Mathematics 0
General data
Course ID:  10001MAT01  Erasmus code / ISCED:  (unknown) / (unknown) 
Course title:  Mathematics 0  Name in Polish:  Matematyka 0 
Department:  Faculty of Mathematics, Informatics, and Mechanics  
Course groups: 
(in Polish) Przedmioty minimum programowego  zamienniki dla studentów 1go semestru (S1CH) 

ECTS credit allocation (and other scores): 
9.00 view allocation of credits 

Language:  Polish  
Type of course:  obligatory courses 

Short description: 
Basic properties of elementary functions like the sine, cosine, logarithm and exponential function. Derivatives of elementary functions and techniques of differentiation. Basic properties of vectors and matrices, introduction to linear algebra. Mathematics 0 differs from Mathematics A only in the number of problem sessions. Students who have chosen Mathematics 0 take part in problem sessions three times a week, while those who have chosen Mathematics A  twice a week. 

Full description: 
Definitions of elementary functions: sine, cosine, tangent, exponential function, logarithms, root functions. Inverse trigonometric functions. Limits of functions. Continuity: intermediate value theorem, Weierstrass Maximum Principle. Definition of the derivative. Tangent to the graph of a function. Differentiation rules. Sketching graphs of functions: monotonicity, convexity, inflection points, locally extreme values. Taylor formula with Lagrange remainder and Peano remainder, approximation, error estimates. Taylor series. Primitive function. Simple integrals. Basic techniques of integration: substitution and integration by parts. Vectors in the plane and in the 3dimensional space. Scalar product and vector product. Matrices: addition, multiplication by a number and by a matrix. Determinants. Linearity with regard to columns or rows, skew symmetry, row reduction, Cramer's formulae, eigenvalues and eigenvectors. Orthogonal matrices, symmetric matrices, transposed matrix. Prerequisities: basic high school algebra, solving of linear systems with 2 or 3 unknowns, canonical form of a quadratic trinomial, second degree equations and inequalities, polynomial factorization by finding rational roots or by grouping terms in simple cases. 
Classes in period "Winter semester 2020/21" (past)
Time span:  20201001  20210131 
see course schedule 
Type of class: 
Class, 90 hours more information Lecture, 30 hours more information 

Coordinators:  Marcin Chałupnik  
Group instructors:  Marcin Chałupnik, Michał Korch, Łukasz Kubat, Bartosz Źrałek  
Students list:  (inaccessible to you)  
Examination:  Examination 
Copyright by University of Warsaw.