Mathematics 2 1200-1MATH2
List of topics:
Improper integrals – simplest cases.
Vectors on a plane and in space; operations on vectors; scalar product, vector product.
Systems of linear equations as an introduction to matrices; Cramer's formulas; eigenvalues of matrices, determinants; operations on matrices, in particular matrix multiplication; inverse matrices; diagonalization of matrices. Vector product using matrix determinants.
Continuity and differentiability of functions of many variables, derivative matrix (Jacobi matrix).
Differential operators (divergence, gradient, rotation, laplacian).
Second order partial derivatives, symmetry of of the second differential matrix. Local extremes, saddles.
Definition of an integral of a function of many variables, calculation of area and volume, calculation of integrals over simple areas on a plane and in space.
Connections between the differential operators and two-dimensional or three-dimensional integrals: Gauss’s and Stokes’ theorems.
Complex numbers: operations and various representations.
Elements of the theory of differential equations: equations with separated variables, linear equations. Solving second order linear equations with constant coefficients.
Total student workload: 220 hours, including:
- class participation: 90 hours
- homework: 40 hours
- preparation for classes, revision of previous material: 30 hours
- consultations: 15 hours
- preparation for tests and exams: 45 hours
Main fields of studies for MISMaP
Type of course
Mode
Requirements
Prerequisites (description)
Course coordinators
Learning outcomes
A student who has passed Mathematics 2 should:
• be able to solve systems of linear equations in various cases using matrix calculus;
• be able to use differential operators;
• be able to use differential calculus of functions of several variables to the extent necessary to study the properties of these functions (extrema);
• be fluent in complex numbers operations;
• know the theoretical foundations and techniques for solving typical ordinary differential equations, in particular linear problems.
• be able to use integral calculus of functions of several variables in simpler cases.
The student knows:
K_W03: mathematical concepts and understands the importance of mathematics as the foundation of science. Understands: the basics and methods of linear algebra, the basics and methods of differential and integral calculus.
The student is able to:
K_U03: use methods of linear algebra and methods of differential and integral calculus to solve selected chemical problems.
The student is ready to:
K_K01: determine the scope of their knowledge and skills and to improve their professional competences (in the field of mathematics).
Assessment criteria
During the semester, there are two tests and a written exam at the end. One can get a maximum of 40 points for each of these assignments.
Only those students who have scored at least 20 points on the two tests are eligible to take the exam. A total of less than 20 points on the two tests means that the course has not been passed.
Additionally, a maximum of 10 points can be obtained for active participation in classes.
According to the Polish grading system:
130-125 points (100% - 96%) - 5! (excellent)
124-112 points (95% - 86%) - 5 (very good)
111-100 points (85% - 76%) 4.5 (good +)
99-86 points (75% - 66%) 4.0 (good)
85-73 points (65% - 56%) 3.5 (satisfactory +)
72-60 points (55% - 46%) 3 (satisfactory)
Less than 60 points (0% - 45%) - 2 (unsatisfactory) = failure of the course.
Bibliography
„Mathematical Analysis II” Claudio Canuto, Anita Tabacco. Springer 2015
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: