- #1
ice109
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something for a mathematician that likes physics or a physicist that likes math. rigorous but with pictures and examples and the such?
robphy said:Marsden
https://www.amazon.com/dp/0716724324/?tag=pfamazon01-20
Bamberg & Sternberg (but probably more than you want)
https://www.amazon.com/dp/0521406498/?tag=pfamazon01-20
I would take terrible reviews on Amazon.com with a grain of salt. Many of those reviews are by lazy, underprepared, or unprepared students who are looking to vent their frustrations with a book that they were not willing, ready or able to tackle. If none of those suggestions appeal to you, some standard textbooks for a second course in vector calculus / calculus on manifolds include Spivak, Calculus on Manifolds; Munkres, Analysis on Manifolds; C. H. Edwards, Advanced Calculus of Several Variables; and H. M. Edwards, Advanced Calculus: A Differential Forms Approach. Of those, the last book by H. M. Edwards is probably the closest to what you're looking for. But I would warn you that, since you cannot identify that vector analysis is the same as vector calculus or that it would likely be covered fairly extensively in a math methods book, you may not be adequately prepared to tackle any of these books.ice109 said:the first one is a calc book apparently and has terrible reviews and the second one is a math methods book with terrible reviews but thanks anyway
Vector analysis is a branch of mathematics and physics that deals with the properties and behavior of vectors, which are quantities that have both magnitude and direction. It involves the manipulation and analysis of vectors using mathematical tools such as calculus and linear algebra.
Vector analysis is essential in understanding and solving problems in physics, engineering, and other fields that involve the use of vectors. It provides a rigorous and visual approach to analyzing vector quantities, making it easier to comprehend and apply in real-world situations.
Vector analysis has numerous applications in various fields, including mechanics, electromagnetics, fluid dynamics, and computer graphics. It is used to describe and analyze the motion of objects, the forces acting on them, and the behavior of waves and fields.
Scalar analysis deals with quantities that have only magnitude, while vector analysis deals with quantities that have both magnitude and direction. This fundamental difference leads to different mathematical techniques and visual representations for solving problems in each type of analysis.
There are many textbooks, online courses, and video tutorials available for learning vector analysis. Some popular resources include "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba, "The Feynman Lectures on Physics" by Richard P. Feynman, and the Khan Academy's vector calculus course.