MATHEMATICAL ANALYSIS I

General Info

• Course Title: Mathematical Analysis I
• Course Code: NAOME1101
• Semester: 1st
• Course Type: G.B.¹
• Weekly Teaching Hours: 4 (Lectures)
• Credits (ECTS): 5
• Offered to ERASMUS+ students: Yes
• Course Website: https://eclass.uniwa.gr/modules/course_home/register.php?course=NA185
• Professors: Evagellos Mellas, Dimitrios Mitsoudis

Course Content / Syllabus

1. Real functions Even and odd functions, monotonicity, periodicity. Common functions, Sums, Differences, Products, and Quotients. 2. Limits and continuity Limit of a function and limit laws. Precise definition. Continuity: Definition, properties, basic theorems. 3. Differentiation Rates of change, Tangents and the Derivative at a Point. The derivative as a function. Differentiation rules. The chain rule. Applications of derivatives: Extreme values of functions, Mean value theorem, Monotonic Functions and the first derivative test, Concavity, Applied optimization. Linearization and differential, Taylor’s polynomial. 4. Integration Area and estimation with finite sums. Definition and properties of Riemann integral, Applications. 5. The relationship between differentiation and integration Indefinite integral. The fundamental theorem of Calculus. Techniques of integration. Improper integrals. 6. Sequences and series Sequences. Infinite series: Definition, properties, convergence tests. Power series. Taylor and Maclaurin series. 7. Complex numbers Definition, arithmetic operations. Conjugate, modulus and argument of a complex number, Polar and exponential form. Square root, logarithm and powers of a complex number. Elementary complex functions.

Course Outline