Mathematics (110491-1160):
 Lecture - Mondays 11:40-13:20 in room C-1b, Classes: Wednesdays 8:00-10:35 in room G-322, Wednesdays 10:45-13:20 in room G-322.

# Books:

 Stewart James - Calculus Early Transcendentals, Brooks/Cole, Belmont CA, USA, 2011 Howard Anton, Chris Rorres - Elementary Linear Algebra with Suplemental Applications, Clarence Center Inc, Denver MA, 2010 Stanley J. Farlow, Gary M. Haggard - Applied mathematics, Random House New York USA, 1988 J. Kłopotowski, W. Marcinkowska-Lewandowska, M. Nykowska, I. Nykowski - Matematyka J. Laszuk - Zbiór zadań z matematyki..., Wyd. MAGIC, Warszawa 2003r. M. Krych - Analiza matematyczna dla ekonomistów, Wydawnictwa Uniwersytetu Warszawskiego, 2010r. W. Krysicki, L. Włodarski - Analiza matematyczna w zadaniach, część I i II, Państwowe Wydawnictwo Naukowe, Warszawa 1986r. J. Banaś, S. Wędrychowicz - Zbiór zadań z analizy matematycznej, Wydawnictwo Naukowo-Techniczne, Warszawa 2001r.

 SGH e-book Ważniak - mathematical analysis Ważniak - linear algebra Octave and its extension Octave-Forge with the exemplary manual

• Two tests for 30 points each. There is no possibility to retake the tests.
• If someone did not write the first test (for justified reasons), then the second test is graded for 60 points.
• The grade on the basis of the average of the written tests by the conversion table:  AVARAGE POINTSFROM TESTS GRADE < 16 2 from 16 3 from 19 3.5 from 22 4 from 25 4.5 from 28 5
• Sending on time good solutions of all homeworks increases the grade from the classes by half a degree.
• The grade 5 from the classes increases exam grade by one degree. Grades 4 and 4.5 increase exam grade by half a degree.
• Cheating on tests and exams will not be tolerated. If a student get caught cheating, the test/exam will be confiscated and rated to zero points.

# Course overview:

1. Mathematical logic. First order logic. Quantifiers. Basics of set theory.
2. Introduction to functions. Cartesian product. Relations. Functions. Basic function properties. Function composition and inversion. Images and preimages.
3. Univariate functions. Domain and range. Elementary functions. Absolute value.
4. Sequences. Arithmetic and geometric sequences. Partial sum of geometric series. Factorials. Sequence limit. The number e.
5. Function graphs. Continuity and points of discontinuity. Vertical and horizontal asymptotes. Monotonicity and extrema.
6. Limit of a function. Computing simple limits.
7. First order derivative. Geometrical interpretation. Tangent line and its equation. Main formulas of differential calculus.
8. Monotonicity and extrema of a differentiable function. Computing local and global extrema.
9. Second order derivatives. Computing derivatives. Convexity and a second derivative. The rate of change.
10. Applications of derivatives to economics. Elasticity and marginal costs. First and second order partial derivatives and partial elasticity. Local extrema of bivarate functions.
11. Univariate integral. Indefinite integral, basic integral calculus formulas. Definite integral and area.
12. Vectors and subsets of lines and line segments in lines, line segments and planes in generalization for bases, standard bases and dimension in.
13. Matrices. Matrix size, special matrices. Matrix algebra. Inverse matrices. Matrix equations.
14. Linear system. Row elementary operations - equivalent matrices. Solving linear system by elementary operations. General solutions. Basis solutions.
15. Determinants. Recursive Laplace definition. Properties of determinants. Cofactors and inverse matrices. Cramer's rule.
Sample exams from previous years
Contact: [email protected]