SOLVING A REAL ANALYSIS PROBLEM USING ONLY DIAGRAMS
0:00 INTRO
0:25 DEFINITION OF CHARACTERISTIC FUNCTION OF A SET
0:45 EXAMPLE OF A CHARACTERISTIC FUNCTION
0:55 EXAMPLE OF A STEP FUNCTION
1:17 GRAPH OF A CHARACTERISTIC FUNCTION
01:50 WHEN A CHARACTERISTIC FUNCTION IS CONTINUOUS?
02:30 EXAMPLE OF A DISCONTINUOUS CHARACTERISTIC FUNCTION
02:40 EXAMPLE OF A DISCONTINUOUS FUNCTION
04:15 EXPLANATION OF THE FUNCTION GIVEN IN THE PROBLEM
05:52 PROPERTIES OF SUM OF TWO CHARACTERISTIC FUNCTIONS
08:55 PROPERTIES OF LINEAR COMBINATION OF CHARACTERISTIC FUNCTIONS
14:20 GRAPH OF THE GIVEN FUNCTION f(x)
24:40 f(x) IS A STEP FUNCTION
24:47 A FUNCTION IS RIEMANN INTEGRABLE IF AND ONLY IF IT IS CONTINUOUS ALMOST EVERYWHERE
24:55 DEFINITION OF CONTINUOUS ALMOST EVERYWHERE FUNCTIONS
26:00 SUM OF TWO RIEMANN INTEGRABLE FUNCTIONS IS RIEMANN INTEGRABLE
26:40 DEFINITION OF A LEBESGUE INTEGRABLE FUNCTION
26:58 STEP FUNCTIONS ARE MEASURABLE
27:20 EXAMPLE OF A LEBESGUE INTEGRABLE FUNCTION
28:47 EXAMPLE OF A FUNCTION WITH JUMP DISCONTINUOUS
29:20 MY ADVICE TO PEOPLE PREPARING FOR COMPETITIVE EXAMS LIKE CSIR/GATE/NBHM...
EXERCISE: DO THE SAME PROBLEM WITH THE PRODUCT OF CHARACTERISTIC FUNCTIONS INSTEAD OF SUM. HINT: HOW PRODUCT OF TWO CHARACTERISTIC FUNCTIONS BEHAVE?
THE PRODUCT OF TWO CHARACTERISTIC FUNCTIONS IS EQUAL TO THE CHARACTERISTIC FUNCTION OF THE INTERSECTION.
PLEASE DO LIKE SHARE AND SUBSCRIBE IF YOU FIND IT USEFUL
EVERY DAY I UPLOAD ONE NEW PROBLEM ASKED IN CSIR/GATE/NBHM OR ANY OTHER COMPETITIVE EXAM.
_______________________________________________________________________________________________
RIEMANN INTEGRABLE FUNCTIONS,
LEBESGUE INTEGRABLE FUNCTIONS,
STEP FUNCTIONS ARE MEASURABLE,
CHARACTERISTIC FUNCTIONS,
GRAPH OF A CHARACTERISTIC FUNCTIONS,
STEP FUNCTION,
EXAMPLE OF A STEP FUNCTION,
CONTINUOUS FUNCTIONS,
EXAMPLE OF A DISCONTINUOUS FUNCTIONS WITH JUMP DISCONTINUITY,
CONTINUOUS ALMOST EVERYWHERE FUNCTIONS
_______________________________________________________________________________________________
TELEGRAM GROUP FOR DISCUSSIONS: https://t.me/joinchat/TWe0jY6iblg0ZjNl
________________________________________________________________________________________________
ALL PREVIOUS YEAR QUESTION PAPERS
CSIR JUNE 2011 QUESTION PAPER:
https://drive.google.com/file/d/129MO...
CSIR DECEMBER 2011 QUESTION PAPER:
https://drive.google.com/file/d/10SqJ...
CSIR JUNE 2012 QUESTION PAPER:
https://drive.google.com/file/d/1SJw5...
CSIR DECEMBER 2012 QUESTION PAPER:
https://drive.google.com/file/d/1sIJM...
CSIR JUNE 2013 QUESTION PAPER:
https://drive.google.com/file/d/1fBB-...
CSIR DECEMBER 2013 QUESTION PAPER:
https://drive.google.com/file/d/1_fpY...
CSIR JUNE 2014 QUESTION PAPER:
https://drive.google.com/file/d/1BJRY...
CSIR DECEMBER 2014 QUESTION PAPER:
https://drive.google.com/file/d/1jo-f...
CSIR JUNE 2015 QUESTION PAPER:
https://drive.google.com/file/d/1D-cZ...
CSIR DECEMBER 2015 QUESTION PAPER:
https://drive.google.com/file/d/1R5Hb...
CSIR JUNE 2016 QUESTION PAPER:
https://drive.google.com/file/d/1H5e9...
CSIR DECEMBER 2016 QUESTION PAPER:
https://drive.google.com/file/d/1jKhU...
CSIR JUNE 2017 QUESTION PAPER:
https://drive.google.com/file/d/1jSWi...
CSIR DECEMBER 2017 QUESTION PAPER:
https://drive.google.com/file/d/1gtDI...
CSIR JUNE 2018 QUESTION PAPER:
https://drive.google.com/file/d/1ppOC...
CSIR DECEMBER 2018 QUESTION PAPER:
https://drive.google.com/file/d/1c5lS...
CSIR JUNE 2019 QUESTION PAPER:
https://drive.google.com/file/d/10JPI...
Смотрите видео SOLVING A REAL ANALYSIS PROBLEM USING ONLY DIAGRAMS онлайн без регистрации, длительностью часов минут секунд в хорошем качестве. Это видео добавил пользователь Hello Mathematicians 09 Июль 2021, не забудьте поделиться им ссылкой с друзьями и знакомыми, на нашем сайте его посмотрели 163 раз и оно понравилось 8 людям.