Variation function, characterization of variation function, theorems
Course Material
- 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
- Chapters 18
- Department Mathematics
- Teacher
Ms. Wajiha Pervaiz
