The transition from calculus of one variable to the study of functions of several variables is a pivotal moment in a mathematics student's education. It opens the door to differential geometry, vector calculus, linear algebra, and the analytic foundations of physics and engineering. Multivariable Mathematics by Robert Shifrin (often simply referred to as “Shifrin”) was written expressly to bridge this gap. First published in the early 2000s, the text has been adopted by numerous universities for courses titled “Multivariable Calculus,” “Advanced Calculus,” or “Calculus III.” Its popularity stems from a clear exposition, a balanced mixture of theory and application, and a thoughtful progression of ideas that respects the diverse backgrounds of its readers.
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This is arguably more valuable than a static PDF. You can follow along with the lecture videos while using a legally purchased copy or a library reserve copy. The transition from calculus of one variable to