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Jean Baptiste Joseph Fourier was a French mathematician, physicist and engineer, and the founder of Fourier analysis.

### JEE Mathematics Notes: Sequence and Series

Fourier series are used in the analysis of periodic functions. The Fourier transform and Fourier's law are also named in his honour. Graphically, even functions have symmetry about the y-axis,whereas odd functions have symmetry around the origin. Intuition: The area beneath the curve on [-p, 0] is the same as the area under the curve on [0, p], but opposite in sign.

So, they cancel each other out! Intuition: The area beneath the curve on [-p, 0] is the same as the area under the curve on [0, p], but this time with the same sign.

So, you can just find the area under the curve on [0, p] and double it! Intuition: periodic functions have repetitive behavior. A periodic function can be defined on a finite interval. There is also a different normalization in use: the kernels D n and are often multiplied by 2. They are then represented also by the series. Parseval's theorem usually refers to the result that the Fourier transform is unitary, that the sum or integral of the square of a function is equal to the sum or integral of the square of its transform.

Area formulas for all Shapes. Volume formulas for all Shapes. Law of Indices. Fourier Series formula. Mechanics Equation. Modern Physics Equation. Thermal Physics Equation. Waves Optics Equations. Fourier Series - Introduction Jean Baptiste Joseph Fourier was a French mathematician, physicist and engineer, and the founder of Fourier analysis.

Integrating even functions over symmetric domains. If f x is an odd function, then Intuition: The area beneath the curve on [-p, 0] is the same as the area under the curve on [0, p], but opposite in sign. If f x is an even function, then Intuition: The area beneath the curve on [-p, 0] is the same as the area under the curve on [0, p], but this time with the same sign. The smallest such T is called the period of f x. A periodic function can be defined on a finite interval, then copied and pasted so that it repeats itself.

They are then represented also by the series 7. Riemann's Theorem. Parseval's Theorem.From the following B. We provide B.

Tech students with free of cost and it can download easily and without registration need. To impart analytical ability in solving mathematical problems as applied to the respective branches of Engineering. To apply advanced matrix knowledge to Engineering problems and equip themselves familiar with the functions of several variables. To improve their ability in solving geometrical applications of differential calculus problems To expose to the concept of three-dimensional analytical geometry.

Second-order linear homogeneous equations with constant coefficients; differential operators; solution of homogeneous equations; Euler-Cauchy equation; linear dependence and independence; Wronskian; Solution of nonhomogeneous equations: general solution, complementary function, particular integral; solution by variation of parameters; undetermined coefficients; higher order linear homogeneous equations; applications.

Eigen values, Eigen vectors, Cayley Hamilton theorem, basis, complex matrices; quadratic form; Hermitian, SkewHermitian forms; similar matrices; diagonalization of matrices; transformation of forms to principal axis conic section. Laplace Transform, Inverse Laplace Transform, Linearity, transform of derivatives and Integrals, Unit Step function, Dirac delta function, Second Shifting theorem, Differentiation and Integration of Transforms, Convolution, Integral Equation, Application to solve differential and integral equations, Systems of differential equations.

Vector and Scalar functions and fields, Derivatives, Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field.

Applications: Finding the current in electrical circuits. Eigen values — Eigen vectors — Properties — Cayley-Hamilton theorem Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form — Rank — Positive, negative and semi definite — Index — Signature.

Applications: Free vibration of a two-mass system. Curve tracing: Cartesian, Polar and Parametric forms. Multiple integrals: Double and triple integrals — Change of variables —Change of order of integration. Applications: Finding Areas and Volumes.

Applications: Evaluation of integrals. Gradient- Divergence- Curl — Laplacian and second-order operators -Vector identities. Applications: Equation of continuity, potential surfaces. Line integral — Work is done — Potential function — Area- Surface and volume integrals Vector integral theorems: Greens, Stokes and Gauss Divergence theorems without proof and related problems. Applications: Work is done, Force. The Main Unit of the book are: 1 Algebra 1. Share this article with your classmates and friends so that they can also follow Latest Study Materials and Notes on Engineering Subjects.

I want to download m3 material but not avalible plz send to my email. Leave A Reply Cancel Reply. Save my name, email, and website in this browser for the next time I comment. Notify me of follow-up comments by email. Notify me of new posts by email. Study Material Books. Content in this Article. Related Topics. This field is for validation purposes and should be left unchanged. Hemant Garg says 2 years ago. Balaji nilla says 2 years ago. Harika says 2 years ago.

Chandrika says 1 year ago. Please upload m1 S.Mathematically, a sequence is defined as a map whose domain is the set of natural numbers which may be finite or infinite and the range may be the set of real numbers or complex numbers. We can represent it as. A sequence is often confused with a set. Though they both appear to be same yet they are different. A sequence is almost the same as a set except for the fact that in a set the elements cannot repeat while it is not so in case of a sequence.

Moreover, there is no importance of order in a set, while the order matters a lot in sequence. The following example will further clear the difference between the two:.

Gate Engineering Mathematics : Quick Revision - Must Watch - Part #1 Linear Algebra & Vectors

A sequence is said to be in Arithmetic Progression when they increase or decrease by a constant number.

This constant number is called the common difference d of the arithmetic progression. When three numbers are in A. Similarly we can find the two arithmetic means between two number. The concept of arithmetic mean has been already discussed in the previous sections.

This concept can be extended till the mth power for terms and such mean is termed as the arithmetic mean of mth power. Mathematically, the arithmetic mean for mth power is defined as. The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression then it is said to be in harmonic progression. The harmonic mean of two numbers is in fact the reciprocal of arithmetic mean of the reciprocal of the numbers.

Another concept closely related to harmonic mean is that of weighted harmonic mean. Harmonic mean is in fact a special case of weighted harmonic mean where all the weights are equal to 1 and is equal to any weighted harmonic mean having all equal weights. Let d be the common difference of the A. Since the terms within the brackets are either in an A. Open System A system Skip to content. The value of the sum of n terms in a G. P depends on the value of r.

We have different values according to whether r is equal to 1 or is not equal to 1.

## Engineering Mathematics-3 Study Material - Download M-III Text Book & Lecture Notes PDF

Harmonic Progression The simplest way to define a harmonic progression is that if the inverse of a sequence follows the rule of an arithmetic progression then it is said to be in harmonic progression. Formula for Harmonic mean Let H be the harmonic mean between two numbers a and b. So, a, H, b are in H. Weighted Harmonic Mean Another concept closely related to harmonic mean is that of weighted harmonic mean. Relation between A. Don't miss out! Subscribe To Our Newsletter. Learn new things. Get an article everyday.

Give it a try.The population parameters are in general, not known and their estimates given by the corresponding sample statistic are used. Greek letters are used to denoted population parameters and Roman letters for sample statistic. Sampling aims at gathering the maximum information about the population with the minimum effort, cost and time. The object of sampling studies is to obtain the best possible value of the parameters under specific conditions.

Sampling determines reliability of these estimates. The logic of the sampling theory is the logic of induction in which we pass from a particular sample to general population. Such a generalization from sample to population is called statistical inference. Consider all possible sample of size n which can be drawn from a given population at random.

For each sample, mean can be computed. The mean of the samples will not be identical. If these different means are grouped according of their frequencies, the frequency distribution so formed is called sampling distribution of the mean.

Similarly sampling distribution of the standard deviation etc, can be obtained. When drawing each sample, the previous sample is put back so that the parent population remains the same.

This is called sampling with replacement and all subsequent formulae will pertain to sampling with replacements. It is used to assess the difference between expected and observed values. Standard deviation of the sampling distribution is called standard error S. Thus standard error of the sampling distribution of means is called standard error of means. The reciprocal of the standard error is called precision. The sampling distribution of large samples is assumed to be normal. Collection of all possible samples is population. It is impractical to collect data on each sample of a population.Mathematics is a very important subject in terms of school, college exams as well as competition exams.

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## Engineering Books Pdf

We just providing the link already available on internet. If any way it violates the law or has any issues then kindly Contact Us. Thank You! Railway new practice set assistant loco pilot. Please enter your comment! Please enter your name here.Maths formulas PDF enables students to complete the syllabus in a unique do-learn-do pattern of study.

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Perimeter of a Trapezoid Formula. Area of a Sector of a Circle Formula.