The mathematical analysis. Volume 2

Mapping Intimacies ◽

10.12737/1072172 ◽

2020 ◽

Author(s):

Galina Zhukova ◽

Margarita Rushaylo

Keyword(s):

Field Theory ◽

Quality Control ◽

Fourier Series ◽

Mathematical Analysis ◽

Differential Calculus ◽

Analytic Geometry ◽

Postgraduate Students ◽

Several Variables ◽

Basic Concepts ◽

Control Knowledge

The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. In volume 2 we study analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Taylor series and Maclaurin, and Fourier series; applications to the analysis and solution of applied problems. Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For self-training and quality control knowledge given test questions. For teachers, students and postgraduate students studying mathematical analysis.

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Mathematical analysis in examples and tasks. Part 2

10.12737/1072162 ◽

2020 ◽

Author(s):

Galina Zhukova ◽

Margarita Rushaylo

Keyword(s):

Field Theory ◽

Graduate Students ◽

Mathematical Analysis ◽

Differential Calculus ◽

Advanced Mathematics ◽

Analytic Geometry ◽

Several Variables ◽

Background Material ◽

Basic Concepts ◽

Independent Work

The purpose of the textbook is to help students to master basic concepts and research methods used in mathematical analysis. In part 2 of the proposed cycle of workshops on the following topics: analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Fourier series; applications to the analysis and solution of applied problems. These topics are studied in universities, usually in the second semester in the discipline "Mathematical analysis" or the course "Higher mathematics", "Mathematics". For the development of each topic the necessary theoretical and background material, reviewed a large number of examples with detailed analysis and solutions, the options for independent work. For self-training and quality control of the acquired knowledge in each section designed exercises and tasks with answers and guidance. It is recommended that teachers, students and graduate students studying advanced mathematics.

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The mathematical analysis. Volume 1

10.12737/1072169 ◽

2020 ◽

Author(s):

Galina Zhukova ◽

Margarita Rushaylo

Keyword(s):

Mathematical Analysis ◽

Differential Calculus ◽

Real Variable ◽

Hyperbolic Functions ◽

Integral Calculus ◽

Postgraduate Students ◽

First Semester ◽

Improper Integrals ◽

Basic Concepts ◽

Sets Theory

The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. Volume 1 explores the following topics: theory of sets, theory of limits; differential calculus of functions of one variable; investigation of the properties of functions and graphing; integral calculus of functions of one real variable (indefinite, definite and improper integrals), the technique of integration; hyperbolic functions; applications to the analysis and solution of practical problems. These topics are studied in universities, as a rule, in the first semester in the framework of self-discipline "Mathematical analysis" or the course "Higher mathematics", "Mathematics". Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For teachers, students and postgraduate students studying mathematical analysis.

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Mathematical Hull Design for Sailing Yachts

10.5957/csys-1981-007 ◽

1981 ◽

Author(s):

John S. Letcher

Keyword(s):

Historical Perspective ◽

Analytic Form ◽

Surface Shape ◽

Analytic Geometry ◽

Representation System ◽

Construction Methods ◽

Small Craft ◽

Hull Design ◽

Basic Concepts ◽

Mathematical Design

Mathematical representations of hull surface shape have largely supplanted graphical fairing and lofting of lines in the shipbuilding and aircraft industries, but have had little application so far to small craft. Past methods of hull design are surveyed to put mathematical design into historical perspective and point up its many advantages. The basic concepts of analytic geometry of surfaces needed for yacht hull design are briefly introduced with references. Several special aspects of the geometry of yacht hulls, arising from considerations of aesthetics, hydrodynamics, and construction methods are discussed and cast into analytic form for inclusion in a hull design scheme. The paper explains in detail a particular representation system called FAIRLINE/1, simple enough to fit into the program and memory limitations of a TI-59 calculator, yet extremely versatile. A program listing and several example hull designs created with this program are presented.

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