Integration theory | Signed measure | Msc3 mathematics скачать в хорошем качестве

Integration theory | Signed measure | Msc3 mathematics

Integration Theory and Functional Analysis Mac3 Sem #mscmathematics #mathematics #prsuuniversity #yksahu Signed measure, Hahn decomposition theorem, Jordan decomposition theorem, Mutually singular measure, Radon- Nikodym theorem. Lebesgue decomposition, Lebesgue-Stieltjes integral, Product measures, Fubini’s theorem. Baire sets, Baire measure, Continuous functions with compact support, Regularity of measures on locally compact support, Riesz-Markoff theorem. Unit II Normed linear spaces, Metric on normed linear spaces, Holder’s and Minkowski’s inequality, Completeness of quotient spaces of normed linear spaces. Completeness of l p , Lp , Rn , Cn and C [a, b]. Bounded linear transformation. Equivalent formulation of continuity. Spaces of bounded linear transformations, Continuous linear functional, Conjugate spaces, Hahn-Banach extension theorem (Real and Complex form), Riesz Representation theorem for bounded linear functionals on Lp and C[a,b]. Unit III Second conjugate spaces, Reflexive spaces, Uniform boundedness principle and its consequences, Open mapping theorem and its application, projections, Closed Graph theorem, Equivalent norms, weak and strong convergence, their equivalence in finite dimensional spaces. Unit IV Compact operations and its relation with continuous operator. Compactness of linear transformation on a finite dimensional space, properties of compact operators, Compactness of the limit of the sequence of compact operators. The closed range theorem. Inner product spaces, Hilbert spaces, Schwarz’s inequality, Hilbert space as normed linear space, Convex sets in Hilbert spaces. Projection theorem. Unit V Orthonormal sets, Bessell’s inequality, Parseval’s identity, Conjugate of Hilbert space, Riesz representation theorem in Hilbert spaces. Adjoint of an opertor on a Hilbert space, Reflexivity of Hilbert space, Self-adjoint operator, Positive operator, Normal and unitary operators, Projections on Hilbert space, Spectral theorem on finite dimensional spaces, Lax-Milgiam theorem. Operations Research-- Linear programming problem LPP Simplex method Operations Research History, Scope Msc3 Prsu Raipur This video is provided by Academy Higher mathematics mahasamund CG Operations research (British English: operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making.[1] The term management science is occasionally used as a synonym.[2] Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries. @ykmathsguru1196 #mscmathematics #prsuuniversity #mathematics #chattisgarh Don’t worry I will get the MSC Mathematics program syllabus issued by Pandit Ravishankar Shukla University. Here is the syllabus Semester 1 Paper-I Advanced Abstract Algebra (I) Paper-II Real Analysis (I) Paper-III Topology Paper-IV Complex Analysis (I) Paper-V Advanced Discrete Mathematics (I) Semester 2 Paper-I Advanced Abstract Algebra (II) Paper-II Real Analysis (II) Paper-III General and Algebraic Topology Paper-IV Complex Analysis (II) Paper-V Advanced Discrete Mathematics (I) Semester 3 Paper-I Integration theory and Functional Analysis (I) Paper-II Partial Differential Equations and Mechanics (I) Paper-III Fundamentals of Computer Science 100 -Theory and Practical Paper-IV Operations Research (I) Paper-V Programming in C (with ANSI features) (I) Theory and Practical For full information please check the file MSC Mathematics program syllabus