Chapter 4 Jacobians, Functional Dependence and Implicit Functions
4.1 Introduction
A Jacobian, called after the German mathematician Carl Guston Jacob Jacobi (1804 - 1851), is a determinant formed by the first order partial derivatives. Jacobians play very important role in change of variables. Jacobian change of variable is a technique that can be used to solve integration problems, which would otherwise be difficult using normal techniques. In geometry, the area, volume etc. in one coordinate system is transformed to another coordinate system through Jacobians. Therefore, acquaintance with the notion of Jacobian is necessary for further development of the subject. The goal of Jacobian change of variables is to convert form a physical space ...
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