class.
- CalcClips: tutorial videos are integrated throughout the e-book and available in pre-built Guided Learn & Practice assignments meant for formative exercise exploration.
- Dynamic Figures: powered by Desmos, take students’ experience further with conceptual and computational questions about the interactive Dynamic Figures. These book-specific figures are embedded directly in the e-book and included with assessment in pre-built Guided Learn & Practice assignments.
- LearningCurve adaptive quizzing: offers individualized question sets and feedback for each student based on their responses. Questions are tied directly to the e-book and focus on conceptual understanding over computation.
- Active learning resources: including in-class activity guides and free access to the iClicker student response app support hands-on learning in classes of all modalities.
General Themes of the Revision Include:
- Rewrite portions to increase readability without reducing the level of mathematical rigor. This includes increasing clarity, improving organization, and building consistency.
- Add applications, particularly in life science and earth science, to broaden the scientific fields represented in the book. In particular, there are a number of new examples and exercises in climate science.
- Add conceptual and graphical insights to assist student understanding in places where pitfalls and confusion often occur.
- Add diversity to the Historical Perspectives and historical marginal pieces. Maintain threads throughout the book by previewing topics that come up later and revisiting topics that have been presented before.
- Expand the perspective on curve sketching to include analyzing given curves using calculus tools, beyond just sketching a curve.
- “Tighten” the presentation of mathematics in the text, improving rigor without increasing formality. This includes correcting previous errors and omissions.
Authors
-
Jon Rogawski
Jon Rogawski received his undergraduate and master’s degrees in mathematics simultaneously from Yale University, and he earned his PhD in mathematics from Princeton University, where he studied under Robert Langlands. Before joining the Department of Mathematics at UCLA in 1986, where he was a full professor, he held teaching and visiting positions at the Institute for Advanced Study, the University of Bonn, and the University of Paris at Jussieu and Orsay. Jon’s areas of interest were number theory, automorphic forms, and harmonic analysis on semisimple groups. He published numerous research articles in leading mathematics journals, including the research monograph Automorphic Representations of Unitary Groups in Three Variables (Princeton University Press). He was the recipient of a Sloan Fellowship and an editor of the Pacific Journal of Mathematics and the Transactions of the AMS. As a successful teacher for more than 30 years, Jon Rogawski listened and learned much from his own students. These valuable lessons made an impact on his thinking, his writing, and his shaping of a calculus text. Sadly, Jon Rogawski passed away in September 2011. Jon’s commitment to presenting the beauty of calculus and the important role it plays in students’ understanding of the wider world is the legacy that lives on in each new edition of Calculus.
-
Colin Adams
Colin Adams is the Thomas T. Read professor of Mathematics at Williams College, where he has taught since 1985. Colin received his undergraduate degree from MIT and his PhD from the University of Wisconsin. His research is in the area of knot theory and low-dimensional topology. He has held various grants to support his research, and written numerous research articles. Colin is the author or co-author of The Knot Book, How to Ace Calculus: The Streetwise Guide, How to Ace the Rest of Calculus: The Streetwise Guide, Riot at the Calc Exam and Other Mathematically Bent Stories, Why Knot?, Introduction to Topology: Pure and Applied, and Zombies & Calculus. He co-wrote and appears in the videos “The Great Pi vs. E Debate” and “Derivative vs. Integral: the Final Smackdown.” He is a recipient of the Haimo National Distinguished Teaching Award from the Mathematical Association of America (MAA) in 1998, an MAA Polya Lecturer for 1998-2000, a Sigma Xi Distinguished Lecturer for 2000-2002, and the recipient of the Robert Foster Cherry Teaching Award in 2003. Colin has two children and one slightly crazy dog, who is great at providing the entertainment.
-
Robert Franzosa
Robert (Bob) Franzosa is a professor of mathematics at the University of Maine where he has been on the faculty since 1983. Bob received a BS in mathematics from MIT in 1977 and a Ph.D. in mathematics from the University of Wisconsin in 1984. His research has been in dynamical systems and in applications of topology in geographic information systems. He has been involved in mathematics education outreach in the state of Maine for most of his career. Bob is a co-author of Introduction to Topology: Pure and Applied and Algebraic Models in Our World. He was awarded the University of Maine’s Presidential Outstanding Teaching award in 2003. Bob is married, has two children, three step-children, and one recently-arrived grandson.
Table of Contents
Chapter 1: Precalculus Review
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology: Calculators and Computers
Chapter 2: Limits
2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines
2.2 Investigating Limits
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Indeterminate Forms
2.6 The Squeeze Theorem and Trigonometric Limits
2.7 Limits at Infinity
2.8 The Intermediate Value Theorem
2.9 The Formal Definition of a Limit
Chapter 3: Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of General Exponential and Logarithmic Functions
3.10 Related Rates
Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Second Derivative and Concavity
4.5 L’Hôpital’s Rule
4.6 Analyzing and Sketching Graphs of Functions
4.7 Applied Optimization
4.8 Newton’s Method
Chapter 5: Integration
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Indefinite Integral
5.4 The Fundamental Theorem of Calculus, Part I
5.5 The Fundamental Theorem of Calculus, Part II
5.6 Net Change as the Integral of a Rate of Change
5.7 The Substitution Method
5.8 Further Integral Formulas
Chapter 6: Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution: Disks and Washers
6.4 Volumes of Revolution: Cylindrical Shells
6.5 Work and Energy
Chapter 7: Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
7.5 The Method of Partial Fractions
7.6 Strategies for Integration
7.7 Improper Integrals
7.8 Numerical Integration
Chapter 8: Further Applications of the Integral
8.1 Probability and Integration
8.2 Arc Length and Surface Area
8.3 Fluid Pressure and Force
8.4 Center of Mass
Chapter 9: Introduction to Differential Equations
9.1 Solving Differential Equations
9.2 Models Involving y=k(y-b)
9.3 Graphical and Numerical Methods
9.4 The Logistic Equation
9.5 First-Order Linear Equations
Chapter 10: Infinite Series
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests and Strategies for Choosing Tests
10.6 Power Series
10.7 Taylor Polynomials
10.8 Taylor Series
Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections
Chapter 12: Vector Geometry
12.1 Vectors in the Plane
12.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product
12.5 Planes in 3-Space
12.6 A Survey of Quadric Surfaces
12.7 Cylindrical and Spherical Coordinates
Chapter 13: Calculus of Vector-Valued Functions
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed
13.4 Curvature
13.5 Motion in 3-Space
13.6 Planetary Motion According to Kepler and Newton
Chapter 14: Differentiation in Several Variables
14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives
14.4 Differentiability, Tangent Planes, and Linear Approximation
14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule
14.7 Optimization in Several Variables
14.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter 15: Multiple Integration
15.1 Integration in Two Variables
15.2 Double Integrals Over More General Regions
15.3 Triple Integrals
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates
15.5 Applications of Multiple Integrals
15.6 Change of Variables
Chapter 16: Line and Surface Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Parametrized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields
Chapter 17: Fundamental Theorems of Vector Analysis
17.1 Green’s Theorem
17.2 Stokes’ Theorem
17.3 Divergence Theorem
Product Updates
Achieve for Calculus is built in partnership with adopting institutions and educators. Macmillan is responsive to the needs of these courses and provides frequent user-informed updates to support a range of teaching and learning goals.
2025 Update:
New for Math courses, the AI Tutor in Achieve helps students learn mathematics and complete homework successfully without giving away the answers. Using advanced OpenAI models and Macmillan Learning content, the thoroughly-tested and responsibly-developed AI Tutor provides real-time help on everything from prerequisite mathematics content to current concepts and skills students are working to build.
- Built on the Socratic method, the AI Tutor asks questions to encourage deep thinking and individual agency over learning and problem solving.
- Once enabled by the instructor, the AI Tutor is available to provide individualized guidance in all question types, including those with embedded videos and graphs. The AI Tutor is also available in edited or instructor-authored exercises.
- For expression entry, the AI Tutor includes a math palette so students can engage with the Tutor about the question without having to design a shorthand for mathematical symbols or formatting.
- The AI Tutor is available in numerous foreign languages. Being multilingual means a person is thinking in multiple languages, not just speaking. Mathematical tasks are often challenging to understand, particularly word problems and deeper conceptual tasks; however, those tasks offer opportunities to engage authentically with the concepts as they relate to real-world applications.
2024 Update:
Desmos Dynamic Figure Bank
- This bank contains a selection of Dynamic Figures from the book, powered by the Desmos graphing calculator, that you can use for demoing purposes in class. The selected figures represent visualizations for key topics from single and multivariable Calculus. Click on a chapter, navigate to a figure, and interact with it directly on the page. Each Dynamic Figure is labeled with its figure number from the book and a brief description. Each figure is also available in Achieve in the e-book and paired with assessment questions in the Guided Learn and Practice assignment for the relevant section.
Placement Exam
- Achieve for Calculus now features a customizable 20-question placement exam for institutions that require placement or pre-class evaluation.
Interactive Video Activities
- Over 30 new Interactive Video Activities have been added to allow students to review fundamental prerequisite math topics by watching a brief video and answering conceptual and reflection questions at specified timestamps throughout the video. This format allows students to practice key math skills in an interactive, self-paced lesson.
2023 Update:
- Over 100 Desmos-powered Graded Graph exercises, which allow students to manipulate points and functions on an autograded graph, are available in the question bank.
- Video feedback, embedded within the feedback tab of homework exercises, is available for 250 of the most frequently assigned questions, providing brief step-by-step tutorial videos to guide students toward the correct answer.
- A new video index is available in the Resources tab, linking each section of the text to correlated videos from the popular Patrick JMT YouTube channel.
- New “Identify the Error” question types are available in the question library and pre-built assignments. These exercises ask students to think conceptually to recognize the mistaken step or concept. These 100+ new exercises, marked with "(ITE)" in the question bank, provide an opportunity to show mastery of the entire problem, instead of simply finding the final correct answer.
- Chapter-level adaptive quizzes are now available as an end of chapter study tool, in addition to existing section-level adaptive quizzes.
For more information on Achieve platform updates, visit the Achieve What’s New page here.
Hallmark Features of Achieve for Rogawski’s Calculus:
Achieve focuses on engaging students through pre-class and post-class assessment, interactive activities, and a full e-book. Achieve is a complete learning environment with easy course setup, gradebook, and LMS integration.
- Homework: Achieve’s proprietary grading algorithm combines Macmillan’s homegrown parser and the computer algebra system, SymPy, to accept every valid equivalent answer unless clearly declared (e.g. simplified form, factored form). Improper formatting triggers syntax warnings for answers entered incorrectly. Personalized feedback and individualized guidance through the AI Tutor, as well as fully worked solutions, provide in-question guidance for students as they solve. Homework is easy to format for students by using the intuitive Math Palette, and exercises are easy to author and edit for instructors using Macmillan’s built-in question editor.
- Guided Learn and Practice: assignments include interactive content, videos, and instructional feedback to prepare students before they come to class.
- CalcClips: tutorial videos are integrated throughout the e-book and available in pre-built Guided Learn & Practice assignments meant for formative exercise exploration.
- Dynamic Figures: powered by Desmos, take students’ experience further with conceptual and computational questions about the interactive Dynamic Figures. These book-specific figures are embedded directly in the e-book and included with assessment in pre-built Guided Learn & Practice assignments.
- LearningCurve adaptive quizzing: offers individualized question sets and feedback for each student based on their responses. Questions are tied directly to the e-book and focus on conceptual understanding over computation.
- Active learning resources: including in-class activity guides and free access to the iClicker student response app support hands-on learning in classes of all modalities.
General Themes of the Revision Include:
- Rewrite portions to increase readability without reducing the level of mathematical rigor. This includes increasing clarity, improving organization, and building consistency.
- Add applications, particularly in life science and earth science, to broaden the scientific fields represented in the book. In particular, there are a number of new examples and exercises in climate science.
- Add conceptual and graphical insights to assist student understanding in places where pitfalls and confusion often occur.
- Add diversity to the Historical Perspectives and historical marginal pieces. Maintain threads throughout the book by previewing topics that come up later and revisiting topics that have been presented before.
- Expand the perspective on curve sketching to include analyzing given curves using calculus tools, beyond just sketching a curve.
- “Tighten” the presentation of mathematics in the text, improving rigor without increasing formality. This includes correcting previous errors and omissions.
Rogawski’s Calculus & Achieve: Teaching the Why of Calculus, not just the How
With an emphasis on strengthening conceptual comprehension, graphical understanding and personalized problem-solving muscle, Rogawski’s Calculus & Achieve–powered by the AI Tutor and Desmos Studio PBC–present a modern, applications-rich solution for calculus students of all levels. Long preferred for its clear jargon-less explanations, graphical insights, and a wealth of exercises, Rogawski’s Calculus is available in the Achieve platform to support the way today’s students learn: through just-in-time resources and videos, hands-on graphing, and the in-question AI Tutor that adapts to each individual’s learning needs and understanding. The Achieve platform includes easy-to-use instruction tools; simple customization at the course, resource, or question level; and resources like adaptive quizzing and active learning support that offer more than just homework.
Rogawski’s Calculus & Achieve provide the calculus content and guidance students deserve, and the platform that instructors prefer–built hand-in-hand with math educators who teach the why or calculus, not just the how.
Success Stories
Here are a few examples of how Achieve has helped instructors like you improve student preparedness, enhance their sense of belonging, and achieve course goals they set for themselves.
Prof. Kiandra Johnson, Spelman College
See how the resources in Achieve help you engage students before, during, and after class.
Prof. Jennifer Duncan
Use diagnostics in Achieve for a snapshot into cognitive and non-cognitive factors that may impact your students’ preparedness.
Prof. Ryan Elsenpeter
Here’s why educators who use Achieve would recommend it to their peers.
Instructor Resources
Instructor Resources
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Test Bank for Calculus
Jon Rogawski; Colin Adams; Robert Franzosa | Fourth Edition | ©2019 | ISBN:9781319221287
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Our courses currently integrate with Canvas, Blackboard (Learn and Ultra), Brightspace, D2L, and Moodle. Click on the support documentation below to find out more details about the integration with each LMS.
Integrate Macmillan courses with Blackboard
Integrate Macmillan courses with Canvas
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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.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
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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.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
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We can help! Contact your representative to discuss your specific needs for your course. If our off-the-shelf course materials don’t quite hit the mark, we also offer custom solutions made to fit your needs.
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ISBN:9781319221195
Access all your course tools in one place!
ISBN:9781319055844
Take notes, add highlights, and download our mobile-friendly e-books.
ISBN:9781319055837
Save money with our hole-punched, loose-leaf textbook.
ISBN:9781319406950
This package includes Achieve and Loose-Leaf.
FAQs
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Are you a campus bookstore looking for ordering information?
MPS Order Search Tool (MOST) is a web-based purchase order tracking program that allows customers to view and track their purchases. No registration or special codes needed! Just enter your BILL-TO ACCT # and your ZIP CODE to track orders.
Canadian Stores: Please use only the first five digits/letters in your zip code on MOST.
Visit MOST, our online ordering system for booksellers: https://tracking.mpsvirginia.com/Login.aspx
Learn more about our Bookstore programs here: https://www.macmillanlearning.com/college/us/contact-us/booksellers
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Our courses currently integrate with Canvas, Blackboard (Learn and Ultra), Brightspace, D2L, and Moodle. Click on the support documentation below to find out more details about the integration with each LMS.
Integrate Macmillan courses with Blackboard
Integrate Macmillan courses with Canvas
-
-
-
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.
-
-
-
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.
-
-
-
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.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
-
-
-
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.
Visit our comparison table for details: https://www.macmillanlearning.com/college/us/digital/achieve/compare
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-
We can help! Contact your representative to discuss your specific needs for your course. If our off-the-shelf course materials don’t quite hit the mark, we also offer custom solutions made to fit your needs.
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Calculus
With an emphasis on strengthening conceptual comprehension, graphical understanding and personalized problem-solving muscle, Rogawski’s Calculus & Achieve–powered by the AI Tutor and Desmos Studio PBC–present a modern, applications-rich solution for calculus students of all levels. Long preferred for its clear jargon-less explanations, graphical insights, and a wealth of exercises, Rogawski’s Calculus is available in the Achieve platform to support the way today’s students learn: through just-in-time resources and videos, hands-on graphing, and the in-question AI Tutor that adapts to each individual’s learning needs and understanding. The Achieve platform includes easy-to-use instruction tools; simple customization at the course, resource, or question level; and resources like adaptive quizzing and active learning support that offer more than just homework.
Rogawski’s Calculus & Achieve provide the calculus content and guidance students deserve, and the platform that instructors prefer–built hand-in-hand with math educators who teach the why or calculus, not just the how.
Sample Achieve