Differential and Integral Calculus I
Course Syllabus
| Course Code: | Α3Υ |
| Semester: | 1st |
| ECTS units: | 5 |
| Weekly Teaching Hours: | 5 |
| Course Page: | https://eclass.duth.gr/courses/TME166/ |
| Instructors: | SPARTALIS STEPHANOS |
Course Description
Sets, relations, functions. Elements of combinatorial analysis. Elements of the theory of real numbers and real functions. Limits and continuity of functions. Derivative function of a real function of a real variable. Geometric interpretation. Higher order derivative. Differential and linear function approximation. Exponential, logarithmic and trigonometric functions. Study of a graph of a function. The indefinite integral. Methods of integration. The Riemann definite integral – Applications. Generalized integrals. Taylor- McLaurin polynomials. Sequences – Series.
Purpose of the course
To introduce students to a comprehensive view of the properties and basic rules of infinitesimal calculus thinking concerning the study of real functions of a real variable. Familiarization with the concepts of continuity, limit, marginal or instantaneous measure of change, “infinitesimal sum”, error, counterfactuals, etc. Practice on the techniques and methods of integration and derivation.
