Students in economics and business should be familiar with basic mathematical techniques and comfortable with applying the corresponding mathematical tools in practice.
The books Mathematics A and Mathematics B are written for students of economics and business. It presents the basic mathematical techniques and intends to help students achieve the level of understanding needed to approach the economic and business literature. The book alternates between a rigorous treatment of several topics and examples and applications.
The books also aim to assist students in further developing their mathematical logic. This is important for students to become acquainted with mathematical methods. Experience shows that for non-mathematicians the main difficulty often consists in formalizing practical problems into mathematical statements or expressions. This is a crucial step if one wishes to obtain some help from mathematics. However, the mathematical way of structuring arguments often represents a serious obstacle to non-mathematicians. Therefore, the books attempt to explain and describe verbally the logical arguments needed to derive a specific mathematical framework or expression. Also, when presenting economic applications, the book emphasizes the economic interpretation of mathematical conditions or assumptions.
The content
Covered by Mathematics A (English) and Mathematik A (German)
- mathematical logic
- sequences
- series
- financial mathematics
- functions
- exponential function
- logarithms
- properties of continuous functions
- derivatives
- limits and differentiability
- differentials
- rate of change
- elasticities
- properties of differentiable functions (extreme points, monotonicity, concavity)
- Taylor polynomials
- functions of two variables
- contour lines
- partial derivatives
- total differentials
- partial elasticities
- implicit function theorem
- homogeneous functions
- production functions.
Covered by Mathematics B (English) and Mathematik B (German)
- extreme points without constraints
- extreme points with constraints
- definite integral
- indefinite integral
- improper integral
- fundamental theorem of calculus
- applications of integration (density functions, surfaces)
- operation with matrices
- inverse matrix
- determinants
- properties of vectors
- linear dependence and independence of vectors
- rank of a matrix
- gradient
- vector spaces
- existence and uniqueness of solutions of systems of linear equations
- Gaussian method
- eigenvalues and eigenvectors
- difference equations of order one