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
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