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
Course coordinators
Type of course
Mode
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