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Updated in [August 13th, 2023]

Skills and Knowledge Acquired:
By taking this course, students will acquire a comprehensive understanding of Advanced Calculus of Higher Mathematics, including topics such as Parseval's Identity of Fourier Series, Harmonic Analysis of Fourier Series, Complex Fourier Series, Fourier Transform, Z-Transform, Power Series, and Binomial Series. Students will gain knowledge of the equations, mathematical proofs, and problem solutions associated with each topic. Additionally, students will develop skills in graphical and numerical analysis, as well as the ability to differentiate and integrate power series.


Contribution to Professional Growth:
This course contributes to professional growth by providing a comprehensive overview of Advanced Calculus of Higher Mathematics. Through animation, videos, and examples, the course covers topics such as Parseval's Identity of Fourier Series, Harmonic Analysis of Fourier Series, Complex Fourier Series, Fourier Transform, Z-Transform, Power Series, and Binomial Series. By learning these topics, students will gain a better understanding of the fundamentals of Advanced Calculus of Higher Mathematics, which can be applied to a variety of professional fields. Additionally, the course's appealing, attractive, and fast-paced lectures make it an ideal choice for those who want to quickly gain a comprehensive understanding of the subject.


Suitability for Further Education:
This course is suitable for preparing further education. It covers a wide range of topics related to Advanced Calculus of Higher Mathematics, including Parseval's Identity of Fourier Series, Harmonic Analysis of Fourier Series, Complex Fourier Series, Fourier Transform, Z-Transform, Power Series, and Binomial Series. The course also includes videos explanation, graphical and numerical phase with formulas, verification and proofs both graphically and mathematically, and plenty of solved numerical problems with relevant examples. This makes it an ideal choice for students who want to gain a comprehensive understanding of the subject.

Course Syllabus

Introduction

Perseval's Identity of Fourier Series - Introduction

Perseval's Identity of Fourier Series - Problems Solutions

Harmonic Analysis of Fourier Series - Introduction

Harmonic Analysis of Fourier Series - Problems Solutions

Complex Fourier Series - Basics and Derivation of Equations

Complex Fourier Series - Problems Solutions

Fourier Transform - Introduction, types, pre-requisites and graphs

Fourier Transform - Problems Solutions for normal Fourier Transform

Fourier Transform - Problems Solutions for sine and cosine Fourier Transforms

Fourier Transform - Convolution Theorem

Intermission

Z-Transform - Introduction, Types and Equation Derivation

Z-Transform - Standard Results of Z-Transform

Z-Transform - Region of Convergence

Z-Transform - Properties of the Region of Convergence

Z-Transform - Properties of Z-Transform

Z-Transform - Finite Sequences (Introductions, graphs)

Z-Transform - Finite Sequences (Problems Solutions)

Z-Transform - Infinite Sequences (Introduction, types, techniques and ROC)

Z-Transform - Infinite Sequences (Problems Solutions)

Inverse Z-Transform - (Introduction, Methods and Derivations)

Inverse Z-Transform - (Problems Solutions)

Power Series - (Definition, equations and Mathematical Derivation)

Power Series - Convergence & Radius of convergence (Theory, Problems Solutions)

Power Series - Interval of Convergence (Theory & Problems Solutions)

Power Series - Differentiation and Integration (Introduction, Standard Results)

Power Series - Differentiation and Integration (Problems Solutions)

Binomial Series - Introduction (Definition, Equation, Prerequisites)

Binomial Series - Finite & Infinite Series - Methods to find the Binomial Series

Binomial Series - Problems Solutions - Finite Series Methods

Binomial Series - Problems Solutions - Infinite Series Method

Binomial Series - General Terms (Definition, Equation, nth terms)

Binomial Series - General Terms (Problems Solutions)

Binomial Series - Binomial Series as a Power Series

Bonus Materials