COURSE GOALS: To acquire knowledge and understanding of the following topics: definite and indefinite integral for real functions of one real variable, basics on real functions of several real variables, basic types of ordinary differential equations (ODEs).
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.4. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments
2.5. use mathematical methods to solve standard physics problems
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely
5. LEARNING SKILLS
5.1 search for and use professional literature as well as any other sources of relevant information
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon passing the course Mathematics 2 the student will be able to:
1. define and explain some of the basic notions of mathematical analysis (integrals and their properties);
2. apply various techniques of integration to solve some well-known types of integrals;
3. apply integral calculus while computing the area bounded by a plane curve or the volume of a space body;
4. define and explain the notions of continuity and limit for functions of several real variables;
5. draw the graph of a function of two real variables;
6. define and explain the notions of partial derivatives and gradient, and apply them for finding the tangent planes to the given surface in the three-dimensional space;
7. define and explain the basic notions related to ODEs, and present some well-known examples;
8. solve some standard types of ODEs (Bernoulli ODE, Clairaut's ODE, Lagrange's ODE);
9. find the particular and general solution of an ODE of the second-order with constant coefficients.
COURSE DESCRIPTION:
1. the notion of Riemann integration and basic properties of definite integral (1 week)
2. the indefinite integral and fundamental theorem of differential calculus (1 week)
3. techniques of integration: substitution and integration by parts (1 week)
4. some special types of integrals: integrals of rational functions and integrals of trigonometric functions (1 week)
5. computing the volume of a body and the length of a curve in the plane (1 week)
6. functions of several real variables: examples of functions of two variables and their graphs; level surfaces (1 week)
7. continuity and limit for functions of two or more real variables; partial derivatives and gradient; tangent plane on a surface in the three-dimensional space (2 weeks)
8. ODEs; basic notions and examples (1 week)
9. solving methods for ODEs: equations with separated variables, homogenous differential equations, first-order linear differential equations (2 weeks)
10. some special ODEs: Bernoulli ODE, Clairaut's ODE and Lagrange's ODE (1 week)
11. ODEs of the second-order with constant coefficients (2 weeks)
REQUIREMENTS FOR STUDENTS:
To attend the lectures (at least 70% of them), regularly work out the homework routine problems and solve minimum 40% of the two written exams.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Grading and assessment of the work of students during the semester:
* two written exams,
* worked out homework problems.
Grading at the end of semester:
* final oral exam.
Contributions to the final grade:
* 10% of the grade is for attending lectures and working out homework problems,
* 60% of the grade is by the results of the two written exams,
* 30% of the grade is by the oral exam.
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- S. Kurepa, Matematička analiza 1: Diferenciranje i integriranje, Tehnička knjiga, Zagreb, 1984
- S. Kurepa, Matematička analiza 2: Funkcije jedne varijable, Tehnička knjiga, Zagreb, 1984
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