Mathematics 2

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Course teacher

Associate teachers

Status of the course

Course objectives

To introduce students to the basic elements of integral calculus, differential calculus of several variables and the basic of differential equations.

Course enrolment requirements and entry competences required for the course

Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

After finishing this course the student is expected to be able to:
- apply the techniques of integration (integration by substitution, integration by parts)
- use the definite integral in its geometrical applications
- solve the first-order differential equations (variables separable, homogeneous differential equations, linear differential equations, exact differential equations)
- solve the second-order linear nonhomogeneous differential equations with constant coefficients

Course content broken down in detail by weekly class schedule (syllabus)

1. Indefinite integral. Table of integrals.
2. Integration by substitution. Integration by parts.
3. Integrating rational fractions. Integrating by algebraic substitution.
4. Definite integral.
5. Improper integrals.
6. Application of definite integral.
7. Functions of several variables. Limit and continuity.
8. Partial derivatives. Differential.
9. Tangent plane and normal line. Maxima and minima.
10. Double integrals.
11. Geometric application of double integrals.
12. Ordinary differential equations.
13. First-order differential equations.
14. Second-order differential equations.
15. Course review. Revision.

Format of instruction:

Student responsibilities

Regular attendance of classes.