Mathematics for Economists I - JPB456

• Title: Mathematics for Economists I
• Czech title: Matematika pro ekonomy I
• Guaranteed by: Department of Political Science (23-KP)
• Faculty: Faculty of Social Sciences
• Actual: from 2024 to 2024
• Semester: winter
• E-Credits: 6
• Examination process: winter s.:
• Hours per week, examination: winter s.:1/1, Ex [HT]
• Capacity: unlimited / unknown (25)
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: taught
• Language: English
• Teaching methods: full-time
• Note: course can be enrolled in outside the study plan; enabled for web enrollment; priority enrollment if the course is part of the study plan
• Guarantor: Ing. Petr Špecián, Ph.D.
• Teacher(s): Ing. Pavel Potužák, Ph.D.

Annotation

The course aims to introduce students to the fundamentals of mathematics for economists, covering essential topics such as calculus and optimization techniques. It provides a mathematical foundation necessary for understanding and solving economic models and quantitative analysis.

Last update: Špecián Petr, Ing., Ph.D. (01.10.2024)

Course completion requirements

Final test for 100 points.

Last update: Špecián Petr, Ing., Ph.D. (01.10.2024)

Literature

Simon, Carl P., Blume, Lawrence E. Mathematics for Economists. 1st edition. W.W. Norton & Company, 1994. ISBN: 978-0393957334.

Last update: Špecián Petr, Ing., Ph.D. (01.10.2024)

Syllabus

1. Introduction. Economic Models, Assumptions, Endogenous and Exogenous Variables, Equilibrium 

2. One-Variable Calculus. Foundations, Functions on R, Linear Functions, The Slope of Nonlinear Functions, Computing Derivatives, Differentiability and Continuity, Higher-Order Derivatives, Approximation by Differentials

3. One-Variable Calculus: Applications. Using the First Derivative for Graphing, Derivatives and Convexity, Graphing Rational Functions, Tails and Horizontal Asymptotes, Maxima and Minima, Applications to Economics

4. One-Variable Calculus: Chain Rule. Composite Functions and the Chain Rule, Inverse Functions and Their Derivatives

5. Exponents and Logarithms. Exponential Functions, Logarithms, Properties of Exp and Log, Derivatives of Exp and Log, Applications

6. Functions of Several Variables. Functions between Euclidean Spaces, Geometric Representation of Functions

7. Calculus of Several Variables. Definitions and Examples, Economic Interpretation, Geometric Interpretation, The Total Derivative, The Chain Rule, Directional Derivatives and Gradients

8. Unconstrained Optimization. First Order Conditions, Second Order Conditions, Global Maxima and Minima, Economic Applications

9. Constrained Optimization: First Order Conditions. Equality Constraints, Examples and Applications

10. Integral Calculus. Indefinite Integrals, Definite Integrals, Improper Integrals, Economic Applications

Last update: Špecián Petr, Ing., Ph.D. (01.10.2024)