Vector Calculus by Joel Feldman
Vector Calculus - Table of Contents
- PART 1. VECTOR CALCULUS CORE CHAPTERS
- 1. Curves and Parametric Equations
- 2. Vector Fields, Divergence, and Curl
- 3. Surface Integrals and Flux Integrals
- 4. Integral Theorems: Green's, Stokes', and Divergence Theorems
- PART 2. MATHEMATICAL APPENDICES
- A. Trigonometry Review
- B. Powers and Logarithmic Functions
- C. Table of Derivatives
- D. Table of Integrals
- E. Table of Taylor Expansions
- F. 3D Coordinate Systems
- G. ISO Coordinate System Notation
- H. Conic Sections and Quadric Surfaces
- I. Review of Linear Ordinary Differential Equations
What You Will Learn in Vector Calculus
Vector Calculus by Joel Feldman (along with co-authors Andrew Rechnitzer and Elyse Yeager) is a high-quality open educational resource developed at the University of British Columbia, designed for second- and third-year undergraduate multivariable calculus courses. The text bridges foundational multivariable techniques with advanced physical and geometric applications, covering core topics such as Curves and Parametric Equations, Vector Fields, Divergence, and Curl, Surface Integrals and Flux Calculations, and Integral Theorems including Stokes' and Gauss's Theorems, alongside comprehensive mathematical reference appendices.
This book serves as an invaluable guide for undergraduate mathematics, physics, and engineering majors as well as self-study learners seeking a transparent treatment of multivariable field theory. Feldman emphasizes intuitive physical interpretations alongside clear mathematical derivations, supporting each concept with fully worked examples, clean diagrams, and progressive exercise sets.
Due to its pedagogical clarity and open access availability, it is widely recognized as an outstanding modern textbook for intermediate and advanced calculus. Rather than focusing solely on computational routines, it fosters conceptual depth and vector intuition essential for electromagnetism, fluid dynamics, and advanced applied mathematics.
Book Details & Specifications
Title:
Vector Calculus by Joel Feldman
Publisher:
University of British Columbia (UBC)
Year:
2022
Pages:
689
Type:
PDF
Language:
English
ISBN-10 #:
N/A
ISBN-13 #:
N/A
License:
CC BY-NC-SA 4.0
Amazon:
Amazon
About the Author: Joel Feldman
The author Joel Feldman
is Professor Emeritus of Mathematics at the University of British Columbia, widely recognized for his research in mathematical physics, constructive quantum field theory, and Fermi liquid theory, as well as his long-standing dedication to undergraduate education.
Through Vector Calculus, Feldman and his colleagues created a streamlined, student-centered text that illuminates complex geometric and physical ideas. His precise explanatory style and structured approach make this book a masterpiece resource for mastering vector fields and multivariable integral theorems.
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