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State and prove fundamental theorem of cyclic groups?
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What does the fundamental theorem of arithmetic state?
Fundamental theorem of arithmetic :- Every composite number can be expressed (factorized) as a product of primes, and this factorization is unique . apart from the other in which factors occur.
State and explain Theorem of transmissibility of forces?
states that the external effect of force are independent of the point of application of the force along its line of action.
State the main reason for using the empirical rule rather than chebyshevs theorem?
The empirical rule can only be used for a normal distribution, so I will assume you are referring to a normal distribution. Chebyshev's theorem can be used for any distribution. The empirical rule is more accurate than Chebyshev's theorem for a normal distribution. For 2 standard deviations (sd) from the mean, the empirical rule says 95% of the data are within that, and Chebyshev's theorem says 1 - 1/2^2 = 1 - 1/4 = 3/4 or 75% of the data are within that. From the standard normal distribution chart, the answer for 2 sd from the mean is 95.44% So, as you can see the empirical rule is more accurate.
What does Pythagoras most famous proof state?
Pythagoras most famous proof is the pythagorean proof . It states that in a right angled triangle , the square of hypoteneus ( the longest side of the triangle ) is equal to the sum of squares of the other two sides .
What are the key differences between the Laplace transform and the Fourier transform?
The key differences between the Laplace transform and the Fourier transform are that the Laplace transform is used for analyzing signals with exponential growth or decay, while the Fourier transform is used for analyzing signals with periodic behavior. Additionally, the Laplace transform includes a complex variable, s, which allows for analysis of both transient and steady-state behavior, whereas the Fourier transform only deals with frequencies in the frequency domain.
Difference between fourier transform and z-transform?
Laplace Transforms are used primarily in continuous signal studies, more so in realizing the analog circuit equivalent and is widely used in the study of transient behaviors of systems. The Z transform is the digital equivalent of a Laplace transform and is used for steady state analysis and is used to realize the digital circuits for digital systems. The Fourier transform is a particular case of z-transform, i.e z-transform evaluated on a unit circle and is also used in digital signals and is more so used to in spectrum analysis and calculating the energy density as Fourier transforms always result in even signals and are used for calculating the energy of the signal.
What is the Syllabus of engg mathematics for Be?
MA1201 MATHEMATICS III 3 1 0 100 AIM The course aims to develop the skills of the students in the areas of boundary value problems and transform techniques. This will be necessary for their effective studies in a large number of engineering subjects like heat conduction, communication systems, electro-optics and electromagnetic theory. The course will also serve as a prerequisite for post graduate and specialized studies and research. OBJECTIVES At the end of the course the students would • Be capable of mathematically formulating certain practical problems in terms of partial differential equations, solve them and physically interpret the results. • Have gained a well founded knowledge of Fourier series, their different possible forms and the frequently needed practical harmonic analysis that an engineer may have to make from discrete data. • Have obtained capacity to formulate and identify certain boundary value problems encountered in engineering practices, decide on applicability of the Fourier series method of solution, solve them and interpret the results. • Have grasped the concept of expression of a function, under certain conditions, as a double integral leading to identification of transform pair, and specialization on Fourier transform pair, their properties, the possible special cases with attention to their applications. • Have learnt the basics of Z - transform in its applicability to discretely varying functions, gained the skill to formulate certain problems in terms of difference equations and solve them using the Z - transform technique bringing out the elegance of the procedure involved. UNIT I PARTIAL DIFFERENTIAL EQUATIONS 9 + 3 Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions - Solution of standard types of first order partial differential equations - Lagrange's linear equation - Linear partial differential equations of second and higher order with constant coefficients. UNIT II FOURIER SERIES 9 + 3 Dirichlet's conditions - General Fourier series - Odd and even functions - Half range sine series - Half range cosine series - Complex form of Fourier Series - Parseval's identify - Harmonic Analysis. UNIT III BOUNDARY VALUE PROBLEMS 9 + 3 Classification of second order quasi linear partial differential equations - Solutions of one dimensional wave equation - One dimensional heat equation - Steady state solution of two-dimensional heat equation (Insulated edges excluded) - Fourier series solutions in Cartesian coordinates. UNIT IV FOURIER TRANSFORM 9 + 3 Fourier integral theorem (without proof) - Fourier transform pair - Sine and Cosine transforms - Properties - Transforms of simple functions - Convolution theorem - Parseval's identity. UNIT V Z -TRANSFORM AND DIFFERENCE EQUATIONS 9 + 3 Z-transform - Elementary properties - Inverse Z - transform - Convolution theorem -Formation of difference equations - Solution of difference equations using Z - transform. TUTORIAL 15 TOTAL : 60 TEXT BOOKS 1. Grewal, B.S., "Higher Engineering Mathematics", Thirty Sixth Edition, Khanna Publishers, Delhi, 2001. 2. Kandasamy, P., Thilagavathy, K., and Gunavathy, K., "Engineering Mathematics Volume III", S. Chand & Company ltd., New Delhi, 1996. 3. Wylie C. Ray and Barrett Louis, C., "Advanced Engineering Mathematics", Sixth Edition, McGraw-Hill, Inc., New York, 1995. REFERENCES 1. Andrews, L.A., and Shivamoggi B.K., "Integral Transforms for Engineers and Applied Mathematicians", Macmillen , New York ,1988. 2. Narayanan, S., Manicavachagom Pillay, T.K. and Ramaniah, G., "Advanced Mathematics for Engineering Students", Volumes II and III, S. Viswanathan (Printers and Publishers) Pvt. Ltd. Chennai, 2002. 3. Churchill, R.V. and Brown, J.W., "Fourier Series and Boundary Value Problems", Fourth Edition, McGraw-Hill Book Co., Singapore, 1987.
State and prove Arzela Ascoli theorem?
I will give a link that explains and proves the theorem.
Definition of kleene's theorem plus example?
kleene's theorem state that those who defined fa
What does each theorem state?
what is mid point theoram?
State and prove fundamental theorem of cyclic groups?
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How do you find the standard form after you have used the De Moivre's theorem?
(cos0 + i sin0) m = (cosm0 + i sinm0)
What does the triangle inequality theorem state?
The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides.
What does the Central Limit Theorem state?
The Central Limit Theorem (abbreviated as CLT) states that random variables that are independent of each other will have a normally distributed mean.
What us state that has a transform boundary?
California is the U.S. state that has a transform boundary, specifically along the San Andreas Fault. This boundary is responsible for the lateral sliding motion between the Pacific Plate and the North American Plate, which leads to earthquakes in the region.
How do you get in the avatar state in burning earth wii?
You can't transform into the Avatar state in The Burning Earth.
