Course Details

Mathematics 2

Academic Year 2025/26

BAA002 course is part of 5 study plans

​ BPA-SI Summer Semester 1st year

​ BPC-SI / VS Summer Semester 1st year

​ BPC-MI Summer Semester 1st year

​ BPC-EVB Summer Semester 1st year

​ BKC-SI Summer Semester 1st year

Course Guarantor

doc. Ing. Vladislav Kozák, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech, English

Credits

5 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289588

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Antiderivative, indefinite integral and their properties. Integration by parts and using substitutions.
  • 2. Integrating rational functions.
  • 3. Integrating trigonometric functions. Integrating irrational functions.
  • 4. Newton and Riemann integral and their properties.
  • 5. Integration methods for definite integrals. Applications of the definite integral.
  • 6. Geometric and engineering applications of the definite integral.
  • 7. Real function of several variables. Basic notions, composite function. Limits of sequences, limit and continuity of two-functions.
  • 8. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Total differential of a function, higher-order total differentials.
  • 9. Taylor polynomial of a function of two variables. Local maxima and minima of functions of two variables.
  • 10. Function in one variable defined implicitly. Function of two variables defined implicitly.
  • 11. Some theorems of continuous functions, relative and global maxima and minima.
  • 12. Tangent to a 3-D curve, Tangent plane and normal to a surface.
  • 13. Scalar field, directional derivative, gradient.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Differentiating revision.
  • 2. Integration by parts and using substitutions.
  • 3. Integrating rational functions.
  • 4. Integrating trigonometric functions.
  • 5. Integrating irrational functions.
  • 6. Integration methods for definite integrals.
  • 7. Geometric applications of the definite integral. Test 1.
  • 8. Geometric and engineering applications of the definite integral.
  • 9. Partial derivative, partial derivative of a composite function, higher-order partial derivatives.
  • 10. Total differential of a function, higher-order total differentials. Taylor polynomial of a function of two variables.
  • 11. Local maxima and minima of functions of two variables. Test 2.
  • 12. Functions defined implicitly. Global maxima and minima.
  • 13. Tangent plane and normal to a surface. Seminar evaluation.