NEXT

• partition and norm of partition
• Riemann integral ,Riemann stieltjes integral
• Riemann Stieltjes integral, refinement, properties of integral
• Properties of integral, theorems based on Reiman Stieltjes integral
• Change of variable,1st and 2nd fundamental theorem of calculus, questions
• Definition of variation, bounded variation, examples
• Function of bounded variation, properties of function of bounded variation
• Variation function, characterization of variation function, theorems
• Mid Term Exams
• 1st kind of improper integrals, comparison test, limit comparison test, Cauchy condition for infinite integrals
• 2nd kind of improper integrals, uniform convergence of improper integrals,
• Weir strass M. Test, Dirichlet test for uniform convergence, questions
• Functions of two variables, partial derivative, total differential, implicit, explicit function
• Harmonic, biharmonic function, the Laplacian in polar, cylindrical and spherical coordinates
• Schwarz’s theorem, young’s theorem, maxima and minimal for function of two variables
• Beta and gamma function, power series
• Assignments, test
• Final Term Exams