MATHEMATICAL ANALYSIS II

General Info

• Course Title: Mathematical Analysis II
• Course Code: NAOME1108
• Semester: 2nd
• Course Type: G.B.¹
• Weekly Teaching Hours: 5 (Lectures)
• Credits (ECTS): 6
• Offered to ERASMUS+ students: No
• Course Website: https://eclass.uniwa.gr/courses/NA216/
• Professors: D. Mitsoudis

Course Content / Syllabus

1. Introduction to Ordinary Differential Equations Definition, First order linear Ordinary Differential Equations (O.D.E.’s), Second order linear O.D.E.’s with constant coefficients. Laplace transform and its application for solving O.D.E.’s. 2. Functions of several variables Definition, graphs, Limits and Continuity in Higher Dimensions. Partial derivatives, Chain rule, Directional derivatives and gradient vectors, Tangent Planes and Differentials. Extreme Values and Saddle Points, Lagrange Multipliers. Taylor's formula for two variables 3. Vector-valued functions Definition, limits and continuity. Differentiation and integration. Parametric equations of curves. 4. Vector Calculus Scalar and vector fields. Differential operators (div, grad, curl). Conservative vector fields. 5. Line and surface integrals Line integrals: definition for a scalar field, derivation, applications. Definition for a vector field, derivation, applications. Path independence. Surface integrals: parametric representation of a surface, the fundamental vector product, surface element, definition and evaluation of surface integral. 6. Multiple integrals Double and triple integrals, properties, techniques of integrations, Substitutions in multiple integrals, Green’s theorem, Stokes’ theorem.

Course Outline