For three-semester or four-quarter courses in Calculus for students majoring in mathematics, engineering, or science
Clarity and precision
Thomas' Calculus: Early Transcendentals helps students reach the level of mathematical proficiency and maturity you require, but with support for students who need it through its balance of clear and intuitive explanations, current applications, and generalized concepts. In the 14th SI Edition, new co-author Christopher Heil (Georgia Institute of Technology) partners with author Joel Hass to preserve what is best about Thomas' time-tested text while reconsidering every word and every piece of art with today's students in mind. The result is a text that goes beyond memorizing formulas and routine procedures to help students generalize key concepts and develop deeper understanding.
Also available with Pearson MyLab Math
Pearson MyLabTM Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. A full suite of Interactive Figures have been added to the accompanying Pearson MyLab Math course to further support teaching and learning. Enhanced Sample Assignments include just-in-time prerequisite review, help keep skills fresh with distributed practice of key concepts, and provide opportunities to work exercises without learning aids to help students develop confidence in their ability to solve problems independently.
- New co-author Chris Heil (Georgia Institute of Technology) and co-author Joel Hass continue Thomas’ tradition of developing students’ mathematical maturity and proficiency, going beyond memorising formulas and routine procedures, and showing students how to generalise key concepts once they are introduced.
- The authors are careful to present key topics, such as the definition of the derivative, both informally and formally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalised so that students are not overwhelmed by abstraction.
- Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text.Â
- A 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 analogues studied earlier in the book.
Assess student understanding of key concepts and skills through a wide range of time-tested exercises
- 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. In the 14th SI Edition, the authors added new exercises throughout, many geometric in nature.
- Writing exercises placed throughout the text ask students to explore and explain a variety of calculus concepts and applications. In addition, the end of each chapter contains a list of questions for students to review and summarise what they have learned. Many of these exercises make good writing assignments.
- Technology exercises (marked with a T) are included in each section, asking students to use the calculator or computer when solving the problems. In addition, Computer Explorations give the option of assigning exercises that require a computer algebra system (CAS, such as Maple or Mathematica).
Support a complete understanding of calculus for students at varying levels
- Each major topic is developed with both simple and more advanced examples to give the basic ideas and illustrate deeper concepts.
- UPDATED! Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 14th SI Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasise clear visualisation.
- ENHANCED! Annotations within examples (shown in blue type)  guide students through the problem solution and emphasise that each step in a mathematical argument is rigorously justified. For the 14th SI Edition, many more annotations were added.
- End-of-chapter materials include review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises with more challenging or synthesising problems.
- A complete suite of instructor and student supplements saves class preparation time for instructors and improves students’ learning.
New to the Book
Co-authors Joel Hass and Chris Heil reconsidered every word, symbol, and piece of art, motivating students to consider the content from different perspectives and compelling a deeper, geometric understanding.
- Updated graphics emphasize clear visualization and mathematical correctness.
- New examples and figures have been added throughout all chapters, many based on user feedback. See, for instance, Example 3 in Section 9.1, which helps students overcome a conceptual obstacle.
- New types of homework exercises, including many geometric in nature, have been added. The new exercises provide different perspectives and approaches to each topic.
- Short URLs have been added to the historical marginnotes, allowing students to navigate directly to online information.
- New annotations within examples (in blue type) guide the student through the problem solution and emphasize that each step in a mathematical argument is rigorously justified.
- All chapters have been revised for clarity, consistency, conciseness, and comprehension.
Detailed content changes
Chapter 1
• Clarified explanation of definition of exponential function in 1.4.• Replaced sin-1 notation for the inverse sine function with arcsin as default notation in 1.5, and similarly for other trig functions.• Added new Exercises: 1.1: 59–62, 1.2: 21–22; 1.3: 64–65,1.5: 61–64, 79cd; PE: 29–32.Chapter 2
• Added definition of average speed in 2.1.• Updated definition of limits to allow for arbitrary domains. The definition of limits is now consistent with the definition in multivariable domains later in the text and with more general mathematical usage.• Reworded limit and continuity definitions to remove implication symbols and improve comprehension.• Added new Example 7 in 2.4 to illustrate limits of ratios of trig functions.• Rewrote 2.6 Example 11 to solve the equation by finding a zero, consistent with previous discussion.• Added new Exercises: 2.1: 15–18; 2.2: 3h–k, 4f–I; 2.4: 19–20, 45–46; 2.5: 69–74; 2.6: 31–32; PE: 57–58; AAE: 35–38.Chapter 3
• Clarified relation of slope and rate of change.• Added new Figure 3.9 using the square root function to illustrate vertical tangent lines.• Added figure of x sin (1>x) in 3.2 to illustrate how oscillation can lead to non-existence of a derivative of a continuous function.• Revised product rule to make order of factors consistent throughout text, including later dot product and cross product formulas.• Added new Exercises: 3.2: 36, 43–44; 3.3: 65–66; 3.5: 43–44, 61bc; 3.6: 79–80, 111–113; 3.7: 27–28; 3.8: 97–100;3.9: 43–46; 3.10: 47; AAE: 14–15, 26–27.Chapter 4
• Added summary to 4.1.• Added new Example 12 with new Figure 4.35 to give basic and advanced examples of concavity.• Added new Exercises: 4.1: 53–56, 67–70; 4.3: 45–46, 67–68; 4.4: 107–112; 4.6: 37–42; 4.7: 7–10; 4.8: 115–118;PE: 1–16, 101–102; AAE: 19&#- 1. Functions
- 2. Limits and Continuity
- 3. Derivatives
- 4. Applications of Derivatives
- 5. Integrals
- 6. Applications of Definite Integrals
- 7. Integrals and Transcendental Functions
- 8. Techniques of Integration
- 9. Infinite Sequences and Series
- 10. Parametric Equations and Polar Coordinates
- 11. Vectors and the Geometry of Space
- 12. Vector-Valued Functions and Motion in Space
- 13. Partial Derivatives
- 14. Multiple Integrals
- 15. Integrals and Vector Fields
- 16. First-Order Differential Equations
- Appendices
- 1. Real Numbers and the Real Line AP-1
- 2 Graphing with Software
- 3. Mathematical Induction AP-6
- 4 Lines, Circles, and Parabolas AP-9
- 5 Proofs of Limit Theorems AP-19
- 6 Commonly Occurring Limits AP-22
- 7 Theory of the Real Numbers AP-23
- 8 Complex Numbers AP-26
- 9. Probability
- 10. The Distributive Law for Vector Cross Products AP-34
- 11. The Mixed Derivative Theorem and the Increment Theorem
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