Subject name Mathematics Code EPM 1.1 Semester 1 Hours 2 2 ECTS credits 6 lec tut Lab Pro Sem Passing conditions* E/Z Department Mathematics Teaching Department Person responsible: Dr Anita Dąbrowicz-Tlałka Subjects required prior to this course: - Prerequisites: Working knowledge of basic mathematics (arithmetic and trigonometry) Aims of the course: The primary concern of Mathematics 1 is with basic mathematical ideas and techniques, enabling students to master standard topics in basic arithmetic, algebra, geometry, trigonometry and theory of the functions of one variable and build up confidence with mathematics to make foundation for more advanced work in technical applications. Teaching methods: Lectures are delivered in a mixed system, utilizing both an overhead or a multimedia projector and the blackboard; respective lecture notes are published in advance in the Internet. Classes are devoted to problems solving. Program contents: Relations, functions and their graphs Domain, range, monotonicity, inverse of function Polynomials Quotients of polynomials The exponential function The logarithm function The trigonometric function and their inverses The absolute value function Absolute value and distances on the number line and in the coordinate plane Absolute value function and their graph Equations and inequalities with absolute value Complex numbers Infinite sequences Convergence and divergence, limit theorems Limits and continuity The definition, the combination theorem for limits, properties of continuous functions Derivatives The definition of the derivative of the function at a point, simple properties Basic and supplementary literature: Lecture notes published on Gdansk University of Technology course management system Moodle: http://www.moodle.pg.gda.pl/course/view.php?id=95 Lial, Hornsby, Schneider College Algebra and Trigonometry Pearson Education 2005 George D. Thomas Thomas Calculus MIT 2005
Details of passing conditions: Class participation is mandatory. Absence from class for medical reasons must be verified by a doctor's certificate. There are 3 tests per semester, 15 p. each, plus 5 bonus points makes 50 p. (maximum). A question, concerning the theory from the lecture, appears in each test. Getting (during classes) more than 25 p. (50%), is equivalent passing I semester. Grades: grade 2 (niedostateczna) 0-49,9 %; grade 3 (dostateczna) 50-69,9 %; grade 3,5 (dość dobra) 70-79,9 %; grade 4 (dobra) 80-89,9 %; grade 4,5 (ponad dobra) 90-94,9 %; grade 5 (bardzo dobra) 95-99,9 %; grade 5,5 (celująca) 100% and an oral or a written exam, which gives an opportunity for student to demonstrate advanced level of knowledge.
Nazwa przedmiotu Mathematics Kod EPM.1.2 Semestr 2 Godziny 2 2 Punkty ECTS 8 w c l p s Sposób zaliczenia E/Z Katedra SNM Odpowiedzialny dr Rafał Kołodziej Necessary lectures n/a Introductory sylabus typical background from secondary education Goals to receive and claims Students should achieve fluency in calculus of real variable, algebra of matrices (systems of linear equations included), english vocabulary related to these fields. Didactical frame Traditional lectures and tutorials ilustrated with software such as DERIVE, MS Excell, calculators. Integration (8h) Integration formulas, The substitution method of integration, Integration by parts, Definite Integrals and their applications the area between two curves, calculating volumes, length of the curve, the area of a surface of revolution Complex numbers (4h) The geometrical interpretation, Inequalities Algebra (8h) Matrices, The determinant of a matrix, The system of linear equations Analytic geometry (10h) Vectors. The dot and the cross product of vectors and properties, The triple scalar-product and applications, Equations of lines and planes, The distance from a plane to a point, The angle between planes and lines Wykaz literatury podstawowej i uzupełniającej http://mathworld.wolfram.com http://en.wikipedia.org/wiki/main_page J. Bendick, M. Levin, L. Simon, Mathematics Illustrated Dictionary, Facts, Figures and People including the new math, McGraw-Hill Book Company, June 1972, ISBN 9780070044609 M. Gewert, Z. Skoczylas, Analiza matematyczna 1 Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 2001 M. Gewert, Z. Skoczylas, Analiza matematyczna 1 Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław 2001 K. Jankowska, T. Jankowski, Zbiór zadań z matematyki, PG, Gdańsk 1997 T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1 Definicje, twierdzenia, wzory, Oficyna Wydawnicza GiS, Wrocław 2002 T. Jurlewicz, Z. Skoczylas, Algebra liniowa 1 Przykłady i zadania, Oficyna Wydawnicza GiS, Wrocław 2002 R. Leitner, Zarys matematyki wyższej I i II, Wydawnictwo Naukowo-Techniczne, Warszawa 2001 R. Leitner, W. Matuszewski, Z. Rójek, Zadania z matematyki wyższej I i II, Wydawnictwo Naukowo-Techniczne, Warszawa 1999 E. Mieloszyk, Liczby zespolone, PG, Gdańsk 2003
E. Mieloszyk, Macierze, wyznaczniki i układy równań, PG, Gdańsk 2003 W. Krysicki, L. Włodarski, Analiza matematyczna w zadaniach I i II, Wydawnictwo Naukowe PWN, Warszawa 1998 Praca zbiorowa pod red. E. Mieloszyka Matematyka Materiały pomocnicze do ćwiczeń, PG, Gdańsk 2004 Praca zbiorowa pod redakcją B. Wikieł Matematyka podstawy z elementami matematyki wyższej, PG, Gdańsk 2008 Warunki zaliczenia przedmiotu 1. There are only following notes: 2, 3.5, 3, 4, 4.5, 5 and 5.5. You pass the exam or the tutorial if you gain the grade greater then 2. Presence on tutorials is obligatory. You have to show a good excuse at once after the absence. It is possible to have 3 absences within the first semester and 2 within the thirst semester. 3. Within a semester you can get up to 50 points. 4. There are 3 tests every with upper limit 15 points and 5 points for various activities which generate the note. Below there is the grade table. 2 3 3.5 4 4.5 5 5.5 to 2-ed exam You passed not so bad good fine best mark excellent less than 25 more than 24 more than 35 more than 39 more than 45 more than 47 to discuss 5. The necessary condition to write the first examination is to pass the exercises. 6. If you gain 40 points or over you automatically pass the examination with the note 3. It is not obligatory. 7. If you do not pass the exercises you can write the second examination. There will not be additional terms. 8. At the first exam you can obtain no more than 50 points. This points are added to those from the exercises and you pass the examination when the sum is greater than 44. 9. Everybody can write the second examination but to pass it one need to write it over the 24 point level.
Subject name Mathematics Code EPM 1.3 Semester 3 Hours 2 2 ECTS credits 6 lec tut Lab Pro Sem Passing conditions* E/Z Department Mathematics Teaching Department Person responsible: Mgr Mirosław Bednarczyk Subjects required prior to this course: Mathematics s.i, s.ii Prerequisites: Working knowledge of basic mathematics (arithmetic and trigonometry) Aims of the course: The primary concern of Mathematics 1 is with basic mathematical ideas and techniques, enabling students to master standard topics in basic arithmetic, algebra, geometry, trigonometry and theory of the functions of one variable and build up confidence with mathematics to make foundation for more advanced work in technical applications. Teaching methods: Lectures are delivered in a mixed system, utilizing both an overhead or a multimedia projector and the blackboard; respective lecture notes are published in advance in the Internet. Classes are devoted to problems solving. Program contents: Infinite series A necessary condition for convergence of a series Series with nonnegative terms Absolute convergence Alternating series and conditional convergence Functions of two variables and their derivatives Limits and continuity Partial derivatives Applications of partial derivatives Multiple integrals Double integrals Triple integrals Differential Equations First order differential equations separable equations, homogeneous equations, linear equations (the method of variation of parameter and the method undetermined coefficients) Second order differential equations with constant coefficients the characteristic equation, the method of variation of parameters and the method undetermined coefficients Basic and supplementary literature: Lecture notes, text problems and laboratory instruction manuals published on Gdansk University of Technology course management system Moodle: http://www.moodle.pg.gda.pl/course/view.php?id=95 Ewa Łobos, Beata Sikora Calculus and differential equations in exercises Gliwice 2006 WPŚ
Details of passing conditions: Class participation is mandatory. Absence from class for medical reasons must be verified by a doctor's certificate. There are 3 tests per semester, 15 p. each, plus 5 bonus points makes 50 p. (maximum). A question, concerning the theory from the lecture, appears in each test. Getting (during classes) more than 25 p. (50%), is equivalent passing I semester. Grades: grade 2 (niedostateczna) 0-49,9 %; grade 3 (dostateczna) 50-69,9 %; grade 3,5 (dość dobra) 70-79,9 %; grade 4 (dobra) 80-89,9 %; grade 4,5 (ponad dobra) 90-94,9 %; grade 5 (bardzo dobra) 95-99,9 %; grade 5,5 (celująca) 100% and an oral or a written exam, which gives an opportunity for student to demonstrate advanced level of knowledge.