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Advanced Calculus of Higher Mathematics
Advanced Calculus of Higher Mathematics through animation,explanations,plenty of solved examples to help you in exam
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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

Complex Fourier Series

Fourier Transform

ZTransform

Power Series

Binomial Series
Perseval's Identity of Fourier Series  Introduction
Perseval's Identity of Fourier Series  Problems Solutions

2What is Perseval's Identity of Fourier Series? where and why we use it?Video lesson

3Check the simple Fourier series before to go for its Perseval's IdentityVideo lesson

4Full range Equations of Perseval's Identity for both pi and LVideo lesson

5Half range Equations of Perseval's IdentityVideo lesson

6Proof of Perseval's Identity Equation when we take it with the pi rangeVideo lesson

7Proof of Perseval's Identity Equation when we take it with the L rangeVideo lesson

8Proof of Half range Cosine Perseval's Identity EquationVideo lesson

9Proof of Half range Sine Perseval's Identity EquationVideo lesson
Harmonic Analysis of Fourier Series  Introduction
Harmonic Analysis of Fourier Series  Problems Solutions

12What is Harmonic Fourier Series? and also know about its equation and variablesVideo lesson

13First Harmonic Fourier series and Second Harmonic Fourier seriesVideo lesson

14Third Harmonic Fourier series and Fourth Harmonic Fourier seriesVideo lesson

15How to find the amplitude of the Harmonic Fourier seriesVideo lesson
Complex Fourier Series  Basics and Derivation of Equations
Complex Fourier Series  Problems Solutions

18Some important prerequisites of the Complex Fourier seriesVideo lesson

19Revise the general background of normal Fourier seriesVideo lesson

20Mathematical equation of Complex Fourier series and from where it comes?Video lesson

21Important Mathematical derivation of basic Complex Fourier series equationVideo lesson

22Derivative of equation for full range Complex Fourier series taken with LVideo lesson

23Derivative of equation for half range Complex Fourier series taken with LVideo lesson

24Derivative of equation for full range Complex Fourier series taken with 'pi'Video lesson

25Derivative of equation for half range Complex Fourier series taken with 'pi'Video lesson
Fourier Transform  Introduction, types, prerequisites and graphs

26Find the solution of 'x' using full range Complex Fourier series taken with 'pi'Video lesson

27Find the solution of 'a' using full range Complex Fourier series taken with 'pi'Video lesson

28Find the value of a cosine function using half range Complex Fourier seriesVideo lesson

29Find the value of a sine function using full range Complex Fourier seriesVideo lesson

30Find the Complex form of an exponential function in a range 1 to 1Video lesson
Fourier Transform  Problems Solutions for normal Fourier Transform

31What is Fourier Transform? Why we need it? and what is its applications?Video lesson

32Three main types of Transforms and their comparisonsVideo lesson

33Types of Fourier Transforms and comparisons based on their conditionsVideo lesson

34Important comparisons of some Fourier transforms in time and frequency domainsVideo lesson

35How Fourier Transform looks graphically in time and frequency domains?Video lesson

36Understand the graphs of different transformsVideo lesson

37Basic equation of Fourier & Inverse Fourier Transforms written in different waysVideo lesson

38Some important prerequisites for Fourier TransformsVideo lesson

39Some more prerequisites for Fourier Transform, which are formulasVideo lesson

40Equations and their derivations of Fourier sine and cosine TransformsVideo lesson

41Equations of Inverse Fourier sine and cosine TransformsVideo lesson

42Prerequisites of Fourier sine and cosine TransformsVideo lesson
Fourier Transform  Problems Solutions for sine and cosine Fourier Transforms

43Find the Fourier Transform of a piecewise function within the domain 1 to 1Video lesson

44Find the Fourier Transform of a piecewise function within the domain (a to a)Video lesson

45Find the value of a function using Fourier Transform and then apply its inverseVideo lesson

46Find the function by using Fourier Transform and then do proof using its inverseVideo lesson

47Identify the Fourier Transform of an exponential functionVideo lesson
Fourier Transform  Convolution Theorem

48Find the Fourier Sine Transform of a function within the domain 1 to 1Video lesson

49Find the Fourier Cosine Transform of a function within the domain 1 to 1Video lesson

50Identify the Fourier Cosine Transform of an exponential functionVideo lesson

51Identify the Fourier Sine Transform of an exponential functionVideo lesson

52Find the Fourier Cosine Transform, then apply its inverse to prove an equationVideo lesson
ZTransform  Introduction, Types and Equation Derivation
ZTransform  Standard Results of ZTransform

56What is ZTransform? Why we need it? and what is its applications?do comparisonVideo lesson

57Three main types of Transforms and their comparisons based on their featuresVideo lesson

58Basic equation of the Z transform, learn how it works?Video lesson

59Derivation of the equation of Z transform with the help of a unite circleVideo lesson

60Onesided Ztransform (left and right )and their representation on a number lineVideo lesson

61Twosided Ztransform (Bilateral ) and its representation on a number lineVideo lesson
ZTransform  Region of Convergence

62Standard Results 1, if signal is in exponential formVideo lesson

63Standard Results 2, if sequence of the signal is any constant numberVideo lesson

64Standard Results 3, if sequence of the signal is any random valueVideo lesson

65Standard Results 4, if sequence of a signal has power more than 1Video lesson

66Standard Results 5, if sequence of a signal has power 3Video lesson

67Standard Results 6, if a sequence is the product of two signals and do its proofVideo lesson

68Standard Results 7,product of two signals,one signal has +ve power, then proofVideo lesson

69Standard Results 8, product of two signals (a^n*n), then prove it mathematicallyVideo lesson

70Standard Results 9,10 if sequence of the signal is trigonometric, then prove itVideo lesson

71Standard Results 11, product of sine and exponential signals,then give a proofVideo lesson

72Standard Results 12, product of cosine and exponential signals,then give a proofVideo lesson
ZTransform  Properties of the Region of Convergence

73What we mean from the region of convergence and why it is important?Video lesson

74Region of Convergence for a onesided finite sequence and check it graphicallyVideo lesson

75Region of Convergence for a twosided finite sequence and check it graphicallyVideo lesson

76Region of Convergence for an infinite sequence and check its typical equationVideo lesson

77Region of Convergence for a leftsided ZTransform and check it graphicallyVideo lesson

78Region of Convergence for a Rightsided ZTransform and check it graphicallyVideo lesson

79Region of Convergence for a Twosided ZTransform and check it graphicallyVideo lesson
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You can view and review the lecture materials indefinitely, like an ondemand channel.
Can I take my courses with me wherever I go?
Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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Course details
Lectures
12
Quizzes
3
Video
20 hours
Certificate of Completion
Full lifetime access
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