Calculus I

1. Demonstrate fundamental skills contained in the course, such as differentiation and integration in one variable
2. Outline basic definitions (limit, derivative, integral) and statements of main theorems
3. Apply differentiation and integration in solving engineering problems
4. Describe and use methods presented in the course
5. Illustrate problem by mathematical model and apply appropriate mathematical method
6. Apply mathematical reasoning adequately

The course is divided in two cycles, 3 hours of lessons per week.

The course is divided in two cycles, 1 hour of exercises per week.

Regular homeworks.

1. Real function of real variable. Domain and image of a function. Basic properties. Graph of a function. Inverse function. Transformation on graphs of a function.
2. Elementary functions. Graphs and basic properties.
3. Elementary functions. Graphs and basic properties.
4. Limit of a function.
5. Limit of a function. Continuity of a function.
6. The derivative of a function.
7. Examination.
8. Techniques of differentiation. Differentiation of implicit and parametric functions.
9. The mean value theorem.The min-max problem. Curve sketching.
10. Applications of the derivative of a function on problem solving. Convexity and concavity of a function. L'Hospital's rule.
11. Definition of definite and indefinite integral, properties. Newton-Leibniz formula. Direct integration.
12. Methods of integration: substitution and partial integration
13. Integration of rational functions, improper integral
14. Applications of the integral - area and arc length
15. Examination.