Titlebook: Calculus of Several Variables; Serge Lang Textbook 1987Latest edition Springer Science+Business Media New York 1987 Fourier series.calculu

宪法没有

雪上轻舟飞过

Introduction to MLP neural networks,When studying functions of one variable, we discussed the existence of an integral of a continuous function over an interval. The investigation of the integral involved lower sums and upper sums.

健谈

Neural networks in complex algebra,In this chapter we carry out the analogue in 3-dimensional space of the integration theory developed in Chapter IX for 2-dimensional space.

起波澜

NN Models for General Nonlinear ProgrammingLet us first recall taht a curve can be described by an equation, like {IE318-1} or it can be given parametrically, as when we set {IE318-2}{IE318-3} with {IE318-4}. A similar situation will occur for surfaces, and we consider first the parametric representation.

者变

https://doi.org/10.1007/978-1-4757-3167-5We consider a new kind of object, matrices.

影响带来

VectorsThe concept of a vector is basic for the study of functions of several variables. It provides geometric motivation for everything that follows. Hence the properties of vectors, both algebraic and geometric, will be discussed in full.

本能

The Chain Rule and the GradientIn this chapter, we prove the chain rule for functions of several variables and give a number of applications. Among them will be several interpretations for the gradient. These form one of the central points of our theory. They show how powerful the tools we have accumulated turn out to be.

空气传播

Higher DerivativesIn the theory of functions of one variable, we derived an expression for the values of a function . near a point . by means of the derivatives of .at.,namely .where . is a remainder term given by .for some number . between . and .. We review the proof of Taylor’s formula in an appendix to this chapter.

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COWER

Double IntegralsWhen studying functions of one variable, we discussed the existence of an integral of a continuous function over an interval. The investigation of the integral involved lower sums and upper sums.