Electronic educational and methodological manual on the sections «Linear algebra and analytical geometry, differential calculus of functions of one and several variables» of the discipline «Mathematics».

2021 ◽  
Author(s):  
Z.M. Usmanova ◽  
S.P. Balandin ◽  
R.G. Zaynullin
Keyword(s):  
Linear Algebra ◽  
Differential Calculus ◽  
Analytical Geometry ◽  
Several Variables

Way to improve efficiency of teaching linear algebra to students with health disabilities by means of enlarged didactic units

2021 ◽  
pp. 65-71
Author(s):  
A.N. Semakin ◽  
◽  
G.P. Emgusheva
Keyword(s):  
Students With Disabilities ◽  
Linear Algebra ◽  
Teaching Methods ◽  
Educational Material ◽  
Educational Process ◽  
Teaching Mathematics ◽  
Abstract Concepts ◽  
State Technical ◽  
Analytical Geometry ◽  
Time Gap

Presented is enlarged didactic units developed by P.M. Erdniev for teaching mathematics, that improves the ability of students to understand educational material. This effect is achieved as a result of organizing the educational process according to the principles of complementarity of teaching methods and the spatial and temporal combination of interrelated elements of knowledge. Among the basic mathematical disciplines taught at Bauman Moscow State Technical University for students with disabilities the most difficult discipline is Linear Algebra, which is due to its content and various problems with students’ health. Linear Algebra is largely based on the theory from Analytical Geometry that is quite well perceived by students with disabilities. A comparative analysis of these disciplines shows that the enlarged didactic units linking these disciplines together can significantly simplify the study of Linear Algebra. However, due to difficulties with scheduling the time gap between these disciplines can be up to two semesters, which makes it impossible to directly use the enlarged didactic units. To solve this problem, we introduce the supporting discipline "Cognitive technologies for supporting the discipline Linear Algebra" which runs in parallel with Linear Algebra and which is based on the material of Analytical Geometry. Forming its content in close connection with Linear Algebra in accordance with the main principles of the enlarged didactic units, we smoothly lead students to the understanding of abstract concepts of Linear Algebra, reducing the complexity of learning.

Optimization of Utility Functions in an Admissible Space of Higher Dimension

2016 ◽  
pp. 102-113
Author(s):  
German Almanza ◽  
Victor M. Carrillo ◽  
Cely C. Ronquillo
Keyword(s):  
Graduate Students ◽  
Linear Algebra ◽  
Algebraic Topology ◽  
Morse Theory ◽  
Utility Functions ◽  
Higher Dimension ◽  
Differential Topology ◽  
Several Variables

S. Smale published a paper where announce a theorem which optimize a several utility functions at once (cf. Smale, 1975) using Morse Theory, this is a very abstract subject that require high skills in Differential Topology and Algebraic Topology. Our goal in this paper is announce the same theorems in terms of Calculus of Manifolds and Linear Algebra, those subjects are more reachable to engineers and economists whom are concern with maximizing functions in several variables. Moreover, the elements involved in our theorems are accessible to graduate students, also we putting forward the results we consider economically relevant.

scholarly journals As concepções de acadêmicos de Engenharia, no início do curso, sobre a Matemática e a aprendizagem Matemática

2020 ◽  
Vol 21 (3) ◽  
pp. 314-323
Author(s):  
Eliéverson Guerchi Gonzales ◽  
Kátia Guerchi Gonzales ◽  
José Matheus Pinheiro da Fonseca da Silva
Keyword(s):  
Linear Algebra ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Education Institution ◽  
Mathematical Concept ◽  
Private Higher Education ◽  
Analytical Geometry ◽  
Mato Grosso ◽  
Learning Mathematics ◽  
Mato Grosso Do Sul

ResumoA pesquisa teve como objetivos investigar e analisar as concepções de Matemática, da aprendizagem de Matemática e do pensamento matemático dos acadêmicos dos primeiros semestres dos cursos de Engenharia Elétrica, Engenharia da Computação e Engenharia Ambiental de uma instituição privada de Ensino Superior, localizada na cidade de Campo Grande, Mato Grosso do Sul, Brasil. Trata-se de uma pesquisa qualitativa realizada com os ingressantes do ano de 2018. Nesta pesquisa foram utilizados questionários, juntamente com entrevistas sob a luz da História Oral. Para análise, foram necessários dois movimentos: um no trabalho das narrativas produzidas pelas entrevistas e outro em relação aos questionários. As análises, a partir dos questionários, permitiram identificar, de modo geral, manifestações de concepção Matemáticas coesas predominante, como também, do pensamento Matemático especulativo. Quanto à concepção em relação à aprendizagem de Matemática, as manifestações foram equivalentes. Sobre as concepções dos estudantes na disciplina de Geometria Analítica e Álgebra Linear (GAAL), a concepção de aprendizagem de Matemática foi a instrumental, a concepção de Matemática se revelou coesa e o pensamento matemático permeou entre o investigativo e o exato. Nas entrevistas, tanto as concepções que se referem à Matemática, de maneira geral, quanto às concepções da disciplina de GAAL, foram as mesmas. Identificam-se as concepções de aprendizagem de Matemática relacional, a concepção de Matemática coesa e o pensamento Matemático especulativo. Palavras-chave: Concepções de Matemática. Geometria Analítica e Álgebra Linear Aprendizagem. AbstractThis paper investigates and analyzes mathematics conceptions, mathematics learning and mathematical thinking of the first semester students from Electrical Engineering, Computer Engineering and Environmental Engineering courses of a private Higher Education institution, located in the city of Campo Grande, Mato Grosso do Sul, Brazil. This is a qualitative research conducted with the freshmen of the year 2018. In this research, questionnaires were used, together with interviews in the light of Oral History. For the analysis, two approaches were necessary: first looking into the narratives produced by the interviews and a second one with associated questionnaires. The questionnaire analyzes allowed us to identify, in general, manifestations of predominant cohesive mathematical conceptions, as well as, of speculative mathematical thinking. As for the comprehension associated with learning mathematics, the manifestations were equivalent. Regarding the students' mathematical concept of Analytical Geometry and Linear Algebra (AGLA), the concept of learning mathematics was the instrumental one, and so the mathematics concept proved to be cohesive with investigative and exact mathematical thinking. In the interviews, both the concepts that refer to mathematics and the AGLA discipline were the same. Concepts of relational mathematics learning, the concept of cohesive mathematics and speculative mathematical thinking were identified. Keywords:. Mathematics Conceptions. Analytical Geometry and Linear Algebra Learning.

scholarly journals INFORMATION PROVISION OF DISTANCE LEARNING SYSTEM

1970 ◽  
Vol 3 (2) ◽  
Author(s):  
Viacheslav M. Oleksenko
Keyword(s):  
Distance Learning ◽  
Linear Algebra ◽  
Information Provision ◽  
Relevant Information ◽  
Theory And Practice ◽  
Learning System ◽  
Analytical Geometry ◽  
Distance Learning System ◽  
And Training

The article deals with the results of the research concerning the relevant information resources elaborated and introduced into the pedagogical process by the author. The peculiarities of the first in Ukraine dictionary on theory and practice of distance learning, distance course “Linear Algebra” and the course-book “Linear Algebra and Analytical Geometry”, which promote the raising in quality of education and training of specialists, are revealed.

scholarly journals Functions of several variables analysis applied in inventory management

2013 ◽  
Vol 61 (7) ◽  
pp. 2221-2227 ◽  
Author(s):  
Martina Janková ◽  
Veronika Novotná ◽  
Tereza Varyšová
Keyword(s):  
Inventory Management ◽  
Differential Calculus ◽  
Maximum Term ◽  
Optimal Price ◽  
Several Variables ◽  
Analysis And Synthesis ◽  
Delay In Payments ◽  
Definite Period ◽  
Theoretical Results ◽  
Dependent Demand

In many cases a retailer is not capable of settling an invoice immediately upon receiving it and is given an option by the supplier to settle the invoice within a definite period. The retailer can sell the goods before the deadline, accumulate revenue and earn interest. If the retailer is not able to meet his obligations within the deadline, he is charged an interest. This paper introduces a newly constructed model which enables a retailer to set an optimal price of goods under permissible delay in payments, and to determine the maximum term of payment. The model is based on the assumption of time-dependent demand and has been developed for non-deteriorating goods. The paper further analyzes a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Theoretical results are demonstrated by an illustrative example. The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations).The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, etc.

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