Courses

  Topological spaces, examples, closure of a set, derived set, subspace, topology, Bases, finite product topology, subbases. Metric spaces, examples, metrizability, Rn  as a metrizable space. Continuous functions, characterization of continuous...
يتم فيه مناقشه تكامل ريمان بصوره اكثر عمق وشمول مع دراسه الخصائص التي تمر المرور عليها في مقررات سابقه   وكلك دراسه المتسلسلات والمتتاليات وخصائصها وفي الفصلين الاخيرين يتم دراسه تكامل ليبق  وخصائصه والفرق بينه وبين تكامل ريمان المعروف 
Description of the course: Caresian ,cylinderical and spherical coordinate systems. Functions of two and three variables. Limits and continuity. partial derivative, the chain rule, extrema of functions of two variables, Lagrange multiplier. Double...
حساب التقارير، التكافؤ المنطقي، الحجج، طرائق البرهان، العلاقات، علاقة التكافؤ، علاقة الترتيب، الجبر البولي، الدارات المنطقية وتبسيطها، الرسوم، الترابط، التماثل، الرسوم المستوية، الأشجار، تطبيقات. Book: Discrete Mathematics and its Applications,...
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. Vector spaces, linear independence, finite dimensional spaces, linear subspaces. Inner product spaces. Linear...
Bounded subsets of the real line; supremum and infimum, completeness axiom; convergent sequences, Cauchy criterion, subsequences; series of numbers, generalized tests of convergence; limits of functions, continuity on an interval, intermediate value...
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...
Main Reference :Multivariable Calculus by J.Corwin and H.Szczarba  
Matrices and their operations. Types of matrices. Elementary transformations. Linear systems of equations. Determinants, elementary properties. Inverse of a matrix. Vector spaces, linear independence, finite dimensional spaces, linear subspaces....
Main  Reference A First Course in Differenatial Equations with modeling Applications  7th edition by:Dennis G.Zill
Main Reference:A trasition to Advanced Mathematics,7th edition, ByDouglas smith,Maurice Eggen,Richard St.Andre.
Basic properties of the field of real numbers, completeness axiom, countable sets. Sequences and their convergence, monotone sequence, Bolzano-Weierstrass theorem, Cauchy criterion. Basic topological properties of the real numbers. Limit of a...