ECTS
ECTS Course Catalogue
Course details
Course code: RSSS10037o15Semester: 2015/2016 winter
Name: Mathematics 1
Major: Environmental Protection
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 4
Hours (Lectures / Tutorials / Other): 15 / 30 / 0
Lecturer: Prof. Dr. Leszek Kuchar
Language of instruction: Polish
Learning outcomes: Knowledge: This course provides an introduction to the advanced mathematics. It is designed to give the student basic competence in the application and interpretation of mathematics through a functions to the calculus and introduction to probability. Upon completion of this course students will: appreciate and understand the role of applied mathematics in his field, develop an ability to apply appropriate methods to summarize and analyze mechanism or process in economy. Skills: It is expected, the student will be able to report the results in appropriate table or graph for inclusion in your thesis or paper, interpret results and appropriate math techniques.
Competences: Social competence: Understands the need to work in interdisciplinary teams especially. Is aware of the need for continuous training and improvement of the knowledge in the field of mathematics and basic probability. Apply the principles of occupational health and safety.
Prerequisites: Basic mathematics
Course content: Determinants, definition. Properties of determinants. Transposition, effect of elementary row operations, multilinearity. Laplace expansion method. Matrix representation of a linear transformation. Matrix operations. Inverse matrices. The rank of a matrix.Linear systems and their solutions. Cramer’s rule for solving n equations in n unknowns. Gaussian elimination. Eigenvalues and eigenvectors. Points and lines in the plane. Functions. Graphs. Aids to graphing. Combining functions. Fitting Functions to Data Polynomial, Trigonometric, Exponential and Logarithmic functions. Definition of limit. Basic limit theorems. One-side limits. Continuity. Intermediate value theorem. Symbol e. Definition and Natural Logarithm. Derivative definition. Tangent line Problem. Differentiable functions. Derivatives of combinations of functions. Chain rule. Higher derivatives. Implicit differentiation. Related rates. Derivatives and Review Excercises. Maximum and minimum values. Mean value theorem. Application of the mean value theorem. Application of extreme values. Concavity and inflection points. Limits and infinity. Rolle’s Theorem. Taylor Theorem. de’Hospital rule.
Recommended literature: Krysicki W. Włodarski L. : Mathematical Analysis and Exercises, Part I. PWN Editions from 8th to 15th Warsaw 1990-2010 (in Polish). Krysicki W. Włodarski L. : Mathematical Analysis and Exercises, Part II. PWN Editions from 8th to 15th Warsaw 1990-2010 (in Polish).
Assessment methods: Knowledge: Written exam. Skills: Assessment of analysis and interpretation of simple economic problems. All exam answers must be own, and must not provide any assistance to other students during exams. The final exam will be comprehensive. Homework assignments will be submitted almost every week.
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