Continuity & Differentiability

Simply Easy Learning

Created by Ridhi Arora, Last Updated 05-Sep-2019, Language:English

Description

Calculus is used in every branch of the physical sciences, actuarial science, statistics, engineering and in other fields wherever a problem can be mathematically modele and an optimal solution is desired.Continuity of functions is one of the core concepts of topology.A continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output while a differentiable function of one real variable is a function whose derivative exists at each point in its domain.This video series is based on Continuity And Differentiability for class 12 students for board level and IIT JEE Mains.

Audience

These video classes have been designed for Class 12 students (Non-medical students and commerce students with Mathematics), those who are preparing for CBSE and other Board Exams for Intermediate, +2 and IIT JEE entrance exams. These classes will also be helpful for students in preparing them for Competitive Examinations for Engineering Institutes like IIT JEE etc.

Course Content

Continuity & Differentiability

8 Lectures 00:41:20
- Continuity & Differentiability Syllabus
  
  Preview
  
  00:08:10
- Recap of Limits
  
  Preview
  
  00:06:02
- Overview of Continuity
  
  00:06:59
- Conditions of Continuity
  
  00:05:33
- Removable Discontinuity
  
  00:05:02
- Irremovable Discontinuity Part 1
  
  00:03:33
- Irremovable Discontinuity Part 2
  
  00:04:09
- Left Continuous & Right Continuous Function
  
  00:01:52
Algebra of Continuous Functions

7 Lectures 00:20:09
- Sum of Continuous Functions
  
  Preview
  
  00:03:30
- Difference of Continuous Functions
  
  Preview
  
  00:02:26
- Product of Continuous Function
  
  00:02:03
- Product of Continuous Functions
  
  00:02:09
- 1/F Is Continuous At X = A, If F(A) ≠ 0
  
  00:02:39
- Quotient Of 2 Continuous Functions
  
  00:03:09
- Composition of Functions
  
  00:04:13
Problems On Continuity

6 Lectures 00:34:45
- Continuity Problem 1
  
  00:04:40
- Continuity Problem 2
  
  00:07:55
- Continuity Problem 3
  
  00:05:43
- Continuity Problem 4
  
  00:05:48
- Continuity Problem 5
  
  00:05:49
- Continuity Problem 6
  
  00:04:50
Always Continuous Functions

10 Lectures 00:47:06
- Constant Function
  
  Preview
  
  00:05:27
- Identity Function
  
  00:04:20
- Polynomial Function
  
  00:07:42
- Rational Function
  
  00:04:14
- Modulus Function
  
  00:02:27
- Exponential Function
  
  00:04:29
- Logarithmic Function
  
  00:02:40
- Trigonometric Function - Sine Function
  
  00:07:10
- Trigonometric Function - Tangent Function
  
  00:04:49
- Inverse Trigonometric Functions
  
  00:03:48
Miscellaneous Problems On Continuity

5 Lectures 00:32:59
- Continuity - Miscellaneous Problem 1
  
  00:07:57
- Continuity - Miscellaneous Problem 2
  
  00:05:25
- Continuity - Miscellaneous Problem 3
  
  00:03:31
- Continuity - Miscellaneous Problem 4
  
  00:08:48
- Continuity - Miscellaneous Problem 5
  
  00:07:18
Differentiability

11 Lectures 01:01:15
- Definition Of Differentiability
  
  00:06:17
- Geometrical Meaning Of Differentiability
  
  00:07:32
- Theorem On Differentiability
  
  00:06:24
- Differentiability Problem 1
  
  00:04:33
- Differentiability Problem 2
  
  00:04:54
- Differentiability Problem 3
  
  00:06:35
- Useful Results On Differentiability
  
  00:05:34
- Continuity & Differentiability Problem 1
  
  00:03:35
- Continuity & Differentiability Problem 2
  
  00:04:43
- Derivative Of F At X For F(X)
  
  00:04:01
- Problem On Differentiable Function
  
  00:07:07
Differentiation

5 Lectures 00:23:33
- Standard Formulas
  
  00:04:32
- Product Rule Part 1
  
  00:04:15
- Product Rule Part 2
  
  00:03:42
- Quotient Rule
  
  00:04:01
- Problems On Differentiation
  
  00:07:03
Composition Of Functions

8 Lectures 00:54:23
- Overview of Composition of Functions
  
  Preview
  
  00:03:53
- Substitution Method Problem 1
  
  00:06:15
- Substitution Method Problem 2
  
  00:07:48
- Composition of Functions - Problem 1 on Chain Rule
  
  00:08:20
- Composition of Functions - Problem 2 on Chain Rule
  
  00:07:04
- Composition of Functions - Problem 3 on Chain Rule
  
  00:06:00
- Composition of Functions - Problem 4 on Chain Rule
  
  00:05:44
- Composition of Functions - Problem 5 on Chain Rule
  
  00:09:19
Inverse Trigonometric Functions Differentiation

10 Lectures 00:52:29
- Differentiation of Sin ^-1 x
  
  00:04:58
- Differentiation of Cos ^-1 x
  
  00:04:06
- Differentiation of Tan ^-1 x
  
  00:04:06
- Differentiation of Cot ^-1 x
  
  00:03:56
- Differentiation of Sec ^-1 x
  
  00:09:15
- Differentiation of Cosec ^-1 x
  
  00:07:25
- Inverse Trigonometric Function Problem 1
  
  00:03:14
- Inverse Trigonometric Function Problem 2
  
  00:04:48
- Inverse Trigonometric Function Problem 3
  
  00:07:32
- Inverse Trigonometric Function Problem 4
  
  00:03:09
Implicit Functions Differentiation

6 Lectures 00:32:40
- Implicit Functions Overview
  
  00:03:49
- Implicit Functions Problem 1
  
  00:05:40
- Implicit Functions Problem 2
  
  00:06:17
- Implicit Functions Problem 3
  
  00:04:30
- Implicit Functions Problem 4
  
  00:06:55
- Implicit Functions Problem 5
  
  00:05:29
Exponential & Logarithmic Functions

1 Lectures 00:09:18
- Concept of Exponential & Logarithmic Functions
  
  00:09:18
Logarithmic Differentiation

5 Lectures 00:22:28
- Logarithmic Differentiation Overview
  
  00:04:25
- Logarithmic Differentiation Problem 1
  
  00:04:39
- Logarithmic Differentiation Problem 2
  
  00:05:08
- Logarithmic Differentiation Problem 3
  
  00:04:28
- Logarithmic Differentiation Problem 4
  
  00:03:48
Differentiation of Infinite Series

4 Lectures 00:17:18
- Differentiation of Infinite Series Overview
  
  00:02:25
- Differentiation Of Infinite Series Problem 1
  
  00:04:24
- Differentiation Of Infinite Series Problem 2
  
  00:06:38
- Differentiation Of Infinite Series Problem 3
  
  00:03:51
Differentiation of Parametric Functions

4 Lectures 00:17:01
- Differentiation of Parametric Functions Overview
  
  Preview
  
  00:03:13
- Differentiation of Parametric Functions Problem 1
  
  00:04:20
- Differentiation of Parametric Functions Problem 2
  
  00:03:33
- Differentiation of Parametric Functions Problem 3
  
  00:05:55
Higher Order Derivatives

5 Lectures 00:23:43
- Higher Order Derivatives Overview
  
  00:05:28
- Higher Order Derivatives Problem 1
  
  00:05:11
- Higher Order Derivatives Problem 2
  
  00:04:40
- Higher Order Derivatives Problem 3
  
  00:03:08
- Higher Order Derivatives Problem 4
  
  00:05:16
Differentiation Using Trigonometric Substitutions

4 Lectures 00:13:06
- Differentiation Using Trigonometric Substitutions Overview
  
  00:03:21
- Differentiation Using Trigonometric Substitutions Problem 1
  
  00:03:06
- Differentiation Using Trigonometric Substitutions Problem 2
  
  00:02:39
- Differentiation Using Trigonometric Substitutions Problem 3
  
  00:04:00
Differentiation of One Function With Respect To Another

3 Lectures 00:13:03
- Differentiation of One Function With Respect To Another Overview
  
  00:01:54
- Differentiation Of One Function With Respect To Another Problem 1
  
  00:05:20
- Differentiation Of One Function With Respect To Another Problem 2
  
  00:05:49
Rolle's Theorem

7 Lectures 00:26:49
- Rolle's Theorem Overview
  
  00:02:50
- Geometrical Interpretation
  
  00:03:07
- Algebraic Interpretation
  
  00:03:27
- Important Results
  
  00:04:08
- Rolle's Theorem Problem 1
  
  00:03:11
- Rolle's Theorem Problem 2
  
  00:06:00
- Rolle's Theorem Problem 3
  
  00:04:06
Lagrange’s Mean Value Theorem

4 Lectures 00:22:31
- Lagrange’s Mean Value Theorem Overview
  
  Preview
  
  00:02:20
- Geometrical Interpretation Of LMV
  
  00:05:44
- Lagrange’s Mean Value Theorem Problem 1
  
  00:09:15
- Lagrange’s Mean Value Theorem Problem 2
  
  00:05:12
Miscellaneous Problems On Differentiation

4 Lectures 00:15:57
- Differentiation - Miscellaneous Problem 1
  
  00:04:36
- Differentiation - Miscellaneous Problem 2
  
  00:02:43
- Differentiation - Miscellaneous Problem 3
  
  00:04:13
- Differentiation - Miscellaneous Problem 4
  
  00:04:25
IIT JEE Exams Questions

10 Lectures 00:48:31
- Continuity & Differentiability - IIT JEE Problem 1
  
  00:05:19
- Continuity & Differentiability - IIT JEE Problem 2
  
  00:05:37
- Continuity & Differentiability - IIT JEE Problem 3
  
  00:07:46
- Continuity & Differentiability - IIT JEE Problem 4
  
  00:03:34
- Continuity & Differentiability - IIT JEE Problem 5
  
  Preview
  
  00:04:57
- Continuity & Differentiability - IIT JEE Problem 6
  
  00:03:27
- Continuity & Differentiability - IIT JEE Problem 7
  
  00:03:01
- Continuity & Differentiability - IIT JEE Problem 8
  
  00:03:30
- Continuity & Differentiability - IIT JEE Problem 9
  
  00:07:47
- Continuity & Differentiability - IIT JEE Problem 10
  
  00:03:33

Ridhi Arora

Ridhi Arora holds a B. Tech Honors - Gold medalist in Computer Science. Ridhi is an ardent learner, a keen observer and a passionate Mathematics faculty for classes 11,12 and IIT JEE Mains. She is among the top 10 most viewed writers in Kota, Rajasthan, on Quora. Ridhi is also associated with Ganit Hub as Algebra HOD and Miracle Live Coaching Private Limited as a Mathematics faculty. Ridhi is a confident and dynamic trainer with a total teaching experience of 5+ years.