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Functional Analysis (2285 words) |
 | Functional Equations with Causal Operators by C. Corduneanu is intended to provide basic theory of functional equations (including functional differential equations) with causal operators. |
| One of the aims while teaching such topics was to present a unified treatment of existence theory, as well as other aspects of the theory of functional differential equations, including ordinary differential equations, equations with delayed argument (both finite and infinite), integral equations of Volterra type and integrodifferential equations involving Volterra integral operators. |
| Beginning Functional Analysis by Karen Saxe (Undergraduate Texts in Mathematics: Springer) The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators relating these points as linear transformations on these spaces. |
| MATH-4210, MATHEMATICAL ANALYSIS II (1030 words) |
| This document contains the list of topics to be presented in this course, a list of textbooks, and some comments and recommendations about these textbooks. |
| Approximation of Continuous Functions: Uniform approximation by polynomials, Weierstrass theorem and separability of the space of continuous functions on a compact interval, approximation of derivatives, Stone-Weierstrass theorem. |
| Functions of Several Variables: Review of linear algebra, directional derivatives, partial derivatives and total differential, gradient, chain rule, equality of mixed partial derivatives, Taylor series in several dimensions, mean value theorem, extrema, inverse and implicit function theorems, multi-dimensional surfaces and their representations, conditional extrema and Lagrange multipliers. |
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