MATHEMATICAL ANALYSIS II

Course ID: IGI-SE>ANALIZAMAT2
Course title: MATHEMATICAL ANALYSIS II
Semester: 2 / Spring
ECTS: 6
Lectures/Classes: 30 / 30 hours
Field of study: Geodesy and Cartography
Study cycle: 1st cycle
Type of course: compulsory
Prerequisites: Mathematical Analysis I
Contact person: dr hab. Ryszard Deszcz; e-mail: ryszard.deszcz@upwr.edu.pl
Short description: In the course Mathematical Analysis II there are contained elements of differential and integral calculus of functions of several variables, and in particular, functions of two variables, elements of differential geometry of curves and surfaces and elements of vector analysis.
Full description: Functions of several variables, double integrals, triple integrals, line integrals, Green’s formula, differential geometry of curves and surfaces, surface integral, elements of vector analysis: the gradient of a scalar field, the divergence and the curl of a vector field, Stokes’ theorem.
Bibliography: 1. Heinbockel J.H., Introduction to Calculus, Vol. I, Vol. II, 2012. (Paper or electronic copies for noncommercial use may be made freely without explicit permission of the author. All other rights are reserved); 2. Trench W.F., Introduction to real analysis, Free Edition 1.06, January 2011. (this book was published previously by Pearson Education); 3. Polyanin A.D., Valentin F.Z., Handbook of exact solutions for ordinary differential equations, 2nd ed., 2003 by Chapman & Hall/CRC, a CRC Press Company Boca Raton, London, New York, Washington, D.C - complementary/optional 4. Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products, seventh ed., 2007, Jeffrey A., Editor University of Newcastle upon Tyne, England, Zwillinger D., Editor Rensselaer Polytechnic Institute, USA, Translated from Russian by Scripta Technica, Inc. Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo, Academic Press, Elsevier Inc.
Learning outcomes: Knowledge Understands the civilization’s significance of Mathematics and its applications, knows elements of differential and integral calculus of functions of several variables, and in particular, functions of two variables. Knows elements of differential geometry of curves and surfaces, and elements of vector analysis. Skills Determine extrema of a function of two variables, use integral calculus of a function of two or three variables to compute of given geometrical quantities, compute gradient and directional derivative of a function, and divergence and curl of a vector field, compute curvature and torsion of a curve, determine tangent plane and normal line at a regular point of a surface, compute the first and second fundamental form of a surface. Social competences Knows limitations of his/her own knowledge and understands the need for further education, understands and appreciates the importance of intellectual honesty in his/her own activities and those of other people; behaves ethically.
Assessment methods and assessment criteria: grade obtained at classes (50%) + grade obtained at lectures (50%)

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