This text on multivariable calculus aids comprehension by providing relatable explanations to the reader. It extends concepts from single variable calculus such as derivative, integral, and significant theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. This book was written with students in mathematics, the physical sciences, and engineering in mind. Students with prior experience with calculus with a single variable are led step-by-step through a wide range of problem-solving strategies and practice problems.

To illustrate the fundamental connection that exists between calculus and contemporary science, certain examples from the physical sciences are used. By deriving and explaining several conservation laws, it is possible to demonstrate the symbiotic link between science and mathematics. Additionally, the vector calculus is applied to express a variety of physical theories using partial differential equations. Students will understand that mathematics is the language that enables scientific ideas to be formulated and that science is a source for the growth of mathematics. This knowledge will be imparted to students through the course of their education.