Titlebook: Mathematical Analysis II; Vladimir A. Zorich Textbook 2016Latest edition Springer-Verlag Berlin Heidelberg 2016 calculus.differential equa

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*Continuous Mappings (General Theory),In this chapter we generalize substantially the properties of continuous maps, established earlier for real-valued functions and for maps of the type .. We present these properties from a unified point of view. In particular, we introduce a number of simple, yet important concepts common for various domains of mathematics.

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Multiple Integrals,Integral calculus, which is already partly known to the reader for functions of one real variable, is developed here for functions of several variables.

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Line and Surface Integrals,We develop the integral calculus. In this chapter we introduce curvilinear and surface integrals and obtain some fundamental and widely used integral formulas generalizing the classical Newton–Leibniz formula.

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Fourier Series and the Fourier Transform,This chapter is entirely devoted to Fourier series and Fourier transforms, given their place and role in analysis, in mathematics, and in applications, especially in physics and engineering.

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*Differential Calculus from a More General Point of View,l tool far beyond real-valued functions, discussed in the first part of the textbook. Formally speaking, this chapter is independent of the material presented earlier, but without the background acquired by reading the first volume, the reader, most likely, would not recognize the rich content of th

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Surfaces and Differential Forms in ,,ve a formula for calculating the area of a surface, and we give an initial idea of the concept of a differential form. All these concepts are essential when working with curvilinear and surface integrals, which will be the main subject of the next chapter.