The goal of the class Infinitesimal Calculus Ι is to provide the basic tools of mathematics needed by engineers in the theoretical part and the calculating part of his/her education.

With the successful completeness of the course the student should know:

• The method of induction.
• Calculate limits of sequences, extremes of functions, Integrals, sums of series, areas of regions, volumes of solids with given sections, center of mass, moments of inertia.
• Expand functions to power series and calculate the values of basic functions to any given error.
• Study functions through their graphs.
• Approximate functions with polynomials and estimate the error of the approximation.
• Evaluate the work of a power in linear movement and the hydrostatic pressure in plane regions.

• Search, analysis and synthesis of data and information.
• Independent work.
• Team work.
• Work in scientific environment.
• Produce free deductive thinking.

1. Real numbers.
2. Principle of Mathematical Induction.
3. Sequences
4. Series (criteria of convergence).
5. Limits and continuity of functions. Derivative of function, differential of functions.
6. Application of derivatives in the study of functions.
7. Definite Integral. Fundamental Theorems of Integral Calculus.
8. Applications of the Integral.
9. Calculation of areas, volumes, areas, and volumes of solids of revolution.
10. Applications in Physics (Inertia and center of mass, Work, Hydrostatic pressure).
11. Indefinite Integral. Techniques of Integration.
12. Improper Integrals.
13. Power series and Taylor series. Applications of Power series.

Assessment Method

Final exam, written (100 %).

• THOMAS ΑΠΕΙΡΟΣΤΙΚΟΣ ΛΟΓΙΣΜΟΣ,  George B. Thomas , Jr., Joel Hass, Christopher Heil, Maurice D. Weir
• Απειροστικός λογισμός, Briggs William, Cochran Lyle, Gillett Bernard, Εκδόσεις Κριτική