# Course details

## Mathematics II

Independent Chairs

Semester: Summer
ECTS:8
Study level: BSc
Course code: 19122
Available in 2022/23: Yes

Course description:

Objective of the course:

• Introduce students to matrix calculus, solving systems of linear equations, analysis of the function of two variables, double integrals and first and second order differential equations.

Learning outcomes:

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

1. Perform basic algebraic operations with matrices and determine the inverse of a regular matrix.
2. Solve a system of linear equations by the Gauss-Jordan method.
3. Examine the convergence of an order of numbers or an order of functions and apply the Taylor order in calculating the values of an elementary function without the use of a
calculator.
4. Determine the natural domain and partial derivatives of the function of two variables.
5. Calculate the gradient and differential of the function of two variables at a given point.
6. Look for local extremes of the function of two variables.
7. Define the area of integration of the double integral.
8. Calculate a simpler double integral in rectangular or polar coordinates.

Course content:
Matrices. Algebraic operations with matrices. Reduced matrix shape and Gauss-Jordan’s algorithm. Inverse matrix. Solving systems of linear equations. Rows of numbers. Rows of functions. Taylor and Fourier’s series. Functions of multiple variables. Definition of an area and graph. Partial derivations. Mean value theorem. Tangential plane. Taylor’s formula. Local extremes. Conditional extremes. Double and triple integrals and applications. Double integral in rectangular coordinates and in polar coordinates. Differential equations. First order differential equations. Linear differential equations of the n-th order. Linear differential equations of n-th order with constant coefficients.

COURSE CONDITIONS AND EXAMINATION RULES
conditions for obtaining the right to register for the exam (10 + 10 + 10):

• 10 drawn student card in the lectures
• 10 drawn student card on the exercises
• 10 points from two written tests of homework (out of a total of 20 points!)

colloquia (partial exams)

• two colloquia for exemption from the written part of the exam – 50% of points is the minimum for exemption

written exam

• Five tasks – 50% points is the minimum to pass

oral exam

• obligatory for everyone – solving a task or a theoretical question

Syllabus (pdf)