Univariate Calculus (English)

   Wednesday, July 19, 2023   

Starting a new Lecture Notes Series on Univariate Calculus

Youtube Lecture Playlist Credits 

Channel Name: Dr. Mathaholic

So Let Us Start to This Journey of Learning 

Univariate Calculus By Lecture Notes together!

Lecture Description of this above Topic:

Lecture 1: Lecture 1: Graph of a function. Definition and Examples using GeoGebra software.

Lecture 2: Lecture 2: What is limit of a function along with different kinds of Graphs and Examples.

Lecture 3: Lecture 3: Understanding definition of Continuity of a function using Graphs and Examples.

Lecture 4: Lecture 4: Derivative of function in one variable along with Geometrical & Physical Interpretation

Lecture 5: Lecture 5: Connection between Differentiability, Continuity and Existence of limit at a given point.

Lecture 6: Lecture 6: Absolute Maxima and Minima of a function along with Extreme value theorem.

Lecture 7: Lecture 7: Local maxima and minima of function. Its connection with Global Extrema and Derivatives.

Lecture 8: Lecture 8 : Critical Points concept and important examples related to it.

Lecture 9: Lecture 9: Open, Closed, Bounded & Unbounded Interval. Counterexample to Extreme Value Theorem.

Lecture 10: Lecture 10: Counterexamples to Rolle's Theorem

Lecture 11: Lecture 11: Lagrange Mean value theorem. Geometrical and Physical interpretation with an example

Lecture 12: Lecture 12: Can you find a flaw in the proof of Cauchy's Mean Value Theorem??

Lecture 13: Lecture 13: Increasing Decreasing functions and its connections with derivatives of a function.

Lecture 14: Lecture 14: Theorem which help us to find local Maxima and local minima of a function.

Lecture 15: Lecture 15: Concave up and Concave down of a function using examples.

Lecture 16: Lecture 16: Inflection points and Important examples one should know.

Lecture 17: How convex functions help us to pay less INCOME TAX!!

Lecture 18: Lecture 17: Asymptotes and its types, along with examples and GeoGebra software.

Lecture 19: Lecture 18: Steps to sketch graph of explicit functions

Lecture 20: Lecture 19: Rough sketch of graph of a function without knowing the function!!

Lecture 21: Optimization Problems using Single Variable Calculus

Lecture 22: An example using Jensen's inequality

Lecture 23: Lecture 20: Riemann Integration as an infinite sum using GeoGebra

Lecture 24: Lecture 21: Example & non-example of a function using Riemann sums.

Lecture 25: Lecture 22: What is so fundamental about Fundamental Theorem of Calculus I? Meaning & examples.

Lecture 26: Question on Application of Fundamental Theorem of Calculus and Chain rule of composite function

Lecture 27: Example on Fundamental Theorem of Calculus I and increasing function

Lecture 28: Lecture 23: Fundamental Theorem of Calculus II. Meaning and examples.

Lecture 29: Lecture 24: Important Inequalities using Lagrange's Mean Value Theorem

Lecture 30: Lecture 25: An example on Fundamental Theorem of Calculus II

Lecture 31: Lecture 26: Which is bigger? π^e or e^π?

Lecture 32: Lecture 27: Volume using Cross section method. Application of definite integrals.

Lecture 33: Lecture 28: Solid of Revolution- When to use Disk method and when to use Washer Method.

Lecture 34: Cylindrical/Shell Method to find volume and its importance over Washer method

Lecture 35: Lecture 31: Improper integrals of Type I. Concept and Examples

Lecture 36: Lecture 32: Improper Integrals of Type II. Concept and Examples.

Lecture 37: Lecture 33: Direct Comparison test for Improper Integrals of Type I and II.

Lecture 38: Lecture 34: Limit Comparison Test for Improper Integrals of Type I and Type II

Lecture 39: Lecture 35: Gamma Functions (Non Elementary function). Concept and tricks to solve examples.

Lecture 40: Lecture 36: Beta function (Non elementary function). Properties and hints on how to solve problems

Lecture 41: Lecture 37: Integral of x*cos^6x dx and x*sin^x dx using Beta and Gamma functions.

Lecture 42: Session 1 : What is a Sequence? Types of Sequences.

Lecture 43: Session 2 : Arithmetic operations on sequences.

Lecture 44: Session 3: Sandwich/ Squeeze Theorem.

Lecture 45: Session 4: Continuity theorem for sequences.

Lecture 46: Session 5 : How L'Hopital rule help us to find limit of a sequence.

Lecture 47: Session 6 : Super exponential function grows very rapidly as compared to factorial function.

Lecture 48: Session 7 : Sequence that converges to exponential function.

Lecture 49: Session 8 : Bounded and Monotonic sequences.

Lecture 50: Session 9: Examples on recursive sequences.

Lecture 51: Session 1 : Definition of a series of real numbers in terms of nth partial sums and examples.

Lecture 52: Session 2 : Geometric series and its applications.

Lecture 53: Session 3 : Arithmetic operations on series.

Lecture 54: Session 4 : nth term test for divergent series.

Lecture 55: Session 5 : Integral test with examples and proof of P- Series test.

Lecture 56: Session 6 : Direct and Limit comparison test for series of real numbers.

Lecture 57: Session 7: Ratio and Root test for series of real numbers.

Lecture 58: Session 8: Alternating series test and examples.

Lecture 59: Session 9: Absolute and conditionally convergent series followed by Riemann Rearrangement theorem.

Lecture 60: Session 10: Power series, Radius and Interval of convergence with examples.

Lecture 61: Session 11: Continuity, Differentiation and Integration of a power series.

Lecture 62: Session 1: Why Fourier Series?- Approximation by sine and cosine curves.

Lecture 63: Session 2:Fundamental period,add-subtraction of periodic,non-periodic functions.Trigonometric series

Lecture 64: Session 3: Fourier series & Fourier coefficients over period 2 \pi and examples.

Lecture 65: Session 4 : Convergence of Fourier series.

Lecture 66: Session 5 : Fourier series over an arbitrary period 2L.

Lecture 67: Session 6: Even-Odd functions and its connection with periodic functions.

Lecture 68: Session 7 : Half range expansion of Fourier series.

Lecture 69: Session 8: Examples & different kind of questions one can ask on Fourier series.