Introduction and
international mindedness
Known as infinitesimal calculus in its early history of calculus, the Newton-Leibnez Formula or the fundamental theorem of calculus shows the relationship between the derivative and integral and was developed in the later 17th century independently by Gottfried Leibniz and Isaac Newton, used for evaluating definite integrals.
In brief, it states that any continuous function over an interval has an antiderivative on that interval. This particularly elegant theorem shows the inverse function relationship of the derivative and the integral function can be used to find the area under the given function. Values input into the Newton-Leibniz formula will give the area under the function in squared units.
Method of exhaustion (Toolkit)
https://drive.google.com/file/d/12C6d48t6oOQAWxRyniZBiH7bIgX0ck6T/view
On the link above will contain a presentation and discussion regarding the method of exhaustion applied in one of the ways in finding the area under the curve, established by Eudoxus. This method is done by inscribing polygons (triangles) between the area of region bounded by a parabola and a straight line.
real-life applications
Throughout the investigation comes to some real-life applications of different concepts used for the method of exhaustion.
Engineering
Calculus could be use for architecture of buildings and bridges, and the optimization in the length of electrical cables in electrical engineering. It can also be used in kinematics where the calculation of speed, direction, and direction are essential such as flight engineering.
Sciences and research
Biology (Medical Science) – Differential calculus used to determine the exact exponential rate of growth in bacterial culture when different variables are applied.
Physics – Use of integration to calculate the Centre of Mass, Centre of Gravity and Mass Moment of Inertia of a sports utility vehicle. Also, calculating velocity and trajectory of an object to be applied in astronomy and electromagnetism.
Chemistry – Determining rate of reaction and information of Radioactive decay reaction.
Statistics and research analysis in businesses
Research analyst and statisticians makes use of calculus to consider the different variables present in businesses and corporations to increase profits by increase efficiency in its processes. Statistics can also be modelled to make best predictions suitable for the company.
IB Learner profiles
Courageous
We are courageous who challenge ourselves into exploring new ideas that leads to investigating theories that are new to us which is the Method of Exhaustion by Eudoxus and also other mathematical theorems that are involved.
INquirers
We nurture our curiosity, developing skills into inquire and research on the investigation. This curiosity is what makes it possible to develop new knowledge and exploring further deep into the topic.
Communicator
We express ourselves confidently and creatively. We collaborate effectively, and be good-listeners to have a good communication in the group that allow us to overcome problems faced in the toolkit.
Caring
We are empathetic people. We are all committed into investigating this toolkit while generating positive aura so that all members can be motivated and exert all of our capabilities to do a job well done.
knowledgeable
During research, we develop and use conceptual understanding on mathematical concepts and theorems across its range of applications. Engaging on these newly found ideas benefits us into being more knowledgeable in mathematics.
mathematical quote and brain teasers
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