Thomas' Calculus: Early Transcendentals, 15th edition

Published by Pearson (2 August 2024) © 2024

  • Joel R. Hass University of California, Davis
  • Christopher E. Heil Georgia Institute of Technology
  • Maurice D. Weir Naval Postgraduate School
  • Przemyslaw Bogacki Old Dominion University
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Title overview

Calculus is more than applying formulas. It's a way of understanding change, solving complex problems and modelling the world around us. Thomas' Calculus: Early Transcendentals helps students develop a deeper understanding of calculus by combining clear explanations, mathematical rigour and meaningful applications. Designed for students studying mathematics, engineering and the sciences, it supports learners as they build confidence with core concepts while developing the analytical thinking needed for future study and professional practice.

Students are encouraged to move beyond procedural problem solving to develop genuine mathematical reasoning. Informal introductions help build intuition before formal definitions and proofs establish a deeper understanding of the underlying concepts. Updated applications, enhanced visualisations and a wide range of practice opportunities help learners connect calculus to real-world challenges, from scientific modelling and engineering problems to emerging topics such as machine learning and neural networks.

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Table of contents

  • 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
  • 17. Second-Order Differential Equations
  • 18. Complex Functions (online)
  • 19. Fourier Series and Wavelets (online)
  • Answers to Odd-Numbered Exercises

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