Titlebook: Solving Problems in Mathematical Analysis, Part II; Definite, Improper a Tomasz Rado?ycki Textbook 2020 Springer Nature Switzerland AG 2020

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書目名稱Solving Problems in Mathematical Analysis, Part II影響因子(影響力)




書目名稱Solving Problems in Mathematical Analysis, Part II影響因子(影響力)學(xué)科排名




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書目名稱Solving Problems in Mathematical Analysis, Part II網(wǎng)絡(luò)公開度學(xué)科排名




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書目名稱Solving Problems in Mathematical Analysis, Part II被引頻次學(xué)科排名




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Problem Books in Mathematicshttp://image.papertrans.cn/s/image/871811.jpg

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https://doi.org/10.1007/978-3-030-36848-7calculus; multivariable functions; Riemann’s integral; definite integrals; improper integrals; lengths of

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Springer Nature Switzerland AG 2020

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Exploring the Riemann and Definite Integral,In this chapter, we explain in detail the idea of the Riemann integrability of functions and its connection to the definite integral obtained by the “antidifferentiation.” We also learn how to apply these notions in practical calculations and how to avoid some hidden traps.

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Examining Improper Integrals,This chapter is concerned with the so-called improper integrals. They constitute the generalization of the definite integral when either the integration interval is infinite or the integrand function is not bounded. We will learn how to examine the convergence of such integrals and apply these results to certain infinite series.

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Applying One-Dimensional Integrals to Geometry and Physics,The present chapter is devoted to the applications of one-dimensional integrals to the calculation of some geometrical quantities like lengths of curves or areas of surfaces as well as physical ones. The formulas for the typical geometrical quantities are collected below. They are discussed in detail when solving the appropriate problems.

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Dealing with Functions of Several Variables,This chapter contains introductory notions referring to the functions of several variables. We learn how to find images and preimages of various sets and deal with the limits and continuity in more than one dimension.

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Investigating Derivatives of Multivariable Functions,In this chapter, we become acquainted with the differentiability and derivatives of functions in several dimensions. The dimensionality makes these notions much more complicated and difficult. Therefore, when solving the following problems, they will be dealt with in detail.