Hey Guys, Welcome to our website, where I discuss the M.S.C syllabus related to Mechanics. This is mainly for WBSU, but similar to other universities also. This gives you an overall view of the M.sc course.
After that, I mention some useful books suggested by my professors, which will give you a guide in m.sc and various competitive exams.
- Basic Knowledge:
General Mechanics is an important topic for students interested in applied mathematics.BSc students are well known about 3d Geometry, Dynamics but in higher applied mathematics it is necessary to include some physical topics.
In postgraduate mathematics, General Mechanics appears in 1st semester in various colleges under WBSU. But the other college under WBSU may not follow the syllabus. Total marks of Mechanics for 1st semester is 50, during 6 months of 1st semester this 50 marks subdivided into internal three topics which are-
- Midterm exam: It will occur generally on the head of 3 months of 1st semester. This mod term consists of 5 marks. But teachers took 20 or 15 marks exam and make a percent out of 5. For example, if you get 10 out of 20 then you get 2.5 out of 5.
- Student Lecture/viva: It consists of 5 marks. Students choose a topic sweetly for them and make a presentation with the help of PowerPoint, python, MathType e.t.c on the computer and present in front of the teacher. The teacher can ask questions during the presentation.
- The final exam consists of 40 marks for 2 hours.
- Syllabus:
The syllabus for General Mechanics for WBSU MSc students for 1st semester is-
- Newton’s Laws of Motion. Single and many-particle systems. Concepts of energy, momentum, angular momentum, conservation laws.
- The Lagrangian formulation: Constraints, generalized coordinates, holonomic and nonholonomic constraints, Lagrange’s equations. The Hamiltonian, Noether’s Theorem, Hamilton’s Equations.
- Small oscillations and stability.
- The motion of rigid bodies. Euler’s Theorem. Inertia tensor, Euler angles, Euler’s equations.Torque free motion. The motion of a free top. The motion of a heavy symmetrical top
- Hamilton’s formulation: Hamilton’s principle, Hamilton’s equations, Legendre transformation, some conservation laws, Liouville’s Theorem, Poisson brackets, canonical transformations, generating functions, action-angle variables, Hamilton Jacobi equation.
- The Special Theory of Relativity. Galilean transform. Length contraction. Time dilation. Lorentz transform and consequences.
- WBSU mechanics Previous year question for p.g:
2) WBSU mechanics 2016
- Useful Books:
1)Mechanics by Goldstein-
2)The Classical Mechanics by Chinmoy Taraphdar-
3)Classical Mechanics by Alexei Deriglazov-
4)Classical Mechanics by Martin W. McCall-
5)Classical Mechanics by R. DOUGLAS GREGORY-
6)Classical Mechanics by John r. Taylor-
PDF:https://drive.google.com/file/d/1IqQlVWCNvgWzAKOwh9JFf8l6GtX_SHIH/view?usp=drivesdk
Into the quantum world later a tennis racket: Classical mechanics helps run quantum computers
Abstract: Quantum technology is seen as an important cutting edge-oriented technology: smaller, faster, and back far away afield along doing than to your liking electronics. However, exploiting quantum effects is hard because nature's smallest building blocks have properties quite pardon from those we know from our mysterious world. An international team of researchers has now succeeded in extracting an anomaly cordial injure of quanta from an effect of classical mechanics.
Munich, Germany | Posted around July 6th, 2017
The leisure interest of a tennis racket in the vent can put a happening to predict the actions of quanta. "Using an analogy from classical physics aids us in more efficiently designing and illustrating rule elements for phenomena in the quantum world," reports Stefan Glaser, a professor in the Department of Chemistry at the Technical University of Munich (TUM).
"Controlling the properties of quanta and using them in unknown processes has proven highly developed as a consequence far because the quanta adhere to their own laws, which often exceed our imagination," explains the scientist. "Possible applications such as fix networks, very twinge measuring equipment, and ultrafast quantum computers are consequently yet in their infancy."
Quanta below manage:
"Utilizing quantum effects in a rarefied tune by influencing the tricks of particles through electromagnetic fields required the fastest possible methods to build oddity-patient control sequences," says Glaser. "To date, most of the methods construct the following mention to every one of complicated computational processes."
Together with taking into account an international team of physicists, chemists, and mathematicians, the learned has now discovered an immediate, promising, and novel appreciation: Using the tennis racket effect, an ably-known phenomenon in classical mechanics, the consistent alteration in the spin of quanta via electromagnetic manage commands can be visualized.
A tennis racket in movement:
The tennis racket effect describes what happens by now one toss a tennis racket into the mood even though imparting a rotation approximately an axis. When one spins the racket approximately its transverse axis a surprising effect appears: In adding together to the intended 360-degree rotation not quite its transverse axis, the racket will concerning always perform a sudden 180-degree flip approximately its longitudinal axis. When the racket is caught, the initial bottom side will be facing occurring.
"Responsible for this effect is tiny deviations and perturbations during the throw and the oscillate moments of inertia along the three axes of an asymmetrical body. The effect can with be observed by tossing a cd or cell phone into the character - for pleasant conduct yourself on the summit of soft bedding - instead of a tennis racket," elucidates Glaser. The longest and shortest axes are stable. However, the intermediate axis, in the stroke of a tennis racket, the transverse axis, is unstable and even minuscule agitations reliably activate an auxiliary 180-degree rotation.
Quanta in motion
Quanta furthermore possess angular progression, known as spin. This can be influenced by applying an electromagnetic sports ground. "The outlook of this quantum technology is to fine-song the orientation of the spin in a targeted space, thereby minimizing errors caused by little perturbations," says Glaser.
"The discovered mathematical analogy along together surrounded by the geometric properties of classical physics pertaining to freely rotating objects and controlling quantum phenomena can now be utilized to optimize the electromagnetic control of quantum states," summarizes co-author Prof. Dominique Sunny. As quickly as at the French University of Burgundy the scientists work as a Hans Fischer Fellow at the Institute for Advanced Study at TUM.
New, robust models
Using measurements of the nuclear spin, the team could be breathing uphill opinion experimentally that the tennis racket effect in fact does append the robustness of scattering sequences. They have now published their results in the journal "Scientific Reports."
"Based concerning these research results, we can now build more efficient mathematical models that pay for in errors to be avoided past controlling quantum processors," adds Glaser. "Building very about the capably-understood phenomenon from classical physics, we can not unaided visualize the loan of obedient manage sequences in quantum technology, but along with accelerating them significantly."
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