For 3-semester or 4-quarter courses in Calculus for students majoring in mathematics, engineering, or science.Clarity and precision Thomas' Calculus: Early Transcendentals goes beyond memorizing formulas and routine procedures to help students develop deeper understanding. It guides students to a level of mathematical proficiency and maturity needed for the course, with support for those who require it through its balance of clear and intuitive explanations, current applications and generalized concepts. The 15th Edition meets the needs of students with increasingly varied levels of readiness for the calculus sequence. This revision also adds exercises, revises figures and narrative for clarity, and updates many applications with modern topics.Hallmark features of this title Key topics are presented both informally and formally. Results are carefully stated and proved throughout, and proofs are clearly explained and motivated. Strong exercise sets feature a wide range from skills problems to applied and theoretical problems. Writing exercises ask students to explore and explain various concepts and applications. A list of questions at the end of each chapter asks them to review and summarize what they have learned. Technology exercises in each section ask students to use the calculator or computer when solving the problems. Computer Explorations offer exercises requiring a computer algebra system such as Maple or Mathematica. Annotations within examples guide students through the problem solution and emphasize that each step in a mathematical argument is justified. New and updated features of this title Many narrative clarifications and revisions have been made throughout the text. A new appendix on Determinants and Gradient Descent has been added, covering many topics relevant to students interested in Machine Learning and Neural Networks. Many updated graphics and figures have been enhanced to bring out clear visualization and mathematical correctness. Many exercise instructions have been clarified, such as suggesting where the use of a calculator may be needed. Notation of inverse trig functions has been changed throughout the text to favor arcsin notation over sin^{-1}, etc.