| i. Continuity at a point and in a region of multivariable functions.
ii. Partial derivative and differentiability of functions of several variables
iii. Functional determinant and implicit functions
iv. Taylor expansion
v. Extremum points and conditional extremum points
vi. Vector Analysis
vii. Dot, cross and mixed product of vectors
viii. Curves in space, Frenet formulas, Surfaces
ix. Hamilton operator, directional derivative, vector operators
x. Multiple integrals, curve and surface integrals, Green’s, Gauss’ and Stokes’ theorems.
APPLIED MATHEMATICS II
PERDIOU ANGELA, PETROPOULOU EUGENIA
|LANGUAGE OF INSTRUCTION and EXAMINATIONS||
|This course is one of the basic courses of Applied Analysis taught in the Department and focuses on the field of multivariable calculus.
The goals are to give the student of civil engineering the knowledge of advanced applied engineering mathematics that he/she needs in his/her science in the areas of differential and integral calculus of functions of several variables and of vector analysis. This knowledge is necessary and is used in many subsequent specialization courses in civil engineering, as well as in the subsequent course Applied Mathematics III of the 3rd semester.
At the end of the course the student will have developed the following skills and competencies:
1. To be able to efficiently use the differential and integral calculus of multivariable functions, as well as vector analysis.
2. To be able to mathematically formulate and solve problems of civil engineering which make use of the above mathematical areas.
3. To be able to efficiently use the computer and computer algebra software in mathematics and civil engineering applications.