Course Details

Mathematics 2 (G)

Academic Year 2025/26

BAA009 course is part of 1 study plan

​ BPC-GK Summer Semester 1st year

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

5 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289943

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Notion of a primitive function. Properties of an indefinite integral. Integration methods for indefinite integral.
  • 2. Integrating a rational function. Integrating a trigonometric function.
  • 3. Integrating selected types of irrational functions. Newton integral, its properties and calculation. Riemann integral.
  • 4. Applying calculus in geomery and physics.
  • 5. Real functions two and more variables, composite functions. Limit and continuity of functions two and more variables. Theorems on continuous functions.
  • 6. Partial derivatives, partial derivatives of a composite function, higher-order partial derivatives. Transformations of differential expressions.
  • 7. The total differential of a function. Higher-order total differentials. Taylor polynomial of a two-function. Local maxima and minima of two-functions.
  • 8. Functions defined implicitly. Two-functions defined implicitly.
  • 9. Global maxima and minima. Simple problems in global maxima and minima using relative maxima and minima. Scalar field and its levels. Directional derivative of a scalar function, gradient.
  • 10. Tangent and normal plane to a 3D curve. Tanget plane and normal to a surface defined explicitly.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Integrating a rational function.
  • 2. Integrating a trigonometric function.
  • 3. Integrating selected types of irrational functions. Newton integral, its properties and calculation. Riemann integral.
  • 4. Geometric and physical applications of calculus.
  • 5. Real functions of two and more variables, composite function. Limit and continuity.
  • 6. Seminar test I. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Transformations of differential expressions.
  • 7. The total differential of a function. Higher-order total differentials. Taylor polynomial of functions of two variables. Local extreme of functions of two variables.
  • 8. Functions defined implicitly.
  • 9. Seminar test II. Global extreme. Scalar field and its levels. Directional derivative of a scalar function, gradient.
  • 10. Tangent and normal plane to a 3D curve. Tangent plane and normal to a surface defined explicitly.