Math 2

• Vector functions and curves
○ Vector functions of one variable;
○ Curves and parametrizations; Arc length;
○ Cylindrical and spherical coordinates.
• Functions of several variables
○ Limits and continuity
○ Partial derivatives
○ Linear approximation; differentiability and Jacobian matrix
○ Gradients and directional derivatives
○ Taylor series and approximations
• Multiple Integration
○ Double integration in Cartesian and polar coordinates;
○ Triple integrals and change of variables in triple integrals
• Cylindrical coordinates
• Spherical coordinates
• Vector Fields
○ Conservative fields
○ Line integrals (in general)
○ Line integrals of vector fields
○ Surface integrals
○ Oriented surfaces and flux integrals

• Construct parameterizations of elementary curves and curved surfaces. Apply the parameterization of a curve to determine its arc length.• Being able to work with cylindrical and spherical coordinates, and to apply these formulas in the construction of parameterizations.• Understand the concept of functions of two or more variables, and the connections between the function description, the graph of the function, and its level curves/level surfaces.• Investigate whether a function of two or more variables is continuous in a given point.• Determine and apply (first and higher order) partial derivatives of a function, e.g. in the determination of the tangent plane to the graph or the Taylor polynomial around a given point. Being able to apply the chain rule.• Understand and apply the concepts of gradient and directional derivative, e.g. for the investiation of the graph of a function and of its level curves.• Determine double and triple integrals by iterated integration. Understand how to choose a convenient coordinate system from the following options: Cartesian coordinates, polar/cylindrical coordinates, spherical coordinates. Know the corresponding correction terms.• Determine the line integral of a function along a curve in two- or three dimensional space and find the corresponding correction term.• Determine the surface integral of a function over a parametric surface and find the corresponding correction term.• Understand the notions of a vector field and of a conservative vector field. Determine whether a given vector field is conservative.• Determine line integrals along vector fields and know that a line integral along a conservative vector field is independent of the path.• Determine the flux of a vector field across an oriented surface.• Understand the notions of gradient, divergence and rotation of a vector field and their mutual relations.• Being able to apply the mathematical concepts to selected electrical engineering and physics problems.

Calculus B (2WBB0), Math1 (5EZA0)

• Calculus: a complete course (ISBN 978-0-13-573258-8)
• Study guide + hand outs: will be made available in Canvas.