Vector Calculus Semester




НазваниеVector Calculus Semester
Дата20.09.2012
Размер7.23 Kb.
ТипДокументы
Vector Calculus

Semester: Ι

Course description: 1st and 2nd week. Linear spaces, subspaces, bases and dimension. Linear systems, equation of the plane, geometric interpretation of linear systems. Linear maps.

3rd and 4th week. Functions of several variables (scalar fields), level sets, graph of a function of two variables. Partial derivatives.

5th and 6th week. Gradient of a scalar field, properties of gradient. Vector fields, divergence and curl. Vector identities.

7th week. Taylor’s theorem, extrema.

8th week. Line integrals and applications.

9th and 10th week. Double and triple integrals, surface integrals. The theorems of Green, Stokes and Gauss.

11th and 12th week. The classical equations of mathematical physics: Laplace equation, the wave equation, the diffusion equation, Maxwell’s equations, Navier-Stokes equation.

13th week. Applications in geometry and physics.

Courses (hours / week): 4

Laboratory (hours / week): 1.5 (Practice with MATHEMATICA).

ECTS: 6

Grading: Final exam.

Class Notes: Vector Calculus 2011, 100 pages (in Greek).

Suggested Reading:

M.R. Spiegel, Schaum's outline of theory and problems of advanced mathematics, (Schaum's).

R.L. Finney, M.D. Weir, F.R. Giordano, Thomas' Calculus (Addison-Wesley 2002).

J.E. Marsden and A.J. Tromba, Vector Calculus (W.H. Freeman & Company 1996).

H.M. Schey, Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, (W.W. Norton and Company 2005).

D. Bachman, Advanced Calculus Demystified (McGraw-Hill 2007).

A.J. Chorin and J.E. Marsden, A Mathematical Introduction to Fluid Mechanics, (Springer 2000).

I.M. Cohen and P.K. Kundu, Fluid Mechanics, (Academic Press 2007).

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