Calculus 1 (MAT1011) - VDU Biochemijos ir biotechnologijų katedra
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Calculus 1 (MAT1011)

Course code

Course group

Volume in ECTS credits

Course hours

MAT 1011

C

6

160

Course type (compulsory or optional)

Compulsory

Course level (study cycle)

Bachelor

Semester the course is delivered

Autumn

Study form (face-to-face or distant)

Face-to-face

Course title in Lithuanian

AUKŠTOJI MATEMATIKA I

Course title in English

CALCULUS I

Short course annotation in Lithuanian

Dalyko tikslas – supažindinti su tiesinės algebras, analizinės geometrijos ir matematinės analizės pagrindais: matricos, determinanto sąvokomis, jų savybėmis, tiesinių lygčių sistemų sprendimo metodais, vektoriais ir veiksmais su jais, plokštuma ir tiese erdvėje, tiese plokštumoje, antros eilės kreivėmis, ir su matematinės analizės pagrindais: skaičių sekos ir funkcijos ribos, išvestinės, neapibrėžtinio ir apibrėžtinio integralo sąvokomis ir jų taikymais.

Short course annotation in English

This course aims to develop understanding in algebra, analytical geometry and fundamentals of mathematical analysis. The course includes topics as matrixes; determinants and their properties; theory of linear algebraic equations; Gaussian method; vectors; operations with vectors; scalar product; vector product; equation of a plane; equation of a line in space; equation of a line in plane; circle; ellipse; hyperbola; parabola; limit of functions, continuity of functions, derivative of functions, differential, applications of derivatives; indefinite integrals, definite integrals, Newton-Leibniz formula, application of definite integrals. Teaching methods are: lectures and practical works.

 Prerequisites for entering the course

High school mathematics knowledge.

Course aim

Course aim is toprovide understanding of linear algebra, analytical geometry and fundamentals of mathematical analysis.

Content (topics)

1. Matrix definition and operations. Determinant.  

2. Inverse matrix.

3. Solving of linear equations systems by using Inverse matrix, Krammer and Gausian methods.

4. Vectors, linear operations with vectors.  

5. Scalar, vector and parallelepipedal products.

6. Plane and line in space.  

7. Line in plane.

8. Second order curves.

9. Main classes of functions. Limit of function.

10. Continuous functions.

11. Derivatives and differential of a function.

12. Higher-order derivatives.

13. L'Hôpital's rule.

14. Extrema of a function. Function graphing.

15. Indefinite integral. Main integration methods.  

16. Definite integral, Newton - Leibniz formula.

17. Application of definite integral in geometry, physics and mechanics.

Distribution of workload for students (contact and independent work hours)

Lectures – 45 hours, practical works – 30 hours,  individual work – 85 hours.

Structure of cumulative score and value of its constituent parts

Final assessment sums the assessments of written final examination (50%), written mid-term examination (25%) and assessment of practical works (25%).

Recommended reference materials

No.

 

Publication year

Authors of publication and title

Publishing house

Number of copies in

University library

Self-study rooms

Other libraries 

Basic materials

1.

2008

Pekarskas V. Diferencialinis ir integralinis skaičiavimas I ir II dalys. (Differential and Integral Calculus, I, II)

Technologija

I-25, II-22

I-6, II-6

 

2.

2005

Pekarskas V. Trumpas matematikos kursas. (Short Course of Mathematics)

Technologija

20

1

 

3.

2005

Kavaliauskas A. Aukštosios matematikos uždavinynas. (Tasks of Calculus)

Vilniaus universiteto leidykla

2

1

 

Supplementary materials

1.

2006

N.Janušauskaitė,R.Markauskas, V.Sabatauskienė. Tiesinė algebra ir diferencialinis skaičiavimas. (Linear Algebra and Differential Calculus)

Technologija

 

2.

2001

Z.Furmonavičienė, S.Janušauskaitė, A.Marčiukaitienė, N.Ratkienė. Tiesinė algebra ir matematinė analizė (uždavinių sprendimas). (Linear Algebra and Mathematical Analysis (Solutions of problems))

Technologija

 

Course programme designed by

Doc. dr. Sigita Pečiulytė, Department of Mathematics and Statistics, Faculty of Informatics

 

 

 

 

 

Additional information