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QuarkCharmer
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I'm really interested in this subject. Would one be capable of learning this subject with a great working knowledge of Multi-var/Vector Calculus, ODE, Linear Algebra, and complex variables? What are some good books?
bda23 said:Your background seems enough. A book that looks quite good to me, and which is also relatively cheap, is "Calculus of Variations" by Gelfand and Fomin. I am yet to work through it, but it looks good at first glance.
TOC - Chapter 2 gives some requisite backgroundmicromass said:Note that this is a pure mathematics text. If you're more interested in the applications, then there are better texts out there.
The book "Calculus of variations with applications to physics and engineering" from Weinstock looks great!
bda23 said:Your background seems enough. A book that looks quite good to me, and which is also relatively cheap, is "Calculus of Variations" by Gelfand and Fomin. I am yet to work through it, but it looks good at first glance.
The calculus of variations is a branch of mathematics that deals with finding the optimal solution to a functional, which is a mathematical expression that takes in a function as its input and outputs a real number. It is used to solve problems in physics, engineering, and economics, among others.
Some common prerequisites for studying the calculus of variations include a strong understanding of single and multivariable calculus, linear algebra, and differential equations. Familiarity with functional analysis and optimization techniques is also helpful.
The calculus of variations has many applications in various fields, such as physics, where it is used to find the path of least action in mechanics. It is also used in economics to determine the optimal production and consumption strategies, and in engineering to find the optimal design for structures and machines.
The main difference between the calculus of variations and traditional calculus is that the former deals with optimizing functionals, while the latter deals with optimizing functions. In other words, the calculus of variations finds the best function that minimizes or maximizes a given functional, rather than finding the minimum or maximum value of a function at a specific point.
The calculus of variations is closely related to optimization, as it is used to find the optimal solution to a given functional. Many optimization problems can be formulated as problems in the calculus of variations, making it a powerful tool in solving real-world problems in various fields.