Nested Interval theorem,Bolzano Weierstrass theorem,lim inferior and superior of the sequence,definition of series and theorems.
Course Material
- Introduction to real number systems ,concept of least upper bound and greatest lower bounds
- Definition of supremum , Infimum ,relevant problems, ordered field theorems and axioms
- Existence of Real field,Archimedean property,extended real number system.Schwar’z inequality and relevant questions
- Definition of sequence and its types,Bernoulli’s inequality,examples of increasing and decreasing sequences
- Bounded sequence,convergence of sequence,Cauchy sequence,divergent sequence and their examples and theorems
- Concept of monotonic sequence, recurrence relation, cauchy general principal of convergence
- Nested Interval theorem,Bolzano Weierstrass theorem,lim inferior and superior of the sequence,definition of series and theorems.
- The comparison test and its examples,Cauchy condensation test and its examples,convergence and divergence of series
- Alternating series,Leibniz series test,Root test,Ratio test,Dirichlet theorem and different example
- Mid Term Exams
- Introduction to limit of function,examples and sand-witching theorem
- Winter Break
- Concept of continuity and its examples,Intermediate Value Theorem
- Uniform continuity,theorems and examples,types of discontinuities and further applications Concept of differentiation in real analysis and its examples,
- The Chain Rule,Local maxima and minim and its geometric representation,Generalized Mean Value theorem
- Geometric representation of M.V.T, Lagrangian mean value theorem,Darboux’s theorem,L’Hospital rule and their examples ,Taylor’s theorem
- Final Term Exam
- Chapters 17
- Department Mathematics
- Teacher
Ms. Wajiha Pervaiz
