Mathematics for students of economics, finance and management
- Autor: Barbara Batóg Beata Bieszk-Stolorz Iwona Foryś Małgorzata Guzowska Krzysztof Heberlein
- Wydawca: Difin
- ISBN: 978-83-66491-43-4
- Data wydania: 2021
- Liczba stron/format: 252/B5
- Oprawa: miękka
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The theory is presented in an accessible way necessary to solve the proposed tasks. Each chapter contains examples to help to understand the theory and exercises to be solved by students (with answers). This form of presentation of individual issues facilitates individual work, especially for part-time students.
The textbook has been supplemented with a chapter containing practical usage of mathematics in economics, finance, and management. The textbook is the result of many years of teaching experience of the authors during lectures, exercises and consultations with students. All of the chapters are written by scholars working in the Department of Econometrics and Statis- tics, Institute of Economics and Finance at the University of Szczecin.
Table of Contents:
Preface
Chapter 1. INITIAL ISSUES
1.1. Logical sentences and their properties
1.2. Propositional function. Quantifiers
1.3. Set algebra
1.4. Cartesian product
1.5. Relations
1.6. Functions
1.7. Operations and groups
1.8. Vector space and its properties
Chapter 2. MATRICES
2.1. Matrix definition and types
2.2. Operations on matrices
2.3. The determinant of a square matrix
2.4. Inverse matrix
2.5. The rank of a matrix
2.6. Matrix equations
Chapter 3. SYSTEMS OF LINEAR EQUATIONS
3.1. Definition and types of systems of linear equations
3.2. Cramer’s system (Cramer’s rule) 586 Table of Contents
3.3. Methods of solving systems of linear equations
3.4. Homogeneous systems of linear equations
3.5. Gaussian elimination
3.6. Eigenvalues of matrices
3.7. Quadratic forms
Chapter 4. LIMITS AND CONTINUITY
4.1. Metric space
4.2. Sequences and their properties
4.3. Limits of sequences
4.4. Limits and continuity of functions
4.5. Asymptotes
Chapter 5. DERIVATIVE OF A FUNCTION AND ITS APPLICATIONS
5.1. Derivative and differential of functions
5.2. Monotonicity and extrema of functions
5.3. Concavity and inflection points
5.4. L'Hospital's rule
5.5. Sketching graphs of functions
Chapter 6. FUNCTIONS OF MANY VARIABLES AND THEIR EXTREMA
6.1. Definition of a function of many variables
6.2. Partial derivatives
6.3. Higher-order partial derivatives
6.4. Total differential
6.5. Extrema of functions of many variables
6.6. Constrained (conditional) extrema
Chapter 7. INTEGRAL CALCULUS
7.1. Indefinite integral and its properties
7.2. Integration by substitution
7.3. Integration by parts
7.4. Integration of rational functions
7.5. Definite integral and its properties
7.6. Application of definite integral
7.7. Improper integrals
Chapter 8. APPLICATIONS IN ECONOMICS, FINANCE, AND MANAGEMENT
8.1. Application of systems of linear equations
8.2. Application to input-output analysis in economics – Leontief model
8.3. The market(s) model and national income models
8.4. Elements of financial mathematics
8.5. Application of differential calculus
8.6. Application of integral calculus
Appendix 1. ELEMENTARY FUNCTIONS AND THEIR PROPERTIES
Appendix 2. SPECIAL MATHEMATICAL FORMULAS
Index
References
Barbara Batóg
absolwentka matematyki, doktor nauk ekonomicznych, specjalność statystyka i ekonometria, Katedra Ekonometrii i Statystyki Instytutu Ekonomii i Finansów Uniwersytetu Szczecińskiego.
Master of mathematics, doctor of economics, specializing in statistics and econometrics.
Beata Bieszk-Stolorz
dr hab. prof. US, absolwentka matematyki, doktor nauk ekonomicznych, specjalność statystyka, ekonometria i analiza trwania, Katedra Ekonometrii i Statystyki Instytutu Ekonomii i Finansów Uniwersytetu Szczecińskiego.
Master of mathematics, habilitated doctor of economics, specializing in statistics, econometrics, and duration analysis.
Iwona Foryś dr hab., profesor Uniwersytetu Szczecińskiego, wieloletni wykładowca na kierunkach związanych z zarządzaniem nieruchomościami, studiach podyplomowych oraz kursach specjalistycznych polskich i zagranicznych uczelni. Autorka licznych publikacji, monografii i artykułów, ekspertyz dla praktyki z zakresu gospodarowania nieruchomościami, zarządzania nieruchomościami mieszkalnymi i komercyjnymi. Licencjonowany zarządca nieruchomości, aktywny członek Polskiego Stowarzyszenia Zarządców Nieruchomości. Książki autora
Małgorzata Guzowska
absolwentka matematyki, doktor habilitowana nauk ekonomicznych, specjalność ekonomia matematyczna, Katedra Ekonometrii i Statystyki Instytutu Ekonomii i Finansów Uniwersytetu Szczecińskiego.
Master of mathematics, habilitated doctor of economics, specializing in mathematical economics.
Krzysztof Heberlein
absolwent matematyki, doktorant nauk ekonomicznych, specjalność statystyka i ekonometria, Katedra Ekonometrii i Statystyki Instytutu Ekonomii i Finansów Uniwersytetu Szczecińskiego.
Master of mathematics, Ph.D. candidate in economics, specializing in statistics and econometrics.