Course Details

# Mathematics 2

BAA002 course is part of 5 study plans

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

BPA-SI Summer Semester 1st year

Course Guarantor

Institute

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

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.