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Teaching & Academics Math Calculus

Advanced Calculus of Higher Mathematics

Advanced Calculus of Higher Mathematics through animation,explanations,plenty of solved examples to help you in exam
Rating: 4.9 out of 54.9 (11 ratings)
7,772 students
Created by Moein Ud Din
Last updated 10/2020
English
30-Day Money-Back Guarantee

What you'll learn

  • Parseval's Identity of Fourier Series: Introduction,Basics, Equations, Mathematical Proof and Problem Solutions
  • Harmonic Analysis: Introduction, Basics, Different orders of Harmonic series and Problem Solutions
  • Complex Fourier Series : Basics, Prerequisites, Equations derivation & Mathematical Proof and Problem Solutions
  • Fourier Transform: Introduction,Basics, Graphs, Fourier Sine & Cosine Transform, Convolution theorem,Mathematical Proof and Problem Solutions
  • Z-Transform: Introduction, Basics, Region of convergence, Properties,Equation Derivation, Mathematical Proof, Inverse Z-Transform and Problem Solutions
  • Power Series: Introduction, Basics, Region and radius of convergence, Interval of convergence, Differentiation & Integration,Equation Derivation, Mathematical Proof and Problem Solutions
  • Binomial Series: Introduction, Basics, Prerequisites, Methods to solve binomial series, Finite series, Infinite series, General Term, Binomial series as a power series, and Problem Solutions

Requirements

  • Basics of calculus

Description

Learn Advanced Calculus through animation. The course includes videos explanation with plenty of relevant solved examples and. The lectures are appealing, fancy (graphic designing), fast and take less time to walk you through the whole lecture. A prefect choice for students who feel boredom watching long lectures. So join me here and do it in a quick and easy way. This course covers the below list of topics:

  • Parseval's Identity of Fourier Series

  • Harmonic Analysis of Fourier Series

  • Complex Fourier Series

  • Fourier Transform

  • Z-Transform

  • Power Series

  • Binomial Series

Who this course is for:

  • Students who are taking advanced calculus of higher mathematics at college and university level

Course content

34 sections • 191 lectures • 20h 29m total length

  • Preview00:59

  • What is Perseval's Identity of Fourier Series? where and why we use it?
    01:50
  • Check the simple Fourier series before to go for its Perseval's Identity
    01:44
  • Full range Equations of Perseval's Identity for both pi and L
    02:16
  • Half range Equations of Perseval's Identity
    01:03
  • Proof of Perseval's Identity Equation when we take it with the pi range
    06:48
  • Proof of Perseval's Identity Equation when we take it with the L range
    03:40
  • Proof of Half range Cosine Perseval's Identity Equation
    04:15
  • Proof of Half range Sine Perseval's Identity Equation
    03:25

  • Find and prove the expression with power more than two using Perseval's identity
    16:57
  • Check the expression with power less/equal to two using Perseval's identity
    09:25

  • What is Harmonic Fourier Series? and also know about its equation and variables
    02:20
  • First Harmonic Fourier series and Second Harmonic Fourier series
    02:02
  • Third Harmonic Fourier series and Fourth Harmonic Fourier series
    01:57
  • How to find the amplitude of the Harmonic Fourier series
    00:50

  • Find the Fourier expansion up to first harmonic and then find its amplitude
    09:23
  • Find the Fourier expansion of the displacement of armature up to 2nd harmonic
    13:22

  • Some important prerequisites of the Complex Fourier series
    03:28
  • Revise the general background of normal Fourier series
    01:42
  • Mathematical equation of Complex Fourier series and from where it comes?
    04:35
  • Important Mathematical derivation of basic Complex Fourier series equation
    20:24
  • Derivative of equation for full range Complex Fourier series taken with L
    04:00
  • Derivative of equation for half range Complex Fourier series taken with L
    01:31
  • Derivative of equation for full range Complex Fourier series taken with 'pi'
    05:02
  • Preview02:12

  • Find the solution of 'x' using full range Complex Fourier series taken with 'pi'
    14:15
  • Preview04:31
  • Find the value of a cosine function using half range Complex Fourier series
    09:09
  • Find the value of a sine function using full range Complex Fourier series
    10:01
  • Find the Complex form of an exponential function in a range -1 to 1
    04:47

  • What is Fourier Transform? Why we need it? and what is its applications?
    03:55
  • Three main types of Transforms and their comparisons
    02:56
  • Types of Fourier Transforms and comparisons based on their conditions
    04:11
  • Important comparisons of some Fourier transforms in time and frequency domains
    04:30
  • How Fourier Transform looks graphically in time and frequency domains?
    01:09
  • Understand the graphs of different transforms
    06:13
  • Basic equation of Fourier & Inverse Fourier Transforms written in different ways
    09:58
  • Some important prerequisites for Fourier Transforms
    10:51
  • Some more prerequisites for Fourier Transform, which are formulas
    03:10
  • Preview04:20
  • Equations of Inverse Fourier sine and cosine Transforms
    01:31
  • Prerequisites of Fourier sine and cosine Transforms
    00:45

  • Find the Fourier Transform of a piece-wise function within the domain -1 to 1
    14:14
  • Preview09:17
  • Find the value of a function using Fourier Transform and then apply its inverse
    19:10
  • Find the function by using Fourier Transform and then do proof using its inverse
    15:44
  • Identify the Fourier Transform of an exponential function
    11:23

  • Find the Fourier Sine Transform of a function within the domain -1 to 1
    05:56
  • Find the Fourier Cosine Transform of a function within the domain -1 to 1
    03:11
  • Identify the Fourier Cosine Transform of an exponential function
    04:03
  • Identify the Fourier Sine Transform of an exponential function
    03:06
  • Find the Fourier Cosine Transform, then apply its inverse to prove an equation
    06:44

Instructor

Moein Ud Din
Engineer
Moein Ud Din
  • 4.8 Instructor Rating
  • 68 Reviews
  • 18,214 Students
  • 3 Courses

This is Moein Ud Din, I am Electrical & Electronics Engineer, a programmer and instructor of Matlab, C++, PLC and an animation geek. It's my passion to pass my knowledge what I know to the desired entities. Kinda quintessential person, always hounding to make things ideal. I have plan in future to prepare more mathematics and engineering courses, would love to make things change in my own certain way. Critics are most welcome as long as it helps me and my students. Best wishes 


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