Mathematics for Business and Finance

Subject

1. Functions (linear, non-linear, exponential, logarithmic). Solution metghods application on financial problem.
2. Nominal, real and compound interest, future value, present value, loan, installment, investment validation
3. Differentiation theory (numerical sequences, limits, function continuation, derivatives application, univariable function optimization, financial function optimization)
4. Differentiation theory application for financial problems solution, Overall and limited quantities, flexibility. Production, cost, income, profit usefulness functions. Financial functions optimization, dead points.
5. Integration theory (integrals, integration methods, financial applications of integrals)
6. Linear algebra (linear equation systems, vectors, matrixes, determinants
7. Multivariable functions (multivariable function derivation, partial derivatives application, multivariable function optimization). Complex function derivation.
8. Differential equations. Solution and application of 1^st and 2^nd order differential equations

Educational Aims

Aim of this course is to introduce students to the basic concepts of financing functions and terminology. Main target of this course is the training of students on handling financial problems using Mathematical tools like integrals, derivatives, differential equations, matrixes etc.

More specific, the lessons which are offered are from the following topics:

• Vectors, Matrixes, Determinants
• Linear equation systems, Function limits
• Derivatives, Integrals
• Multivariable functions, Partial derivatives
• Cost functions, Sale functions, Demand functions
• Limited financial quantities, Financial quantities variation rates
• Local extremum of financial quantities as a time function
• Customer surplus, Producer surplus, Social surplus
• 1^st order linear differential equations, 2^nd order linear differential equations

By the end of this course the student will be able to:

• Integrate financial functions and to interpret the results
• Predict the variation of a product price and quantity
• To determine the price and the price extremum of a product as a time function depending on market conditions
• Estimate the equilibrium price and quantity of a product
• Investigate the dynamic stability of a market equilibrium
• Exploit the capabilities that mathematical tools offer for the prediction and handling of products market
• know in-depth the basic theoretical knowledge about the subject
• use knowledge and understanding acquired in a manner that indicates a professional approach to their  work or profession
• have competences typically demonstrated by developing and supporting arguments and solving problems within their field of knowledge
• communicate information, ideas, problems and solutions to both specialist and non-specialist public
• develop knowledge acquisition skills needed to continue to post graduate studies with a high degree of autonomy
• gather and interpret relevant data (in their knowledge field) to form judgments that include reflection on relevant scientific issues

Student Evaluation

Written examination after the end of the semester (100%) including:

• Solving financial problems using mathematical tools
• Benchmarking theory elements

Bibliography

1. Essential Mathematics for Economics and Business, Bradley Teresa, Paperback: 682 pages, Publisher: John Wiley & Sons; 3rd Revised edition edition (27 May 2008), Language: English, ISBN-10: 0470018569.
2. Fundamental Methods of Mathematical Economics, Alpha C Chiang, Hardcover: 800 pages, Publisher: McGraw-Hill/Irwin; 3 edition (Feb. 1 1984), Language: English, ISBN-10: 0070108137
3. Financial Science Mathematics, Sarafopoulos George, Mylonas Nick, Publisher: Tziola, 1st edition, 2016 (in Greek language).
4. Invitation to Mathematics of Financial and Management Science Vol. B’, Loukakis Manolis, Publisher: Sofia, 1st edition, 2016 (in Greek language).