MTH620 - Mathematics Project Fractional Calculus and its Applications Spring 2019

Fractional Calculus and its Applications.

 

Supervisor Name: ---Saima Kanwal

Supervisor Email: ---saimakanwal@vu.edu.pk--

 

Project Description:

 In calculus, one learns how to define the derivative of a function and the integral of a function and how to calculate derivatives and integrals of higher orders. At this point when studying mathematics, to contemplate generalizing derivatives and integrals to a more general idea, we generalize the concept of derivatives and integrals to an arbitrary order. In this project we will discuss derivatives and integrals that have been studied in calculus to a more general setting, along with the study of ordinary differential equations. We will start with some history of fractional calculus, look at some different definitions of how to define derivatives and integrals of arbitrary order, prove some properties and look at some basic examples, and then finally look at fractional differential equations.

 

 

 

We will require following deliverables during this semester:

Deliverables:

  • Introduction

 

  • Preliminaries

 

In this portion you will first explain what the background of this topic. Any preliminaries of the topic should be discussed in brief form. You will write all the definitions, theorems, and related results which are required to form the basis of your main topic.

 

  • Introduction of the topic to be explored

 

You will write the introduction of the topic after all the pre requisites. This will include the aims and objective of your topic. Further you will propose the methods which you will opt to solve your project related problems.

 

 

  • Main Body

 

  • Provide a paragraph which explains how the problem will be approached.
  • Carefully outline the steps you will take and give some explanation of why you are taking that approach. 
  • Clearly state the assumptions, visual components (diagrams, tables, graphs) and define all variables used in your problem.
  • Explain how each formula is derived or give a reference in which the formula can be found.   

 

  • Remarks and Conclusion

This is the part of your project report in which you will interpret and explain the mathematical solution to the problem or question presented in the original assignment.

 

  • Presentation

 

This will be the power point presentation of your project which you will be presenting during your final viva.

 

Note:

For final viva/presentation you will have to come up with Application/project/configuration complete and PPT slides of same project in running state to avoid any inconvenience.

 

Instruction for Writing Project

Please read the guidelines carefully to avoid wastage of time and other resources involved in revision of the Project.

  • The Top, Bottom and Right margins should be 1”, while the Left (binding side) margin should be of 1.5 inches to allow binding.
  • Times New Roman script shall be used to write a project.
  • The typeface/font size in the main body of the thesis should be 12-point. Footnotes should be 10-point.
  • Line spacing in main body of text should be 1.5. Anyhow, single line space should be used in footnotes. Long quotations should also be single spaced and indented.
  • Introductory pages should be numbered in lower case Roman numerals (i, ii, iii ...). The title page is counted as page “i” but the page number is not printed.
  • For the body of the thesis including text, chapter title pages, section dividing pages, illustrations, appendices, and bibliography, use Arabic numerals (1, 2, 3 ...). The numbering begins with one (1) and runs consecutively to the final page or end of the manuscript. Do not use suffixes to the Arabic numerals, such as 12a.
  • All page numbers of the thesis or dissertation are placed in the centre at the bottom of the page. Page numbers must be at least two single spaces below the nearest line of text. All page numbers must be in the same font and size as the text.
  • The Project must be presented in English.
  • The title of the Project should be exactly the same, in all aspects, as approved and notified by the ASRB. The case of the alphabets (upper/lower), effects of the text fonts (subscript, superscript, italic, etc.), special characters including punctuation, word dividers and general typographical characters (., “, &, ?, /, :, ;, etc) should be reproduced in the same manner as in the notified title.

Tags: -, 2019, Applications, Calculus, Fractional, MTH620, Mathematics, Project, Spring, and, More…its

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