Courses list

Wersja polska

Course code: RESS10145o14
Semester: 2014/2015 winter
Name: Mathematics
Major: Economics
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 8
Hours (Lectures / Tutorials / Other): 30 / 30 / 0
Lecturer: dr hab. Ryszard Deszcz
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: Algebra, Calculus I and II, Bacic probability according Course Plan (see below). ALGEBRA: 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.Calculus I Functions: Points and lines in the plane. Functions. Graphs. Aids to graphing. Combining functions. Trigonometric functions.Limits and continuity: Definition of limit. Basic limit theorems. One-side limits. Continuity. Intermediate value theorem. Derivatives: Derivative definition. Differentiable functions. Derivatives of combinations of functions. Chain rule. Higher derivatives. Implicit differentiation. Related rates. Application of the derivative: Maximum and minimum values. Mean value theorem. Application of the mean value theorem. Application of extreme values. Concavity and inflection points. Limits and infinity. de’Hospital rule.Taylor theorem. Calculus II Integral: Definite Integral. Properties of the definite integral. Fundamental theorem of calculus. Indefinite integrals and integration rules. Integration by substitution.Techniques of integration: Integration by parts. Trigonometric integrals. Trigonometric substitution. Partial fractions. Improper integrals. Trapezoidal and simpson’s rule. Applications of the integral: Volumes (Cross-sectional and shell methods). Length of curves. Surface area. Moments and centers of gravity. Area in polar coordinates.PROBABILITY: Sample space, events and probability of events. Conditional probability. Concept of random variable. Discrete and continuous probability distribution. Mean of a random variable. Variance and covariance. Some discrete and continuous probability distribution. Normal distribution. Course Responsible: Prof. Dr. Leszek Kuchar (Department of Mathenatics, Wroclaw University of Environmental and Life Sciences).

Recommended literature: Krysicki W. Włodarski L. : Mathematical Analysis and Exercises, PWN Editions from 8th to 15th Warsaw 1990-2010 (in Polish). Krysicki W. Bartos J. Dyczka W. Królikowska K. Wasilewski M. : Probability with Statistics and Exercises, Part I, PWN Ed., Warsaw, 2013 (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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