Courses list

Wersja polska

Course code: RSSS10152o14
Semester: 2014/2015 summer
Name: Mathematics 2
Major: Environmental Protection
Study Type: first cycle
Course type: compulsory
Study Semester: 2
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: Antiderivatives and Indefinite Integration. Basic Integration Rules. Applying Integration Rules. Integration by Substitution. Integration by Parts. Techniques of integration. Review of Integration Techniques by substitution. Definite Integral. Rimann Sums. Fundamental Theorem of calculus. Properties of the definite integral. Indefinite integrals and integration rules. Trigonometric integrals. Trigonometric substitution. Partial fractions. Improper integrals. Trapezoidal and simpson’s rule. Volumes (Cross-sectional and shell methods). Length of curves. Surface area. Moments and centers of gravity. Area in polar coordinates. Functions of Several Variables. Limits and Continuity. Partial Derivatives, Chain Rule and Directional Derivatives. The Gradient, Tangent Plane Approximation and Differentials. Extreme Value. Application for Extreme Value Finding: Least Square Method. Example of Differential Equation. First-Order Linear Differential Equation.

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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