Learning basic mathematical analysis, including differentiation and integration.

Upon completing the course, the student is expected: - to understand concepts of a sequence and function, convergence and differentiability, to be able to evaluate limit values and the derivative of an arbitrary function and, using differential calculus, to investigate its behavior, sketch its graph and find its asymptotic expansion, and to determine tangent and perpendicular lines on a curve; - to understand the concept of a multivariable function, to be acquainted with equations of some space surfaces, to master partial derivatives, and to be able to determine Taylor polynomials and find local extremums (especially in the two-variable case); - to know concepts of indefinite, definite and improper integrals and successfully use basic rules in computing integrals, and to be able to apply them in evaluating a planar area and the arc length of curve; - to be able to recognize and solve some basic types of ordinary differential equations of the first order.

Limits and continuity (convergence of sequences and functions, methods of computing a limit, asymptotics); Derivatives (tangent and normal lines, rules for differentiation, higher order derivatives); Applications of derivatives (computing limits, local and global extrema, convexity, investigating functions, Taylor polynomials); Indefinite integrals (antiderivative, integration of elementary functions, integration of rational, trigonometric, exponential and irrational functions); Definite integrals and their applications (areas, length of a curve); Partial derivatives (multivariable functions, Taylor polynomials, local extrema); First-order differential equations (separating variables, homogeneous, linear and Bernouli DE).

Limits and continuity, derivatives, applications of derivatives, indefinite integrals, definite integrals with applications, partial derivatives, first-order differential equations.

Defined by the curriculum.

Total assigned hours: 90

New material: 22
Elaboration and examples (recapitulation): 18

Auditory exercises: 30
Laboratory exercises: 0
Calculation tasks: 10
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 5
Research study work: 0

Review and grading of calculation tasks: 1
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 3
Test: 0
Final exam: 1

Activity during lectures: 0
Test/test: 70
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 40

D. Đukic, I. Aranđelović, D. Jandrlić, A. Pejčev, R. Mutavdžić, J. Tomanović, M. Vucić, Mathematics 1, Faculty of Mechanical Engineering, Belgrade, 2020.; I. Aranđelović, D. Jandrlić, A. Pejčev, D. Đukic, R. Mutavdžić, J. Tomanović, Mathematics 2, Faculty of Mechanical Engineering, Belgrade, 2019.