Thomas' Calculus 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. Features ? 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