Calculus 2

During the course, we generalize the concepts known from Differential and Integral Calculus 1 to functions of several variables and learn about differential equations and their applications.

Limits and continuity of functions of several variables.

Differential calculus of functions of several variables (differential, partial derivatives, gradient, implicit function theorem, Sylvester's theorem, convexity, concavity, Taylor polynomial).

Elements of integral calculus of functions of several variables.

Ordinary differential equations (methods of solving of linear equations, the concept of a characteristic equation, examples of simple ordinary differential equations with separated variables, appearing in physics and other applications).

James Stewart, Essential Calculus, Cengage Learning

Student obtaining credit for the course:

1) is able to calculate the limits of functions of several variables and examine the continuity of such functions,

2) knows the concept of derivative and partial derivative, can analytically calculate derivatives of functions,

3) knows how to determine the extrema of functions of several variables,

4) can examine the concavity/convexity of the function of several variables,

5) understands the meaning of the implicit function theorem,

6) knows how to expand a function into a Taylor series,

7) can integrate functions of several variables,

8) can solve linear differential equations with constant coefficients; knows the concept of the characteristic equation,

9) can solve simple differential equations with separated variables,

10) understands the importance and usefulness of vector analysis in the context of describing biological and physical problems.

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