﻿ Mathematics 1 – Differential calculus – Curriculum

# Curriculum.

 Course title Mathematics 1 (Differential calculus) Code M101 Status Lectures(30), Exercises (45) Level Basic course Year 1. Semester 1. ECTS 6 ECTS credits Lecturer Mihaela Ribičić Penava, Associate Professor; Marija Miloloža Pandur,  Assistant Professor, Assistant Course objective At the introductory level, the goal of the course is to introduce students to fundamental ideas and methods of mathematical analysis, which are the basis for many other courses. During lectures, basic concepts and their usefulness and applications will be considered. During exercises, students should apply appropriate techniques and solve specific problems. Prerequisites High school knowledge. Learning outcomes: Differentiate between and give typical examples of convergent and divergent sequences of real numbers, continuous and discontinuous functions, differentiable and non-differentiable real functions of one variable. Apply the techniques for computing: the limit of real number sequences, limits and derivatives of real functions of one variable. Recognise the conditions on the functions which enable the application of fundamental theorems of differential calculus and give the appropriate geometrical interpretation. Interpret the results of the application of differential calculus to simpler optimisation problems. Understand and reproduce the correct mathematical proof of claim applying basic forms of mathematical and logical inference.
 Teaching activity ECTS Learning outcome Students activity Methods of evaluation Points min max Class attendance 1 1-5 Class attendance Evidence list 0 4 Knowledge test (preliminary exam) 2 1-5 Preparation for the written examination. Evaluation 25 48 Final exam 3 1-5 Repetition of teaching materials. Oral exam 25 48 Total 6 50 100
 Consultations By arrangement or after class Gained competencies At the introductory level introduce students to the basic ideas and methods of mathematical analysis, which are the basis for many other courses. Lectures will be given in an informal manner, illustrating their utility and application. At exercises, students learn the necessary techniques and apply them to solve real problems. Content (Course curriculum) Field of real numbers, infimum, and supremum of a set, absolute value, intervals. Field of complex numbers. Principle of mathematical induction. Functions. Notion of a function.  Properties of functions.  Elementary functions (polynomials, rational functions, and irrational functions, exponential and logarithmic functions, trigonometric and inverse trigonometric functions). Composite function. Bijective function.  Inverse function. Notion of sequence and subsequence, the main properties, and convergence. Number e. Limit and function continuity. Notion of function limit. Limits properties. One-sided limits. Infinite limits and limits in the infinity. Asymptotes. Continuity and continuous function properties. Differential calculus. The tangent and velocity problem. Notion of derivative. Differentiation rules. Derivatives of elementary functions. Implicit function derivative. Derivative of parametric function. Higher-order derivatives. The fundamental theorems of differential calculus. Differential calculus applications. Notion of differential. L’Hôspital’s rule. Function analysis (monotonicity, extremes, convexity, asymptotes). Recommended reading Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964. D. Jukić, R. Scitovski, Matematika I, Department of Mathematics, University of Osijek, Osijek, 2000 Additional reading S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989. S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990. B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička   knjiga, Zagreb, 1986. Instructional methods Lectures and exercises are mandatory. Exam formats The exam consists of a written and oral part. After the completion of lectures and exercises, students can take the exam. Acceptable mid-term exam scores replace the written examination. Language Croatian Quality control and successfulness follow up An anonymous questionnaire