Mathematics 1 1200-1MATH1
List of topics:
Sequences and limits of sequences: definitions, various
criteria for convergence.
Continuity of functions; limits of functions. Differentiality;
definition of derivative; counting derivatives by definition
and by using differentiation rules.
Investigation of functions (critical points and monotonicity;
inflection points and convexity; asymptotes).
Simultaneously, applying the new piece of knowledge:
revision of definitions and properties of basic functions (sine,
cosine, tangent, cotangent, logarithm, exponential, roots).
Introduction of cyclometric functions (arc-functions).
Primal function. Integration as an inverse operation to
2differentiation.
Calculation of indefinite integrals.
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, especially - matrix multiplication;
inverse matrix; diagonalization of matrices. Vector product
using matrix determinants.
Optimization tasks.
Taylor formula and Taylor series.
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
Type of course
Mode
Course coordinators
Learning outcomes
A person who has passed Mathematics 1 should:
• be fluent in using elementary functions;
• have basic knowledge of vector spaces;
• understand the concepts of: numerical sequence; sequence limit; function limit; be able to examine the existence of limits and find the limits of sequences and functions
• understand the concept of a derivative; be able to use differential calculus of single-variable functions to the extent necessary to examine the properties of these functions
• understand the concept of an integral; be able to use integral calculus of single-variable functions;
• be able to approximate elementary functions with polynomials, expand elementary functions into Taylor series, and have basic knowledge of series convergence.
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 I” 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: