• Semester 2, position 1

The aim of the course Mathematics 2 is to introduce students to basics of the following topics: Indefinite and definite integrals and their applications, differential calculus of real-valued multi-variable functions (wich depend on several independent real variables), first-order differential equations.

Upon successful completion of this course, students should be able to: 1) Solve indefinite, definite, and improper integrals of real valued functions of a real variable. 2) By applying learned techniques of integral calculus: to calculate areas in the plane, to calculate arc length, to calculate area and volume by rotating an area. 3) Calculate partial derivates - differentiation of the real-valued and vector –valued functions that takes more independent real variables . 4) By applying learned techniques of differentiation calculus: to find extremas of real valued functions with more independent real variables to investigates areas defined as hodograph of vector valued functions by application of fractional differentiation 5) Solve differential equations of first order: separable differential equations, homogeneous, linear, Bernoulli differential equations, and differential equation with total differential. 6) By application of learned technique for solving differential equations of first order: to determine equations of orthogonal and isogonal trajectories to family of one parameter straight lines

transcendental functions, definite integral, definition, existence, basic properties, basic theorem of integral calculus, methods of integration of definite integral, improper integrals, quadrature of plane figure, cubature of solid of revolution, rectification of curve, surface of solid of revolution, differential calculus of real-valued multi-variable functions (which depend on several independent real variables), Taylor's theorem, local extreme values of a function with two independent variables, surface as hodograph of a vector-function depends on two independent variables, tangent plane and normal to surface, first-order differential equations, the method of separation of variables, first-order homogenous differential equations, first-order linear and Bernoulli differential equations, exact differential equations, integration factor, orthogonal and isogonal trajectories.

transcendental functions, definite integral, definition, existence, basic properties, basic theorem of integral calculus, methods of integration of definite integral, improper integrals, quadrature of plane figure, cubature of solid of revolution, rectification of curve, surface of solid of revolution, differential calculus of real-valued multi-variable functions (which depend on several independent real variables), Taylor's theorem, local extreme values of a function with two independent variables, surface as hodograph of a vector-function depends on two independent variables, tangent plane and normal to surface, first-order differential equations, the method of separation of variables, first-order homogenous differential equations, first-order linear and Bernoulli differential equations, exact differential equations, integration factor, orthogonal and isogonal trajectories.

The course attendance condition is determined by the curriculum of study program.

Written handouts from lectures in Mathematics 2: Lesson 1, Lesson 2, Lesson 3, Lesson 4, Lesson 5, Lesson 6, Lesson 7, Lesson 8, Lesson 9. All the necessary literature is on: http://147.91.27.133 or ftp://147.91.27.133

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 30
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 10
Test: 0
Final exam: 5

Activity during lectures: 10
Test/test: 60
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 35

Д. Тошић, М. Албијанић, Д. Миленковић, Елементи диференцијалног и интегралног рачуна, Службени гласник, Београд 2012; С. Нешић: Збирка задатака из математике 1, Машински факултет, Београд, 1995; З. Мамузић, Б. Ђерасимовић, В. Симоновић: Основи математичке анализе са елементима диференцијалне геометрије и рачунарства, Научна књига, Београд, 1991; С. Нешић, Р. Радовановић: Збирка задатака из математике 2, Машински факултет, Београд, 1990.;; Миодраг М. Спалевић, Иван Д. Аранђеловић, Драган Ј. Додер, Александар В. Пејчев, Душан Љ. Ђукић. Јелена Д. Томановић: Диференцијалне једначине, Машински факултет Београд 2017