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Dr. Mathaholic

Univariate Calculus

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69 items
Last updated on Jun 16, 2022
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Lecture 1: Graph of a function. Definition and Examples using GeoGebra software.
9:31
Lecture 2: What is limit of a function along with different kinds of Graphs and Examples.
17:37
Lecture 3: Understanding definition of Continuity of a function using Graphs and Examples.
13:09
Lecture 4: Derivative of function in one variable along with Geometrical & Physical Interpretation
11:56
Lecture 5: Connection between Differentiability, Continuity and Existence of limit at a given point.
11:53
Lecture 6: Absolute Maxima and Minima of a function along with Extreme value theorem.
14:11
Lecture 7: Local maxima and minima of function. Its connection with Global Extrema and Derivatives.
16:48
Lecture 8 : Critical Points concept and important examples related to it.
5:55
Lecture 9: Open, Closed, Bounded & Unbounded Interval. Counterexample to Extreme Value Theorem.
10:08
Lecture 10: Counterexamples to Rolle's Theorem
9:59
Lecture 11: Lagrange Mean value theorem. Geometrical and Physical interpretation with an example
8:59
Lecture 12: Can you find a flaw in the proof of  Cauchy's Mean Value Theorem??
3:46
Lecture 13: Increasing Decreasing functions and its connections with derivatives of a function.
17:14
Lecture 14: Theorem which help us to find local Maxima and local minima of a function.
14:56
Lecture 15: Concave up and Concave down of a function using examples.
10:40
Lecture 16: Inflection points and Important examples one should know.
17:18
How convex functions help us to pay less INCOME TAX!!
8:19
Lecture 17: Asymptotes and its types, along with examples and GeoGebra software.
20:45
Lecture 18: Steps to sketch graph of explicit functions( see pinned comment)
23:35
Lecture 19: Rough sketch of graph of a function without knowing the function!!
11:06
Optimization Problems using Single Variable Calculus
19:32
An example using Jensen's inequality
5:28
Lecture 20: Riemann Integration as an infinite sum using GeoGebra
31:12
Lecture 21: Example & non-example of a function using Riemann sums.
23:39
Lecture 22: What is so fundamental about Fundamental Theorem of Calculus I? Meaning & examples.
20:33
Question on Application of Fundamental Theorem of Calculus and Chain rule of composite function
4:19
Example on Fundamental Theorem of Calculus I and increasing function: Exam 2017
2:37
Lecture 23: Fundamental Theorem of Calculus II. Meaning and examples.
12:47
Lecture 24: Important Inequalities using Lagrange's Mean Value Theorem
17:38
Lecture 25: An example on Fundamental Theorem of Calculus II
3:43
Lecture 26: Which is bigger? π^e or e^π?
9:16
Lecture 27: Volume using Cross section method. Application of definite integrals.
14:15
Lecture 28: Solid of Revolution- When to use Disk method and when to use Washer Method.
21:32
Cylindrical/Shell Method to find volume and its importance over Washer method.(see pinned comment)
24:08
Lecture 31: Improper integrals of Type I. Concept and Examples
17:13
Lecture 32: Improper Integrals of Type II. Concept and Examples.
16:13
Lecture 33: Direct Comparison test for Improper Integrals of Type I and II.
19:10
Lecture 34: Limit Comparison Test for Improper Integrals of Type I and Type II.(see pinned comment)
14:24
Lecture 35: Gamma Functions (Non Elementary function). Concept and tricks to solve examples.
22:16
Lecture 36: Beta function (Non elementary function). Properties and hints on how to solve problems
16:15
Lecture 37: Integral of x*cos^6x dx and x*sin^x dx using Beta and Gamma functions.
9:26
Session 1 : What is a Sequence? Types of Sequences.
13:37
Session 2 : Arithmetic operations on sequences.
12:21
Session 3: Sandwich/ Squeeze Theorem.
10:24
Session 4: Continuity theorem for sequences.
10:20
Session 5 : How L'Hopital rule help us to find limit of a sequence.
8:21
Session 6 : Super exponential function grows very rapidly as compared to factorial function.
3:57
Session 7 : Sequence that converges to exponential function.
4:36
Session 8 : Bounded and Monotonic sequences.
16:39
Session 9: Examples on recursive sequences.
24:53
Session 1 : Definition of a series of real numbers in terms of nth partial sums and examples.
10:59
Session 2 : Geometric series and its applications.
20:44
Session 3 : Arithmetic operations on series.
13:59
Session 4 : nth term test for divergent series.
10:29
Session 5 : Integral test with examples and proof of P- Series test.
13:12
Session 6 : Direct and Limit comparison test for series of real numbers.
14:53
Session 7: Ratio and Root test for series of real numbers.
14:44
Session 8: Alternating series test and examples.(see pinned comment and replies)
19:33
Session 9: Absolute and conditionally convergent series followed by Riemann Rearrangement theorem.
22:01
Session 10: Power series, Radius and Interval of convergence with examples.
30:16
Session 11: Continuity, Differentiation and Integration of a power series.
17:16
Session 1: Why Fourier Series?-  Approximation by sine and cosine curves.
10:30
Session 2:Fundamental period,add-subtraction of periodic,non-periodic functions.Trigonometric series
16:17
Session 3: Fourier series & Fourier coefficients over period 2 \pi and examples.(see pinned comment)
21:48
Session 4 : Convergence of Fourier series.(see pinned comment)
16:15
Session 5 : Fourier series over an arbitrary period 2L.
12:54
Session 6: Even-Odd functions and its connection with periodic functions.
12:27
Session 7 : Half range expansion of Fourier series.
13:38
Session 8: Examples & different kind of questions one can ask on Fourier series.(see pinned comment)
16:22