Real Analysis Part 1
Basic Topology
Course Introduction:
In mathematics world, Real analysis is the branch of mathematic analysis that studies the behavior of real numbers, sequences and series of real number and real valued function. Some particular properties of real valued sequences and functions that real analysis studies includes convergence, limits, continuity, smoothness, differentiation and integrability.
Key content of the course:
- Construction of real numbers
- Order properties of real numbers
- Topological properties of real numbers
- Sequences, limits and convergence
- Uniform convergence
- Continuity, Uniform continuity, absolute continuity
- Series
- Riemann integration
- Lebesgue integration and measure
- Compactness
- Bolzano weierstrass theorem
- Heine Borel theorems
So enroll the course and explore the content. See you in the course!
Your Instructor
Concept based mathematics is started by Jaswinder kaur as per passion in teaching mathematics. She started by posting free mathematics tutorials in her YouTube channel. She is graduate in B.Sc in Physics, Maths and Computer Science and Master in Mathematics. She loved to teach via scratch.
Her teachings mugs up the concepts with figures and graphical representation which you will see in the course.
Course Curriculum
-
PreviewLesson 0.0- Basics of Real Analysis (8:18)
-
StartLesson 0.1 - Basics of Real Analysis(2) (15:28)
-
StartLesson 1- Countable Sets (1) (34:41)
-
StartLesson 2- Countable Sets (2) (64:46)
-
StartLesson 3- Countable Sets (3) (25:00)
-
StartLesson 4- Countable Sets (4) (12:03)
-
StartLesson 5- Algebric and Trancendental numbers (19:12)
-
StartLesson 6- Metric Spaces (1) (33:29)
-
StartLesson 7- Metric Spaces (2) (24:49)
-
StartLesson 8 - Metric Spaces (3) (23:17)
-
PreviewLesson 9 - Neighbourhood (27:40)
-
PreviewLesson 10- Open set (16:48)
-
StartLesson 11- Theorems on Open set (32:27)
-
StartLesson 12- De Morgan's law (12:01)
-
StartLesson 13- Limit Points (24:03)
-
StartLesson 14- Closed set (6:56)
-
StartLesson 15- Derived Set (12:38)
-
StartLesson 16- Theorem on open set and closed set (1) (24:24)
-
StartLesson 17- Theorem on open set and Closed set (2) (9:09)
-
StartLesson 18- Theorem on open and closed set (3) (16:59)
-
StartLesson 19- Theorem on open set and Closed set (4) (16:24)
-
StartLesson 20- Theorem on open set and Closed set (5) (11:50)
-
StartLesson 21- Bounded above and Bounded below (12:26)
-
StartLesson 22- Bounded set (16:22)
-
StartLesson 23- Discrete Metric Space (14:47)
-
StartLesson 24- Isolated point dense set (14:03)
-
StartLesson 25- Set open relative to metric space (14:04)
-
StartLesson 26- Compact Set (15:42)
-
StartLesson 27- Expected theorem for Compact set (1) (22:31)
-
StartLesson 28- Expected theorem for Compact set (2) (10:21)
-
StartLesson 29- Expected theorem for Compact set (3) (10:54)
-
StartLesson 30- Expected theorem for Compact set (4) (10:35)
-
StartLesson 31- Expected theorem for Compact set (5) (9:22)
-
StartLesson 32- Infinite subset of compact set (k) (11:21)
-
StartLesson 33- Compactness of K-cell (1) (12:57)
-
StartLesson 34- Compactness of K-cell (2) (18:54)
-
StartLesson 35- Heine Borel Theoram (7:59)
-
StartLesson 36- Weierstrass Theorem (13:02)
-
StartLesson 37- Perfect Set (1) (19:08)
-
StartLesson 38- Perfect Set (2) (10:32)