# Course details

## Mathematics I

Independent Chairs

Semester: Winter
ECTS:8
Study level: BSc
Course code: 19121
Available in 2022/23: Yes

Course description:

Objective of the course:

• Introduce students to the basics of vector algebra, differential and integral calculus of functions of one variable, and their applications.

Learning outcomes:

After the completion of the course the students will be able to:

1. Use algebraic operations with vectors in 2D and 3D Euclidean space or coordinate system after coordination.
2. Define the concepts of function, domain and graph and reproduce graphs of elementary functions.
3. Determine the natural domains of simpler elementary functions
4. Use tabular derivations and derivation rules when deriving complex functions, products and quotients.
5. Apply the derivation of the function to find the tangent, local extremes and solve the limits by L’Hospital’s rule.
6. Distinguish the concepts of definite and indefinite integrals and use the Newton-Leibniz formula using tabular integrals.
7. Solve the integral by the method of substitution and the method of partial integration.
8. Connect the notion of a definite integral and the area between two curves.

Course content:
Directed line segment. Vectors. Cartesian coordinate system. Scalar product and Vector product. Mixed product. Composition of functions. Inverse function. Monotone functions and local extremes. Convexity, concavity and points of inflection. Exponential function. Trigonometric functions. Cyclometric functions. Arrays. Limes series. Limes and continuity of function. Basic rules of derivation. Derivation of the composition of functions. Derivation of the inverse function. Higher order derivatives. Derivation of an implicitly given function. Basic theorems of differential calculus. Application of derivations to the search for insreasing and decreasing intervals and local extremes of function. Application of derivations to the search for convexity and concavity intervals and inflection points of functions. L’Hospital’s rule. Asymptotes. Function flow testing. Integrals. Definition of a definite integral. Antiderivation of function, indefinite integral. Leibniz-Newton’s formula. Direct integration. Substitution method. Partial integration method. Integrating rational functions. Integrating trigonometric functions. Integrating some
irrational functions. Application of definite integrals. Calculating the areas of plane figures. Calculation of the volume of rotating solids.

Syllabus (pdf)