MATHEMATICAL ANALYSIS I

Course ID: IGI-SE>ANALIZAMAT1
Course title: MATHEMATICAL ANALYSIS I
Semester: 1 / Winter
ECTS: 7
Lectures/Classes: 30 / 30 hours
Field of study: Geodesy and Cartography
Study cycle: 1st cycle
Type of course: compulsory
Prerequisites: Mathematics on the secondary school level (comprehensive secondary school of a general profile).
Contact person: dr hab. Ryszard Deszcz; e-mail: ryszard.deszcz@upwr.edu.pl
Short description: In the course Mathematical Analysis I there are contained elements of differential and integral calculus of functions of one variable and ordinary differential equations.
Full description: Limit of a sequence, limits of functions, continuity and derivatives of a function of one variable, Lagrange theorem, de L’Hospital’s rule, Taylor formula, Maclaurin formula, investigation of the shape of a function of one variable, number series, tests for convergence of series, power series, indefinite integrals, definite integrals, Leibniz-Newton formula, improper integrals, first-order ordinary differential equations, second-order ordinary differential equations, Cauchy problem, applications of ordinary differential equations.
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 basic theorems from selected sections of Mathematics, knows elements of differential and integral calculus of functions of one variable. Skills Use differential calculus of a function of one variable to the investigation of a function of one variable, use integral calculus of a function of one variable to compute of given geometrical quantities, solve differentials equations of some types. 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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