المواد الدراسية
Definition of Definite Integral and its Properties, The Anti-derivative, Indefinite Integral and the Fundamental Theorem of Calculus. Change of Variables. Integrals of natural and general exponential functions. Integrals of natural and general...
Matrices and their operations., types of matrices Elementary transformations. Determinants, elementary properties. Inverse of a matrix. Linear systems of equations. Vector spaces, linear independence, finite dimensional spaces, linear subspaces....
The definite integral, fundamental theorem of calculus, the indefinite integral, change of variable, numerical integration. Area, volume of revolution, work, arc length. Differentiation and integration of inverse trigonometric functions. The...
Topological spaces: Definition and examples of topological spaces, Comparison between topological spaces, Open and closed sets, Closure of a set, Interior, boundary , exterior and derived sets, Subspaces. Basis: Definition and examples,...
Introduction to Differential Geometry
Theory of curves in space. Regular curves and reparametrization, Serret-Fernet apparatus, existence and uniqueness theorem for space curves. Local theory of surfaces: Simple surfaces, coordinate transformations...
Vectors in two and three dimensions, scalar and vector products, equations of lines and planes in 3-dimensional space. Surfaces of revolution an their equations in cylindrical and sperical coordinates. Vector valued functions of a real variable,...