After this course the student is able to:
- calculate double and triple integrals over a general defined region;
- apply standard coordinate transformations (polar, cylindrical and spherical) to multiple integrals;
- work with divergence and curl of a vector field
- calculate line and surface integrals of functions and vector fields over general regions;
- apply the theorems of Green, Stokes and Gauss;
- formulate the notions of series, sequences;
- determine the convergence of sequences;
- find the Taylor series expansion of simple functions.
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Calculus B is the direct successor to Calculus A. In Calculus A the focus was differentiation, while in Calculus B the focus lies at multiple integration of functions of two or more variables. We start with an introduction to multiple integration and exercise with various computation techniques. We extend our knowledge to integration over non-straight curves and non-flat surfaces. This is a prerequisite for the great integration theorems of Green, Stokes and Gauss, with which we conclude this course.
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