COURSE GOALS: Acquire basic mathematical knowledge of single variable calculus and understand the theoretical background.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.3. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
1.7. describe the framework of natural sciences
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 1, the student will be able to:
1. define basic notions of single variable calculus;
2. define elementary functions and their basic properties;
3. derive elementary functions;
4. apply derivatives to determining graphs of functions;
5. apply Taylor series to approximation of functions.
* basic set theory, real and complex numbers;
* analytic geometry in a plane;
* real-valued functions of a real variable;
* convergence of sequences of real numbers;
* convergence of series of real numbers, convergence tests;
* continuous functions and limits of functions;
* derivatives of functions and applications to monotonicity of functions;
* Taylor series.
REQUIREMENTS FOR STUDENTS:
Class attendance, completing homework and classwork assignments.
GRADING AND ASSESSING THE WORK OF STUDENTS:
Two written exams during the semester, or written and oral exam at the end of the semester.
- S. Kurepa, Matematička analiza 1: Diferenciranje i integriranje, Tehnička knjiga, Zagreb, 1984
- S. Kurepa, Matematička analiza 2: Funkcije jedne varijable, Tehnička knjiga, Zagreb, 1984
- B. Širola, T. Berić, Matematika 1, skripta, http://web.math.pmf.unizg.hr/nastava/mat1pf/skripta/MAT1pred.pdf