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B.Se.-I Semester I, Mathematics Syllabus, , , , , , , Certificate Course in Applied Mathematics, , Course Code Paper Title Theory/ | Credits, i Practical, BOSOLOIT | Differential Calculus & Integral! Theory 4, | Calculus, , BovOTOaP [Pracieal [Practical [2, Paper - I: Differential Calculus & Integral Calculus, Max. Marks : 25+75, Unit I: Introduction to Indian ancient Mathematics and Mathematicians, should be included under Continuous Internal Evaluation (CIE). Defini, tion of a sequence, theorems on limits of sequences, bounded and, monotonic sequences, Cauchy's convergence criterion, Cauchy sequent, limit‘superior and limit inferior of a sequence, subsequence, Scries of, _ Non-negative terms, convergence and divergence, Comparison tests,, _ Cauchy's integral test, Ratio tests, Root test, Raabe's logarithmic test,, _ de Morgan and Bertrand's tests, alternating series, Leibnitz's theorem,, absolute and conditional convergence,, Unit I: Limit, continuity and differentiability of function of single vari, able, Cauchy's definition, Heine’s definition, equivalence of definition, of Cauchy and Heine, Uniform continuity, Borel’s theorem, boundedness, theorem, Bolzano’s theorem, Intermediate value theorem, extreme value