The following sections will be presented:

• Mathematical Induction – Functions – Graphs – Limits – Continuity – Basic Theorems of Continuous Functions – Supremum and Infimum

• Derivatives – Differentiation Rules – Monotonicity and Convexity – Rolle, Mean Value and L’Hopital Theorems – Derivative of Inverse Functions

• Integrals – Fundamental Theorem of Calculus – The Logarithmic and the Exponential Function – Elementary Methods of Integration

• Sequences – Convergence of Sequences – Cauchy Sequences

• Series – Convergence of Series – Convergence Criteria

The course constitutes an introduction to the fundamental notions of mathematical analysis that are extensively used in financial theory and analysis. Aim of the course is to present the analytic foundations needed for all the quantitative courses of the undergraduate program of studies, as well as the techniques required for the solution of a wide range of theoretical and analytical problems related to economics. The course also aims for the students to obtain a deeper understanding of the mathematical notions that will be presented during the lectures.

Upon successful completion of the course, the students will be able to

• prove mathematical relationships via the method of Mathematical Induction.

• interpret algebraically, numerically and graphically functions, and perform operations with them.

• compute, graphically, algebraically and via definition, limits of functions.

• interpret and apply, graphically, algebraically and via definition, the notion of continuity.

• interpret and compute the supremum and the infimum of a set.

• interpret graphically and compute algebraically the derivative of a function.

• compute the monotonicity, the convexity and the extreme points of non-trivial functions, concluding to the construction of their graph.

• interpret and compute via definition the definite integral of a function, as well as to apply it for finding areas of sectors.

• compute indefinite integrals via elementary methods, such as integration-by-parts and change-of-variable.

• interpret, graphically and via definition, the convergence of a sequence, and to compute its limit by L’ Hopital’s Rule.

• decide on the convergence of an infinite series subject to suitable convergence criteria.

• Adapting to new situations.

• Decision-making.

• Individual/Independent work.

• Critical thinking.

• Development of free, creative and inductive thinking.

Written exam (100%) that includes:
• Choice of questions.
• Questions on theory.
• Problem solving questions.

This is a 2-hour written exam. The individual evaluation grades are explicitly written next to each question.

-Suggested bibliography:

• M. Spivak, Διαφορικός Ολοκληρωτικός Λογισμός, ITE – Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2010.

• Μ. Φιλιππάκης, Εφαρμοσμένη Ανάλυση και Στοιχεία Γραμμικής Άλγεβρας, Εκδόσεις Τσότρας, Αθήνα, 2017.

• Θ. Ρασσιάς, Μαθηματικά Ι, Εκδόσεις Τσότρας, Αθήνα, 2017.

• Δ. Κραββαρίτης, Μαθήματα Ανάλυσης, Εκδόσεις Τσότρας, Αθήνα, 2017.