Mathematical Analysis, part 1

Major: System Analysis
Code of subject: 6.124.00.O.007
Credits: 7.00
Department: Mathematics
Lecturer: Ihor Bobyk
Semester: 1 семестр
Mode of study: денна
Learning outcomes: As a result of the study of the discipline, the student must be able to demonstrate the following learning outcomes: 1. Calculate the limits of a function and investigate the continuity of function. 2. Find derivative functions of one variable. 3. Find indefinite integrals. Calculate and use definite integrals. 4. To find partial derivatives of functions of many variables and to investigate the functions of many variables on the extremum.
Required prior and related subjects: - General Mathematics. School level; - Calculus; - Physics; - Linear algebra and analytic geometry.
Summary of the subject: The academic discipline "Mathematical analysis, part 1" consists of two sections "Differential and integral calculus of a single variable" and "Numerical and functional series". The first section deals with the following topics: (a) Functions of one variable, (b) Limits. Investigations on the continuity of the function, (c) Computation of derivatives and full investigation of functions, (d) Finding uncertain integrals, (e) Calculating definite integrals and their applications. The second section consists of the topics: (a) Sufficient tests of convergence of numerical series, (b) Fields of convergence of power series, (c) Trigonometric of series Fouriers.
Assessment methods and criteria: Student knowledge testing is carried out by means of oral questioning in practical classes, control and independent work in the virtual of learning environment, the terminologicals of dictations, individual calculation and graphic works. Current control - 30 points; Examination Control - 70 points; Total for discipline - 100 points.
Recommended books: 1. Математичний аналіз: Навчальний посібник. – Ч.1. – / під ред. Ю.К.Рудавського. – Львів: Видавництво Національного університету “ЛП”, 2003. – 404 с. 2. Математичний аналіз: Навчальний посібник. / Ю.К.Рудавський, Г.В.Понеділок, І.О.Бобик, О.З.Ватаманюк, Х.Т.Дрогомирецька, О.М.Рибицька, О.З.Слюсарчук.– Львів: Видавництво Національного університету “ЛП”, 2002.– 308 с. 3. Збірник задач з математичного аналізу. Ч.1.– / під ред. Ю.К.Рудавського.– Львів: Видавництво Національного університету “ЛП”, 2001.– 326 с. 4. Коломієць В.О. та ін. Збірник задач з математичного аналізу. Част. 1, Львів, НУ “ЛП”, 2001.