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In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. [1] Some particular properties of real-valued sequences and functions that real analysis studies include convergence , limits , continuity , smoothness , differentiability and integrability .
Convolution. Cauchy product –is the discrete convolution of two sequences; Farey sequence – the sequence of completely reduced fractions between 0 and 1; Oscillation – is the behaviour of a sequence of real numbers or a real-valued function, which does not converge, but also does not diverge to +∞ or −∞; and is also a quantitative measure for that.
p-adic analysis, the study of analysis within the context of p-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts. Non-standard analysis , which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers.
The university is the first multi-campus university in Pakistan, having five modern campuses based in different cities. [3] These campuses are located in Chiniot-Faisalabad, Islamabad, Karachi, Lahore, and Peshawar, providing a standard educational environment and recreational facilities to 11,000 students, out of which 500 are faculty members and a quarter is covered by female students.
An Introduction to Complex Analysis in Several Variables. Van Nostrand. Rudin, Walter (1976). Principles of Mathematical Analysis. Walter Rudin Student Series in Advanced Mathematics (3rd ed.). McGraw-Hill. ISBN 9780070542358. Rudin, Walter (1986). Real and Complex Analysis (International Series in Pure and Applied Mathematics). McGraw-Hill.
Littlewood's three principles are quoted in several real analysis texts, for example Royden, [2] Bressoud, [3] and Stein & Shakarchi. [4] Royden [5] gives the bounded convergence theorem as an application of the third principle. The theorem states that if a uniformly bounded sequence of functions converges pointwise, then their integrals on a ...
The idea behind the school is to create a world-class doctoral research institute in mathematics, but rooted in a developing country like Pakistan. [3] [4] The school was later named after Abdus Salam who was professor of mathematics at the Government College Lahore from 1951 to 1954. The school starts operating in late 2003.
The Government College University (colloquially known as GCU; Punjabi, Urdu: گورنمنٹ کالج یونیورسٹی) is a public research university in Lahore, Punjab, Pakistan. Founded as Government College, Lahore, in 1864 under British administration , it became a university in 2002.