13. SHOW THAT EVERY MONOTONIC SEQUENCE IS CONVERGENT IF AND ONLY IF IT IS BOUNDED || REAL ANALYSIS-I скачать в хорошем качестве

13. SHOW THAT EVERY MONOTONIC SEQUENCE IS CONVERGENT IF AND ONLY IF IT IS BOUNDED || REAL ANALYSIS-I

TO WATCH ALL COURSES OF B.S MATHEMATICS 5TH SEMESTER CLICK THE LINK BELOW    • B.S MATH || 5TH SEMSETER|| PUNJAB UNIVERSI...   ------------------------------------------------------------------------------------------------------------------------------------------------------- TO WATCH COMPLETE PLAY LIST OF REAL ANALYSIS-I B.S MATHEMATICS 5TH SEMESTER CLICK THE LINK BELOW    • REAL ANALYSIS-I || B.S MATHEMATICS 5TH SEM...   ------------------------------------------------------------------------------------------------------------------------------------------------------- This course is specially designed for students of B.S MATHEMATICS 5th semester and students doing M.SC MATHEMATICS annually from Punjab university Lahore Pakistan. ------------------------------------------------------------------------------------------------------------------------------------------------------- COURSE: REAL ANALYSIS- I||PUNJAB UNIVERSITY|| 5TH SEMESTER|| CODE MATH-301 LEVEL: B.S MATHEMATICS CHAPTER # 2 SEQUENCE AND SERIES LECTURE # 13 In this lecture I shall prove an important theorem which can be stated as; Show that every monotonic sequence is convergent if and only if it is bounded. ------------------------------------------------------------------------------------------------------------------------------------------------------- FOLLOWING ARE THE CONTENTS OF REAL ANALYSIS- I Real Number System • Ordered sets, fields, the field of real numbers • Completeness property of R • The extended real number system • Euclidean spaces • Finite, countable and uncountable sets Sequences and Series • Sequences, subsequences, convergent sequences, Cauchy sequences • Monotone and bounded sequences, Bolzano Weierstrass theorem • Series, series of non-negative terms • Partial sums, the root and ratio tests, integral test, comparison test • Absolute and conditional convergence Limit and Continuity • The limit of a function • Continuous functions • Types of discontinuity • Uniform continuity • Monotone functions Differentiation • The derivative of a function • Mean value theorems, the continuity of derivatives • Taylor’s theorem Functions of Several Variables • Partial derivatives and differentiability, derivatives and differentials of composite functions • Change in the order of partial derivative, implicit functions, inverse functions, Jacobians • Maxima and minima ------------------------------------------------------------------------------------------------------------------------------------------------------- Share, Support, Subscribe!!! About: Maths 4 U is a You Tube Channel, where you can learn Mathematics in very simple way. In this channel you can find Mathematics Videos for Intermediate and B.S Mathematics. Further in my channel you can find videos for following Entrance Exams (1) ECAT (2) CSIR (3)GATE (4) NET (5) JEE MAIN (6) JEE ADVANCED (7) IIT-JEE (8) AIEEE, DCE (9) EAMCET, WB -JEE (10) ORISSA JEE & BIHAR CET (11) MP & RAJASTHAN PET (12) KERALA PET (13) PUNJAB & HARYANA CET & OTHER ENGG. INSTITUITES Here you can find Challenging Math's Problems related to daily life. Further you can find MATHS videos for the preparation of COMPETITIVE EXAMS like as CSS, PMS and PPSC. Here you can also find lectures on use of some Mathematics software's like as Math Type, LaTex, Matlab and Mathematica. #Maths4U. #professorazmatali #realanalysis #sequence #convergent_sequence #divergent _sequence