|Course title||Mathematics 3 – Function of several variables|
|Status||Lectures(30), Exercises (30)|
|ECTS||5 ECTS credits|
|Lecturer||Ninoslav Truhar, Full Professor; Ivana Kuzmanović, Senior Assistant|
|Course objective||The objective of the course is to provide insight into the fundamental parts of mathematics related to functions of several variables: the area of definition, continuity and limes, derivatives and integrals of functions of several variables. Students should be encouraged to think critically and to research.|
|Prerequisites||Mathematics 1, Mathematics 2|
|Learning outcomes:||After successfully completed course, students will be able to:
|Teaching activity||ECTS||Learning outcome||Students activity||Methods of evaluation||Points|
|Class attendance||1||20||Class attendance||Evidence list||10||20|
|Knowledge test (preliminary exam)||2||40||Preparation for written examination||Written preliminary exam||40||100|
|Final exam||2||40||Repetition of teaching materials||Oral exam (and written exam)||40||100|
|Consultations||Consultations are held once a week.|
|Gained competencies||In this course students are introduced to the differential and integral calculus of functions of several variables and vector functions. Primarily the focus is on situations in which the geometric view is possible, i.e. real functions of two or three variables, and functions from R to R2 and R3. During lectures, basic concept is introduced, analyzed, and illustrated by examples. During the exercises students train appropriate techniques to approach to specific problems and for solving them.|
|Content (Course curriculum)||Real functions of several variables. Space Rn. Level-curves and level surfaces. Limits and continuity.
Partial derivatives and differentiability of functions of several variables. Partial derivatives of implicit functions and composite functions. Partial derivatives and differentials of higher orders.
Vector functions. Vector functions of one variable – the derivation and integration. Differentiability of vector functions of several variables; Jacobi matrix.
Applications of differential calculus of functions of several variables. Equation of tangent plane to the surface. Taylor’s formula. Extremes and conditional extremes.
Multiple integrals. Double integral – definition, properties, calculation, substitution variables (polar coordinates), applications. Triple integrals (cylindrical and spherical coordinates).
Line integrals (first and second). Concept, properties, calculation, applications.
Surface integrals (first and second). Concept, properties, calculation, applications.
Scalar and vector fields. Directional derivative of a scalar field. Gradient of a scalar field. The divergence of a vector field. Rotation of a vector field. Theorem of Gauss-Ostrogradsky. Stokes’ theorem.
|Instructional methods||Lectures and exercises are mandatory.|
|Exam formats||The exam consists of a written and oral part and it is taken after completion of lectures and exercises. During the semester, students can take two or more colloquiums that replace the written examination.|
|Quality control and successfulness follow up||An anonymous questionnaire|