for the Fall semester course of 2018-2019

The Calculus course is based on the third edition of the book of Knut Sydsaeter Peter Hammond Essential Mathematics for Economic Analysis. The Course Syllabus contains more detailed information. The most important part is as follows:

• Attendance is compulsory in the classes.
• The Office Hours is in S 208/b at Friday 9.00 am. Registration via e-mail is required not later then 10. pm of the actual day before.
• Grading: You will receive 5-5 points at maximum for your 4 Mini quizes and 30 points for the Final exam. Thus 50 points can be collected. 20 points is the limit to not to fail.
• Handouts compiled by the instructor are available here, after each classes.

The week by week schedule is as follows.

1. Sequences
   • Definition of limit of sequences
   • Infinite sequences
   • The squeezing principle for sequences
   • The Euler number <\math e>
2. Series
   • Definition of limit of series
   • The geometric series
   • Convergence tests
   • Absolute convergence
3. Limit and continuity of functions
   • Definition of limit of functions
   • The squeezing principle for functions
   • One side limits
   • Definition of continuity
   • Properties of continuos functions
4. Derivative of functions
   • The concept of the derivative
   • The equation of the tangent line
   • Rules of derivation
   • The concept of the composition of functions
   • Chain rule
   • Mini quiz 1
5. Lagrange’s mean value theorem
   • Inverse function
   • Derivative of the inverse function
   • Derivative of the exponential and logarithm functions.
   • Higher order derivatives
   • The necessary conditions for the extreme value
   • Mean value theorem
   • Increasing and decreasing functions
   • Looking for a local extreme value
6. Discussion of functions
   • L’Hospital rule
   • Second order conditions
   • Convexity
   • Mini quiz 2
7. Integral
   • The concept of the anti-derivative
   • Integral of elementary functions
   • The concept of the integral
   • The fundamental theorem of calculus
8. Technique of integration
   • Integration by parts
   • Substitution
   • Linear differential eqautions
9. Improper integral
   • Definition of impreper integral
   • Integral on the real line
   • Integration by parts
   • Harmonic series
10. Power series
    • The sum of the power series
    • Radius of convergence
    • Derivation and integration of power series
    • Taylor expansion
    • Expansion of the exponential function
    • Mini quiz 3
11. Review
    • Practice
    • Mini quiz 4