Vector Calculus by Michael Corral
About this book :-
"Vector Calculus" by Michael Corral is a clear, student-friendly introduction to "vector calculus" for undergraduates in mathematics, physics, and engineering. The book builds concepts gradually, starting with vectors in two and three dimensions, geometric intuition, and algebraic tools. Corral’s writing focuses on understanding ideas visually and logically, making the subject approachable for self-learners as well as classroom students. It emphasizes clarity over memorization throughout and supports confident mathematical thinking.
Much of the text explores "vector fields" and vector-valued functions, connecting algebra to motion, curves, and physical interpretation. Core operators such as the "gradient", "divergence", and curl are explained with meaning, not just formulas. Worked examples and exercises reinforce concepts, helping readers understand how differentiation and integration extend naturally into multiple dimensions. This balance strengthens intuition and computational skill for practical scientific problem solving.
The final chapters present the major theorems, including "Stokes’ Theorem", Green’s Theorem, and the Divergence Theorem, showing their unifying power. Corral emphasizes why these results work and how they simplify complex problems. Overall, the book offers a concise, intuitive pathway to mastering vector methods, making it a reliable reference for study, teaching, and applied science. Its structure supports deep understanding and long-term retention for serious learners.
Book Detail :-
Title:
Vector Calculus by Michael Corral
Publisher:
lulu.com, Mecmath.net
Year:
2008
Pages:
222
Type:
PDF
Language:
English
ISBN-10 #:
0486466205
ISBN-13 #:
978-0486466200
License:
GNU
Amazon:
Amazon
About Author :-
The author
Michael Corral
is a mathematician and educator known for writing clear, student-friendly textbooks in higher mathematics. He has taught as an adjunct in the "Department of Mathematics" at Schoolcraft College and holds degrees from UC Berkeley and the University of Michigan, combining strong theoretical and applied foundations. His book "Vector Calculus" is a widely used "open-access textbook" for multivariable calculus courses. It emphasizes clarity, structure, and practical understanding, making advanced topics approachable for science and engineering students.
Book Contents :-
1. Vectors in Euclidean Space
2. Functions of Several Variables
3. Multiple Integrals
4. Line and Surface Integrals
A. Answers and Hints to Selected Exercises
B. Proof of the Right-Hand Rule for the Cross Product
C. 3D Graphing with Gnuplot
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