Course Details

Mathematics 4

Academic Year 2025/26

NAA026 course is part of 1 study plan

​ NPC-GK Winter 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

winter

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/295955

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Complex numbers, basic operations, displaying, n-th root. Complex functions.
  • 2. Limit, continuity, derivative of a complex function, Cauchy-Riemann conditions.
  • 3. Analytical functions. Conform mapping implemented by an analytical function.
  • 4. Conform mapping implemented by an analytical function.
  • 5. Planar curves, singular points on a curve.
  • 6. 3D curves, curvature and torsion.
  • 7. Frenet trihedral, Frenet formulas.
  • 8. Explicit, implicit, and parametric equations of a surface.
  • 9. The first basic form of a surface and its use.
  • 10. The second basic form of a surface. Normal and geodetic curvature of a surface. Meusnier's theorem.
  • 11. Asymptotic curves on a surface.
  • 12. Mean and total curvature of a surface.
  • 13. Elliptic, hyperbolic, parabolic and circular points of a surface.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Complex numbers, basic operations, displaying, n-th root. Complex functions.
  • 2. Limit, continuity, derivative of a complex function, Cauchy-Riemann conditions.
  • 3. Analytical functions. Conform mapping implemented by an analytical function.
  • 4. Conform mapping implemented by an analytical function.
  • 5. Planar curves, singular points on a curve.
  • 6. 3D curves, curvature and torsion.
  • 7. Frenet trihedral, Frenet formulas.
  • 8. Explicit, implicit, and parametric equations of a surface.
  • 9. The first basic form of a surface and its use.
  • 10. The second basic form of a surface. Normal and geodetic curvature of a surface. Meusnier's theorem.
  • 11. Asymptotic curves on a surface.
  • 12. Mean and total curvature of a surface.
  • 13. Elliptic, hyperbolic, parabolic and circular points of a surface. Seminar evaluation.