Real Analysis | As per NEP, B.Sc Third year Mathematics Handwritten Notes also Useful and IIT JAM, CSIR NET and GATE PDF Download

Description

Chapters and Topics Included on PDF

Module-I

• Partitions and Darboux Sums
• Upper and Lower Riemann Integrals, Properties of Riemann Integration
• The Fundamental Theorem of Integral Calculus, Mean Value Theorems

Module-II

• Field structure and ordered structure of R, intervals, bounded and unbounded sets, supremum and infimum, completeness in R, absolute value of a real number.
• Sequence of real numbers
• Limit of a sequence
• Bounded and monotonic sequences
• Cauchy’s general principle of convergence
• Algebra of sequence and some important theorems

Module – III

• Series of non-negative terms
• Convergence of positive term series
• Alternating series and Leibnitz’s test
• Absolute and Conditional Convergence of Series of real terms
• Uniform continuity
• Chain rule of differentiability
• Mean value theorems and their geometrical interpretations