You're looking for a guide to multivariable calculus using Edwards and Penney's textbook!
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Transitioning from single-variable to multivariable calculus is often described as moving from a flat, two-dimensional world into the complex, three-dimensional reality we live in. For decades, the Multivariable Calculus textbook by C. Henry Edwards and David E. Penney You're looking for a guide to multivariable calculus