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 B.Sc. Mathematics
Differential EquationsII(ODE)
Ordinary differential equations:
Linear homogeneous equations with constant coefficients, Linear nonhomogeneous equations, The method
of variation of parameters, The CauchyEuler equation, Simultaneous differential equations, Simple eigenvalue problem.SKU: n/a  B.Sc. Mathematics, Level Honours
Improper Integral
• Range of integration, finite or infinite. Necessary and sufficient condition for convergence of improper integral in both cases.
• Tests of convergence : Comparison and Mtest. Absolute and nonabsolute convergence and interrelations.
Statement of Abel’s and Dirichlet’s test for convergence on the integral of a product.• Convergence and working knowledge of Beta and Gamma function and their interrelation .
SKU: n/a  B.Sc. Mathematics, Level Honours, Level Pass
Mathematical Logic
• Introduction, propositions, truth table, negation, conjunction and disjunction. Implications, biconditional propositions, converse, contra positive and inverse propositions and precedence of logical operators.
• Propositional Logic
• Predicate Logic
SKU: n/a  B.Sc. Mathematics, Level Honours
Riemann Integration
• Partition and refinement of partition of a closed and bounded interval. Upper Darboux sum U(P, f) and lower Darboux sum L(P, f) and associated results. Upper integral and lower integral. Darboux’s theorem. Darboux’s definition of integration over a closed and bounded interval. Riemann’s definition of integrability. Equivalence with Darboux definition of integrability (statement only). Necessary and sufficient condition for Riemann integrability.
• Concept of negligible set (or zero set) defined as a set covered by countable number of open intervals sum of whose lengths is arbitrary small. Examples of negligible sets : any subset of a negligible set, finite set, countable union of negligible sets. A bounded function on closed and bounded interval is Riemann integrable if and only if the set of points of discontinuity is negligible. Example of Riemann integrable functions.
• Integrability of sum, scalar multiple, product, quotient, modulus of Riemann integrable functions. Properties of Riemann integrable functions arising from the above results.
• Antiderivative (primitive or indefinite integral). Properties of Logarithmic function.
• Fundamental theorem of Integral Calculus. First Mean Value theorem of integral calculus.
SKU: n/a  B.Sc. Mathematics, Level Honours, Uncategorized
Semester : 4 [ CC 8 + CC 9 + CC 10 + SEC B ] – B.Sc Mathematics Hons. Online course  University of Calcutta (CU)
B.Sc. Mathematics, Level Honours, UncategorizedSemester : 4 [ CC 8 + CC 9 + CC 10 + SEC B ] – B.Sc Mathematics Hons. Online course  University of Calcutta (CU)
CU SYLLABUS WISE LESSONSSTANDARD EXERCISEEXERCISE SOLUTIONMODEL QUESTION SETSLAST 10 YEARS QUESTION PAPER SOLVED6 MONTHS VALIDITYSKU: n/a