Mathematics
1755-F1-MAT-J
Lectures:
The lectures are aimed at providing students with the knowledge of basic tools and concepts of calculus:
the concept of function, definitions and properties of elementary functions: polynomials, exponential, logarithmic and trigonometric; basic properties of number sequences, the concepts of monotonicity, limitations and convergence of number sequences; the concept of the limit of a function at a point, the concept of unilateral boundaries; the concept of the derivative of a function at a point, formulas for derivatives of elementary functions and formulas for a derivative of a linear combination and composition of functions, the interpretation of derivatives of higher orders and their applications; the concept of indefinite and definite integral, the primary functions of selected elementary functions, the geometric interpretation of the definite integral.
Laboratory tutorials:
Laboratory tutorials will equip students with the practical abilities of drawing graphs and studying the properties of basic elementary functions: polynomials, rational, exponential, logarithmic and trigonometric functions;
determining the limits of numerical sequences; setting the limits of elementary functions; calculating derivatives of functions; calculating simple indefinite and definite integrals.
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Term 2024/25Z:
The mathematics lecture aims to familiarise students with the concept of functions, elementary functions, the concept of composite and inverse functions, the concept of numerical sequences and the basic properties of numerical sequences, the limit of a function, the continuity of a function, the concept of derivatives and the determination of derivatives, the interpretation of derivatives as functions, the study of the variability of functions, the concept of definite and indefinite integrals, and the basic methods of calculating integrals.
The exercises are related to the topics discussed in the lecture and are devoted to the acquisition of practical skills by students regarding the content presented in the lecture. During the exercises, students learn how to plot elementary functions and describe their basic properties, examine the basic properties of numerical sequences, determine the limits of functions of a single real variable and examine their continuity. During the exercises, students determine derivatives, examine the variability of functions and calculate definite and indefinite integrals.
Seminars – not applicable
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Total student workload
1. Obligatory hours realized with the teacher participation
– lecture participation – 10 hours,
– laboratory tutorials participation – 25 hours,
– consultations participation, including scientific and research consultations 9 hours,
– final exam participation – 2 hours
Total obligatory hours realized with the teacher participation: 46 hours, which corresponds to 1.84 ECTS points.
2. Student workload balance:
– lecture participation – 10 hours,
– laboratory tutorials participation (including the analysis of case studies, clinical and randomized test results) – 25 hours,
– consultations participation, including scientific and research consultations – 9 hours,
– final exam participation – 2 hours
– preparation for tutorials – 5 hours,
– preparation for tests – 12 hours,
– preparation for final exam – 12 hours.
A total work amount: 75 hours, which corresponds to 3.00 ECTS points.
3. Workload related to conducting research:
– reading the indicated literature -10 hours,
– participation in lectures (including research results and scientific studies methodology) - 2 hours,
– participation in scientific consultations- 2 hours,
– participation in laboratory tutorials (including research results and scientific studies methodology): 15 hours,
– preparation for tutorials including scientific results: 4 hours,
– preparation for final exam including research results and scientific studies in the field of pathophysiology- 5 hours.
A total student workload related to the conducted research is 38 hours, which corresponds to 1.52 ECTS points.
4. Time required for the preparation and participation in evaluating process:
– preparation for test – 12 hours,
– preparation for final exam – 12 hours,
Total time required for the preparation and participation in evaluating process: 24 hours, which corresponds to 0.96 ECTS point.
5. Time required for the practical training completion – not applicable.
Learning outcomes - knowledge
W1: the concept of function, describes the basic properties of functions of one real variable, provides definitions and properties of elementary functions: polynomials, rational, exponential, logarithmic and trigonometric functions - K_B.W24
W2: basic properties of number sequences, explains the concepts of monotonicity, limitations and convergence of number sequences - K_B.W24
W3: the concept of the limit of a function at a point, explains the concept of unilateral boundaries and function continuity - K_B.W24
W4: the concept of the derivative of a function at a point, gives formulas for derivatives of elementary functions and formulas for a derivative of a linear combination and composition of functions, gives the interpretation of derivatives of higher orders and their application to study the properties of function variability - K_B.W24
W5: the concept of indefinite and definite integral, gives the primary functions of selected elementary functions, explains the geometric interpretation of the definite integral - K_B.W24
Learning outcomes - skills
Learning outcomes - abilities The graduate is able to:
U1: draw graphs and study the properties of basic elementary functions: polynomials, rational, exponential, logarithmic and trigonometric functions - K_B.U11
U2: determine the limits of numerical sequences; sets the limits of elementary functions - K_B.U11
U3: calculate derivatives of functions - K_B.U11
U4: performs a study of the course of function variability and draws graphs of elementary functions - K_B.U11
U5: calculate simple indefinite and definite integrals - K_B.U11
Learning outcomes - social competencies
In the scope of social competencies the graduate is ready to:
K1: use objective sources of information - K7
Teaching methods
Lectures:
- informative lecture (conventional) with a multimedia presentation
- problem-oriented lecture
Laboratories:
classical problem-oriented method
Expository teaching methods
- informative (conventional) lecture
Exploratory teaching methods
- practical
Prerequisites
Knowledge of mathematics at the high school level.
Course coordinators
Assessment criteria
Lectures and laboratory tutorials:
The grade for the subject is issued based on the results of the exam according to the number of points obtained in accordance with the table below:
Percentage of points Grade
90-100% Very good
80-89% Good plus
70-79% Good
60-69% Satisfactory plus
50-59% Satisfactory
0-49% Failed/Unsatisfactory
Practical placement
Bibliography
1. Heinbockel J.H., Introduction to Calculus, Vol. I, available as the PDF file from the site: http://www.math.odu.edu/~jhh/Volume-1.PDF.
Supplementary literature:
1. McQuarrie D.A.: Mathematical Methods for Scientists and Engineers, University Science Book, 2003,
Additional information
Additional information (registration calendar, class conductors,
localization and schedules of classes), might be available in the USOSweb system: