# Applied Mathematics

NAME OF THE COURSE Applied Mathematics

Code

 KTB101 Year of study 1

Course teacher

 Nives Baranović Credits (ECTS) 4

Associate teachers

Type of instruction (number of hours)

 P S V T 30 15 0 0

Status of the course

 Mandatory Percentage of application of e-learning 20 %
COURSE DESCRIPTION

Course objectives

Student are introduced to the ideas and methods of approximate solving algebraic and differential equations, interpolation and numerical integration, to concepts of the theory of probability and statistics and their application to particular example and tasks.
By developing a positive attitude toward learning, responsibility for own success and progress, and the acquisition of competencies described above, the students are expected to build a solid foundation for lifelong learning and further education.

Course enrolment requirements and entry competences required for the course

Students should have fundamental competencies related to the calculus.

Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

After the passing the exam, students will be able to:
- use appropriate language, symbolic notation and graphic representation to describe the ideas and methods for numerical solving equations;
- apply the methods described above in the particular tasks;
- describe the concept and define the notions of probability theory;
- understand the concepts and apply the methods described above in real situations;
- define discrete and continuous random variables and their characteristics;
- properly interpret characteristics of random variables on particular examples;
- describe examples of important distribution and identify conditions for their use in problem solving;
- describe the concept and define the notions of statistics theory;
- use a computer and appropriate software as a tool in the statistical data processing;
- understand the process of statistical testing and parametric and non-parametric sample testing.

Course content broken down in detail by weekly class schedule (syllabus)

Introduction to the objectives and learning outcomes, curriculum, methods of evaluation and assessment criteria.
Errors of approximate values. The types of errors. Sources of errors. (2 + 1)
Solving equations approximately. Graphical method. Bisection method. Iteration. Secant method. Tangent method. (4 + 2)
Interpolation and approximation. (2 + 1)
Numerical integration. Rectangular formula. Trapezium formula. Simpson’s formula. (2 + 1)
Numerical solving of differential equations. Euler’s method. Taylor’s method. (2 + 1)
Written exam. (0 + 2)
Definition and properties of probability. (2 + 1)
Conditional probability. Independence of events. (2 + 1)
Random variables. Discrete and continuous random variables. Independence of random variables. (2 + 1)
Numerical characteristics of random variables. Mathematical expectation. (2 + 1)
Dispersion. Mode and median. Moments. The coefficient of skewness and kurtosis. (2 + 1)
Some important distributions. Binomial distribution. Poisson distribution. Normal distribution. Uniform distribution. Exponential distributions. (4 + 2)
Basics of statistics. Population. Sample. Displaying data. The average value of the sample. Sample variance. Sample mode. Sample median. (2 + 1)
Statistical testing. Parametric test. Nonparametric test. Χ2 test. (2 + 1)
Written exam. (0 + 2)

Format of instruction:

 lectures seminars and workshops exercises on linein entirety partial e-learning field work independent assignments multimedia laboratory work with mentor ____________ ____________

Student responsibilities

Screening student work (name the proportion of ECTS credits for eachactivity so that the total number of ECTS credits is equal to the ECTS value of the course):

 Class attendance 0 Research 0 Practical training 0.0 Experimental work 0 Report 0 Samostalni zadaci 0.8 Essay 0 Seminar essay 0 Tests 0 Oral exam 1.6 Written exam 1.6 Project 0

Grading and evaluating student work in class and at the final exam

The first method: Engagement during semester 20% (E), written exam 40% (W) and oral exam 40% (O). During the semester, student can do additional task, write a seminar paper and express own knowledge through activities in class. The final score: z = 0.2(E) + 0.4(W) + 0.4(O).
The second method: written exam 500% and oral exam 50%; final: z = 0.5(W) + 0.5(O).

Required literature (available in the library and via other media)

 Title Number of copies in the library Availability via other media Bogdanic, N. (1980), Primijenjena matematika, Split: Sveučilište u Splitu 1 Baranović, N. (2014.) Primijenjena matematika 0 e-learning (materijal dostupan na moodlu Filozofskog fakulte

Optional literature (at the time of submission of study programme proposal)

Ivanšić, I. (2002). Numerička matematika. Zagreb: Element
Scitovski, R. (2004). Numerička matematika, Osijek: http://www.mathos.unios.hr/nm/materijali/Num.PDF
Elezović, N. (2008). Diskretna vjerojatnost. Zagreb: Element
Elezović, N. (2008). Matematička statistika. Statistički procesi. Zagreb: Element