- Accounting 745
- Accounting Education 12
- Actuarial Science 5
- Adult Education 11
- African Languages 4
- Agricultural Business And Financial Management 5
- Agricultural Economics 17
- Agricultural Engineering 3
- Agricultural Extension 3
- Agricultural Marketing And Cooperatives 11
- Agricultural Science 3
- Agricultural Science Education 1
- Agronomy 1
- Anatomy 1
- Animal Production 3
- Animal Science 5
- Archaeology And Museum 2
- Architecture 4
- Atmospheric And Environmental Physics 2
- Auditing And Forensic Accounting 9
- Banking And Finance 549
- Biochemistry 3
- Biology 2
- Biology Education 16
- Biomathematics 2
- Botany 3
- Brewing Science 5
- Building Technology 17
- Business Administration 476
- Business Education 18
- Business Management 33
- Chemical Engineering 4
- Chemistry 6
- Chemistry Education 6
- Child & Basic Education 14
- Child Right 3
- Civil Engineering 8
- Clothing And Fashion 1
- Commerce 10
- Communication Arts 7
- Computer Science 231
- Computer Science Education 17
- Cooperative And Rural Development 3
- Cooperative Economics 24
- Criminology And Security Studies 22
- Crop Production 9
- Crop Science And Environmental Protection 3
- Curriculum Studies 5
- Defence Studies 7
- Disaster & Risk Management 6
- Economics 362
- Economics Education 14
- Education 2178
- Education Foundation 18
- Education Management And Policy 4
- Educational Administration And Planning 9
- Educational Measurement And Evaluation 5
- Electrical Electronics Engineering 12
- Electronic Accounting 17
- Elementary Education 2
- Energy Economics 4
- English Language Education 16
- English Literary Studies 27
- Environmental Biology 2
- Environmental Geochemistry 1
- Environmental Geology 2
- Environmental Science 9
- Estate Management 44
- Ethics And Civic Education 2
- Fine & Applied Arts 5
- Fisheries And Aquaculture 2
- Food And Nutrition 3
- Food Science & Technology 21
- Forestry And Wildlife 2
- French 22
- French Education 4
- Gender And Women Studies 5
- Genetics And Biotechnology 1
- Geography 2
- Geography Education 4
- Geology 5
- Geophysics 1
- Guidance Counseling 12
- Health & Sex Education 5
- Health Economics 8
- Health Education 46
- Health Environmental Education And Human Kinetics 6
- Health Information Management 7
- History & International Relations 31
- Home And Rural Economics 7
- Home Economics 5
- Hospitality And Catering Management 11
- Human Resource Management 268
- Human Right 1
- Hydrogeology 3
- Industrial Chemistry 8
- Industrial Mathematics 1
- Industrial Physics 1
- Information Technology 17
- Insurance 16
- Integrated Science Education 8
- International Affairs And Strategic Studies 6
- International Law And Diplomacy 24
- Islamic And Arabic Studies 3
- Journalism 8
- Law 16
- Library And Information Science 5
- Linguistics 2
- Marine And Transport 3
- Marine Biology 1
- Marine Engineering 4
- Marketing 151
- Mass Communication 287
- Mathematical Economics 2
- Mathematics 15
- Mathematics Education 10
- Mba Finance 8
- Mechanical Engineering 6
- Medical And Health Science 13
- Medicine And Surgery 2
- Microbiology 17
- Music 4
- Nursing 12
- Office Technology & Management 11
- Petroleum Engineering 4
- Pharmacy 3
- Philosophy 38
- Physics 21
- Physics Education 11
- Political Science 128
- Primary Science Education 2
- Production And Management 1
- Project Management 1
- Psychology 12
- Psychology Education 5
- Public Administration 35
- Public Health 29
- Public Relations 12
- Purchasing And Supply 11
- Pure And Applied Chemistry 1
- Quantity Surveying 13
- Radiography And Radiological Sciences 5
- Religious And Cultural Studies 7
- Science And Computer Education 7
- Science Laboratory And Technology 14
- Secretarial Studies 9
- Smes & Entrepreneurship 145
- Social Science And Humanities 1
- Social Studies Education 8
- Sociology And Anthropology 24
- Soil Science 3
- Sports 1
- Staff Development And Distance Education 4
- Statistics 36
- Surveying And Geo-informatics 3
- Taxation 64
- Teacher Education 8
- Technical Education 1
- Theatre Arts 4
- Theology 17
- Tourism And Hospitality Management 56
- Urban & Regional Planning 13
- Veterinary 1
- Vocational Education 17
- Zoology 4
- MBA-MSC-PGD Thesis research materials
- Click Here For More Departments »
Call 09067754232 or for any enquiries.
DIFFERENTIATION AND ITS APPLICATION
From the beginning of time man has been interested in the rate at which physical and non physical things change. Astronomers, physicists, chemists, engineers, business enterprises and industries strive to have accurate values of these parameters that change with time.
The mathematician therefore devotes his time to understudy the concepts of rate of change. Rate of change gave birth to an aspect of calculus know as DIFFERENTIATION.
There is another subject known as INTEGRATION.
Integration And Differentiation in broad sense together form subject called CALCULUS
Hence in a bid to give this research project an excellent work, which is of great utilitarian value to the students in science and social science, the research project is divided into four chapters, with each of these chapters broken up into sub units.
Chapter one contains the introduction, scope of study, purpose of study, review of related literature and limitation.
Chapter two dwells on the fundamental of calculus which has to do with functions of single real variable and their graph, limits and continuity.
Chapter three deals properly with differentiation which also include gradient of a line and a curve, gradient function also called the derived function.
Chapter four contains the application of differentiation, summary and conclusion
1.2 Scope Of The Study And Limitation
This research work will give a vivid look at differentiation and its application.
It will state the fundamental of calculus, it shall also deal with limit and continuity.
For this work to be effectively done, there is need for the available of time, important related text book and financial aspect cannot be left out.
1.3 Purpose Of The Study
The purpose of this project is to introduce the operational principles of differentiation in calculus. Also to analyse many problems that have long be considered by mathematicians and scientists.
1.4 Significance Of The Study
The significance of this study cannot be over emphasized especially in this modern era where everything in the entire world is changing with respect to time, because the rate of change is an integral part of operation in science and technology, hence there is need to ascertain the origin of calculus and its application.
Finally, the goal of this work is to review the application of differentiation in calculus.
1.5 LITERATURE REVIEW
Calculus, historically known as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivations, integrals and infinite series.
Ideas leading up to the notion of function, derivatives and integral were developed through out the 17th century but the decisive step was made by Isaac Newton and Gottfried Leibniz.
Ancient Greek Precursors (Forerunners) Of The Calculus
Greek mathematicians are credited with a significant use of infinitesimals.
Democritus is the first person recorded to consider seriously the division of objects into an infinite number of cross-sections, but his inability to rationalize discrete cross-section with a cone’s smooth slope prevented him from accepting the idea, at approximately the same time.
Zeno of Elea discredited infinitesimals further by his articulation of the paradoxes which they create.
Antiphon and later Eudoxus are generally creadited with implementing the method of exhaustion which implementing the method of exhaustion which made it possible to compute the area and volume of regions and solids by breaking them up into an into an infinite number of recognizable shapes.
Archimedes of Syracuse developed this method further, while also inventing heuristic method which resemble modern day concept some what. It was not until the time of Newton that these methods were incorporated into a general framework of integral calculus.
It should not be thought that infinitesimals were put on a rigorous footing during this time, however.
Only when it was supplemented by a proper geometric proof would Greek mathematicians accept a proposition as true.
Pioneers of modern calculus
In the 17th century, European mathematicians Isaac barrow, Rene Descartes, Pierre deferment the idea of a deferment.
Blaise Pascal, john Wallis and others discussed the idea of a derivative. In particular, in method sad disquirendam maximum et minima and in De tangetibus linearism Curvarum, Fermat developed an adequality method for determining maxima, minima and tangents to various curves that was equivalent to differentiation.
Isaac Newton would latter write that his own early ideas about calculus came directly from formats way of drawing tangents
On the integral side cavalieri developed his method of in divisibles in the 1630s and 40s, providing a modern form of the ancient Greek method of exhaustion and computing cavalierr’s quadrate formula, the area under the curves Xn of higher degree, which had previously only been computed for the parabola by Archimedes.
Torricili extended this work to other curves such as cycloid and then the formula was generalized to fractional and negative powers by Wallis in 1656.
In an 1659 treatise, fermat is credited with an ingenious trick for evaluating the integral of any power function directly.
Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which influenced further work in quadrature.
James Gregory influenced by fermat’s contributions both to tangency and to quadrature, was then able to prove a restricted version on the second fundamental theorem of calculus in the mid -17th century. The first full proof of fundamental theorem of calculus was given by Isaac barrow.
Newton and Leibniz building on this work independently developed the surrounding theory of infinitesimal calculus in the late 17 century.
Also, leibniz did a great deal of work with developing consistent and useful notation and concepts.
Newton provided some of the most important applications to physics, especially of integral calculus.
Before Newton and Leibniz the word “calculus” was a general term used to refer to any body of mathematics, but in the following years, “calculus”. Became a popular term for a field of mathematics based upon their insight.
The work of both Newton and Leibniz is reflected in the notation used today.
Newton introduced he notation f for the derivative of function f.
Leibniz introduced the symbol