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This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.

Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal

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Mathematical analysis --- Calculus --- Calcul infinitésimal --- rekenkunde --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Calcul infinitésimal

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Mathematical analysis --- Calculus --- Calcul infinitésimal --- 512 --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal --- Algebra --- 512 Algebra --- Calcul infinitésimal

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TO THE INSTRUCTOR I hear, I forget. I see, I remember. I do, I understand. Anonymous OBJECTIVES OF WORKSHOP CALCULUS 1. Impel students to be active learners. 2. Help students to develop confidence about their ability to think about and do mathematics. 3. Encourage students to read, write, and discuss mathematical ideas. 4. Enhance students’ understanding of the fundamental concepts under- ing the calculus. 5. Prepare students to use calculus in other disciplines. 6. Inspire students to continue their study of mathematics. 7. Provide an environment where students enjoy learning and doing ma- ematics. xi xii To the Instructor THE WORKSHOP APPROACH Workshop Calculus with Graphing Calculators: Guided Exploration with Review provides students with a gateway into the study of calculus. The two-volume series integrates a review of basic precalculus ideas with the study of c- cepts traditionally encountered in beginning calculus: functions, limits, - rivatives, integrals, and an introduction to integration techniques and d- ferential equations. It seeks to help students develop the confidence, understanding, and skills necessary for using calculus in the natural and - cial sciences, and for continuing their study of mathematics.

Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Global analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal

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The umbral calculus

Calcul infinitésimal --- Infinitesimaalrekening. --- Calculus. --- Geometry, Analytic. --- Analytical geometry --- Geometry, Algebraic --- Algebra --- Conic sections --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Graphic methods