Calculus 2 1000-712RRC2
Course content:
Indefinite integral; Newton's integral and its geometric interpretation; one-variable integral calculus (integration by parts, integration by substitution, calculation of areas of figures, length of a curve, volume and surface area of solids).
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).
Course coordinators
Learning outcomes
Student finishing the course:
1) can integrate by parts, uses some of the most common substitutions,
2) is able to calculate the areas of figures, the volume and surface area of solids, the length of a curve,
3) is able to calculate the limits of functions of several variables and examine the continuity of such functions,
4) knows the concept of derivative and partial derivative, can analytically calculate derivatives of functions,
5) knows how to determine the extrema of functions of several variables,
6) can examine the concavity/convexity of the function of several variables,
7) understands the meaning of the implicit function theorem,
8) knows how to expand a function into a Taylor series,
9) can integrate functions of several variables,
10) can solve linear differential equations with constant coefficients; knows the concept of the characteristic equation,
11) can solve simple differential equations with separated variables,
12) understands the importance and usefulness of vector analysis in the context of describing biological and physical problems.
Assessment criteria
exam
Bibliography
James Stewart, Essential Calculus, Cengage Learning
Additional information
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