Multivariable Calculus by Don Shimamoto

Book Contents :-
Part-I Preliminaries 1. Rn Part-II Vector-valued functions of one variable 2. Paths and curves Part-III Real-valued functions 3. Real-valued functions: preliminaries 4. Real-valued functions: differentiation 5. Real-valued functions: integration Part-IV Vector-valued functions 6. Differentiability and the chain rule 7. Change of variables Part-V Integrals of vector fields 8. Vector fields 9. Line integrals 10. Surface integrals 11. Working with differential forms

About this book :-
"Multivariable Calculus" by "Don Shimamoto" is a comprehensive textbook designed for students learning "multivariable calculus" in a college-level course. It introduces core concepts such as "partial derivatives", multiple integrals, vector fields, and vector-valued functions, helping learners extend single-variable calculus to higher dimensions. The book emphasizes understanding over rote memorization, making complex topics approachable and applicable. The text is organized to build knowledge progressively, starting with vector-valued functions of a single variable, moving to real-valued functions of multiple variables, and finally addressing vector-valued functions of several variables. It also covers key theorems such as "Green’s theorem", "Stokes’ theorem", and the "divergence theorem", showing the relationship between integrals over regions and their boundaries. Real examples and structured exercises help students apply concepts and develop problem-solving skills, making the abstract theory more tangible. Published under a "Creative Commons license", this open-access textbook is freely available online, supporting both self-study and formal coursework. Its clear explanations, practical exercises, and applied focus make it ideal for students who want to gain a solid foundation in "vector calculus" and multivariable analysis. Overall, the book balances conceptual understanding with computational practice, preparing learners to tackle advanced problems in mathematics, physics, and engineering.

Book Detail :-
Title: Multivariable Calculus by Don Shimamoto
Publisher: Don Shimamoto
Year: 2019
Pages: 326
Type: PDF
Language: English
ISBN-10 #: 1708246991
ISBN-13 #: 978-1708246990
License: CC BY 4.0
Amazon: Amazon

About Author :-
The author Don Shimamoto is a lecturer at "Swarthmore College" and the author of "Multivariable Calculus". His textbook teaches "multivariable calculus" concepts such as partial derivatives, multiple integrals, vector fields, and Green, Stokes, and Gauss theorems, designed for clarity and student understanding. Shimamoto emphasizes active problem-solving and conceptual engagement to strengthen "mathematical reasoning". Supporting "open educational resources", his book is freely available, making advanced calculus accessible to learners.

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