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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:
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Parseval’s Identity of Fourier Series
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Harmonic Analysis
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Complex Fourier Series
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Fourier Transform
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Z-Transform
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Power Series
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Binomial Series
Perseval's Identity of Fourier Series - Introduction
Perseval's Identity of Fourier Series - Problems Solutions
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2What is Perseval's Identity of Fourier Series? where and why we use it?Video lesson
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3Check the simple Fourier series before to go for its Perseval's IdentityVideo lesson
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4Full range Equations of Perseval's Identity for both pi and LVideo lesson
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5Half range Equations of Perseval's IdentityVideo lesson
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6Proof of Perseval's Identity Equation when we take it with the pi rangeVideo lesson
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7Proof of Perseval's Identity Equation when we take it with the L rangeVideo lesson
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8Proof of Half range Cosine Perseval's Identity EquationVideo lesson
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9Proof of Half range Sine Perseval's Identity EquationVideo lesson
Harmonic Analysis of Fourier Series - Introduction
Harmonic Analysis of Fourier Series - Problems Solutions
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12What is Harmonic Fourier Series? and also know about its equation and variablesVideo lesson
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13First Harmonic Fourier series and Second Harmonic Fourier seriesVideo lesson
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14Third Harmonic Fourier series and Fourth Harmonic Fourier seriesVideo lesson
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15How to find the amplitude of the Harmonic Fourier seriesVideo lesson
Complex Fourier Series - Basics and Derivation of Equations
Complex Fourier Series - Problems Solutions
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18Some important prerequisites of the Complex Fourier seriesVideo lesson
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19Revise the general background of normal Fourier seriesVideo lesson
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20Mathematical equation of Complex Fourier series and from where it comes?Video lesson
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21Important Mathematical derivation of basic Complex Fourier series equationVideo lesson
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22Derivative of equation for full range Complex Fourier series taken with LVideo lesson
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23Derivative of equation for half range Complex Fourier series taken with LVideo lesson
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24Derivative of equation for full range Complex Fourier series taken with 'pi'Video lesson
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25Derivative of equation for half range Complex Fourier series taken with 'pi'Video lesson
Fourier Transform - Introduction, types, pre-requisites and graphs
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26Find the solution of 'x' using full range Complex Fourier series taken with 'pi'Video lesson
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27Find the solution of 'a' using full range Complex Fourier series taken with 'pi'Video lesson
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28Find the value of a cosine function using half range Complex Fourier seriesVideo lesson
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29Find the value of a sine function using full range Complex Fourier seriesVideo lesson
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30Find the Complex form of an exponential function in a range -1 to 1Video lesson
Fourier Transform - Problems Solutions for normal Fourier Transform
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31What is Fourier Transform? Why we need it? and what is its applications?Video lesson
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32Three main types of Transforms and their comparisonsVideo lesson
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33Types of Fourier Transforms and comparisons based on their conditionsVideo lesson
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34Important comparisons of some Fourier transforms in time and frequency domainsVideo lesson
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35How Fourier Transform looks graphically in time and frequency domains?Video lesson
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36Understand the graphs of different transformsVideo lesson
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37Basic equation of Fourier & Inverse Fourier Transforms written in different waysVideo lesson
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38Some important prerequisites for Fourier TransformsVideo lesson
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39Some more prerequisites for Fourier Transform, which are formulasVideo lesson
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40Equations and their derivations of Fourier sine and cosine TransformsVideo lesson
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41Equations of Inverse Fourier sine and cosine TransformsVideo lesson
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42Prerequisites of Fourier sine and cosine TransformsVideo lesson
Fourier Transform - Problems Solutions for sine and cosine Fourier Transforms
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43Find the Fourier Transform of a piece-wise function within the domain -1 to 1Video lesson
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44Find the Fourier Transform of a piece-wise function within the domain (-a to a)Video lesson
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45Find the value of a function using Fourier Transform and then apply its inverseVideo lesson
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46Find the function by using Fourier Transform and then do proof using its inverseVideo lesson
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47Identify the Fourier Transform of an exponential functionVideo lesson
Fourier Transform - Convolution Theorem
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48Find the Fourier Sine Transform of a function within the domain -1 to 1Video lesson
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49Find the Fourier Cosine Transform of a function within the domain -1 to 1Video lesson
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50Identify the Fourier Cosine Transform of an exponential functionVideo lesson
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51Identify the Fourier Sine Transform of an exponential functionVideo lesson
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52Find the Fourier Cosine Transform, then apply its inverse to prove an equationVideo lesson
Z-Transform - Introduction, Types and Equation Derivation
Z-Transform - Standard Results of Z-Transform
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56What is Z-Transform? Why we need it? and what is its applications?do comparisonVideo lesson
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57Three main types of Transforms and their comparisons based on their featuresVideo lesson
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58Basic equation of the Z transform, learn how it works?Video lesson
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59Derivation of the equation of Z transform with the help of a unite circleVideo lesson
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60One-sided Z-transform (left and right )and their representation on a number lineVideo lesson
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61Two-sided Z-transform (Bilateral ) and its representation on a number lineVideo lesson
Z-Transform - Region of Convergence
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62Standard Results 1, if signal is in exponential formVideo lesson
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63Standard Results 2, if sequence of the signal is any constant numberVideo lesson
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64Standard Results 3, if sequence of the signal is any random valueVideo lesson
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65Standard Results 4, if sequence of a signal has power more than 1Video lesson
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66Standard Results 5, if sequence of a signal has power 3Video lesson
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67Standard Results 6, if a sequence is the product of two signals and do its proofVideo lesson
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68Standard Results 7,product of two signals,one signal has +ve power, then proofVideo lesson
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69Standard Results 8, product of two signals (a^n*n), then prove it mathematicallyVideo lesson
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70Standard Results 9,10 if sequence of the signal is trigonometric, then prove itVideo lesson
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71Standard Results 11, product of sine and exponential signals,then give a proofVideo lesson
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72Standard Results 12, product of cosine and exponential signals,then give a proofVideo lesson
Z-Transform - Properties of the Region of Convergence
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73What we mean from the region of convergence and why it is important?Video lesson
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74Region of Convergence for a one-sided finite sequence and check it graphicallyVideo lesson
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75Region of Convergence for a two-sided finite sequence and check it graphicallyVideo lesson
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76Region of Convergence for an infinite sequence and check its typical equationVideo lesson
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77Region of Convergence for a left-sided Z-Transform and check it graphicallyVideo lesson
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78Region of Convergence for a Right-sided Z-Transform and check it graphicallyVideo lesson
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79Region of Convergence for a Two-sided Z-Transform and check it graphicallyVideo lesson
How long do I have access to the course materials?
You can view and review the lecture materials indefinitely, like an on-demand 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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