Getting equipped with the concept of algebraic geometry is always a challenging task for many students. Algebraic geometry is a vast vertical of mathematics which deals with shape, size, and properties of different figures in different dimensions. The Modern algebraic geometry is based on the abstract algebraic techniques mainly for solving geometrical problems. Some contemporary forms of geometry include differential geometry, euclidean geometry, topology, and algebraic geometry. Also, it is based on the practical and theoretical knowledge that create difficulties for the students to grasp this concept. If the students are note able to understand this aspect, it can result in their poor performance.
Algebraic geometry is one complex topic of geometry that deals with plane algebraic curves like hyperbolas, lines, circles, and parabolas; quartic and elliptic curves including Cassini ovals and lemniscates. It dates back to 5th century B.C. during the time of Hellenistic Greeks. The number theory can be combined with algebraic geometry for another active field of mathematics referred to as Arithmetic geometry. Here are some crucial topics that come under algebraic geometry.
According to our algebraic geometry assignment help experts, there are some different verticals related to it. These are as follows:
Algebraic geometry is a vast field that includes many topics and sub-topics. But, due to the involvement of geometrical terms and diagrams, it becomes a problematic work for most of the students. Also, the students who are new to this concept always lack and it results in their poor performance in the examination. Moreover, getting knowledge through the internet without any guidance will only confuse the student's mind as tons of geometrical terms available. Due to its complex structure, only a few numbers of students are able to do it efficiently. So, if you want to hold a perfect grip on this concept then EssayCorp is there to assist you. Over the years, our experts offer the best professional assistance to all the students who seek for algebraic geometry assignment help. With our team of skilled experts, students can get the can get rid of all their mathematics problems especially algebraic geometry assignments and projects. Our professionals hold years of experience in the field of mathematics and also acquire a lot of practical skills that help in getting your assignment done before the deadline. Besides it, our writers provide quality content with detailed research on the assigned topic.
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Three particles A, B and C lie in that order in a straight smooth groove so that they can only move along the x-axis. Both A and C are of unit mass whilst B is of mass M. Particle B is joined to the other two by identical linear springs of unit stiffness.
(a) If the three particles are displaced from equilibrium by distances x1, x2 and x3 show that the equations of motion are d2x1/dt2 = x2 - x1, M d2x2/dt2 = x3 - 2x2 + x1, d2x3/dt2 = x2 - x3.
(b) Prove that the frequencies of the three normal modes are given by ? = 0, 1 and ?2 = 1 + (2/M). [5 marks]
(c) Describe the motions of the particles corresponding to the normal modes.[4 marks]