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- Objectives<\/strong>:
The objective is to find the relation between the variables x and y out of the given data (x,y).<\/li>\n\n\n\n- This aims to find such relationships which exactly pass through data or satisfy the data under the condition of least sum of squares of errors. The aim of numerical methods is to provide systematic methods for solving problems in a numerical form using the given initial data.<\/li>\n\n\n\n
- This topic deals with methods to find roots of an equation and solving a differential equation.<\/li>\n\n\n\n
- Numerical methods are important because finding an analytical procedure to solve an equation may not always be available.<\/li>\n\n\n\n
- In the diverse fields like electrical circuits, electronic communication, mechanical vibration and structural engineering, periodic functions naturally occur and hence their properties are very much required. Indeed, any periodic and non-periodic function can be best analyzed in one way by Fourier series and transforms methods.<\/li>\n\n\n\n
- The unit aims at forming a partial differential equation (PDE) for a function with many variables and their solution methods. Two important methods for first order PDE\u2019s are learnt. While separation of variables technique is learnt for typical second order PDE\u2019s such as Wave, Heat and Laplace equations.<\/li>\n\n\n\n
- In many Engineering fields the physical quantities involved are vector-valued functions.<\/li>\n\n\n\n
- Hence the unit aims at the basic properties of vector-valued functions and their applications to line\u00a0integrals, surface integrals and volume integrals.<\/li>\n<\/ul>\n\n\n\n
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<\/a><\/h4>\n\n\n\nUNIT \u2013 I: <\/strong>Vector Calculus: Vector Calculus: Scalar point function and vector point function, Gradient- Divergence- Curl and their related properties. Solenoidal and irrotational vectors \u2013 finding the Potential function. Laplacian
operator. Line integral \u2013 work done \u2013 Surface integrals -Volume integral. Green\u2019s Theorem, Stoke\u2019s theorem and Gauss\u2019s Divergence Theorems (Statement & their Verification).<\/p>\n\n\n\nUNIT \u2013 II: <\/strong>Fourier series and Fourier Transforms: Definition of periodic function.<\/p>\n\n\n\n
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- Fourier expansion of periodic functions in each interval of length two<\/li>\n\n\n\n
- Determination of Fourier coefficients \u2013 Fourier series of even and odd functions<\/li>\n\n\n\n
- Fourier series in an arbitrary interval \u2013 even and odd periodic continuation \u2013 Half-range Fourier sine and cosine expansions.<\/li>\n\n\n\n
- Fourier integral theorem – Fourier sine and cosine integrals. Fourier transforms \u2013 Fourier sine and cosine transforms \u2013 properties \u2013 inverse transforms \u2013 Finite Fourier transforms.<\/li>\n<\/ul>\n\n\n\n
UNIT \u2013 III: <\/strong>Interpolation and Curve fitting<\/strong><\/p>\n\n\n\n
Interpolation: Introduction- Errors in Polynomial Interpolation \u2013 Finite differences- Forward Differences Backward\u00a0differences \u2013Central differences Symbolic relations of symbols. Difference expressions \u2013 Differences\u00a0of a polynomial-Newton\u2019s formulae for interpolation – Gauss Central Difference Formulae \u2013Interpolation with\u00a0unevenly spaced points-Lagrange\u2019s Interpolation formula.\u00a0Curve fitting: Fitting a straight line \u2013Second degree curve-exponential curve-power curve by method of least\u00a0squares.<\/span><\/p>\n\n\n\n
TEXTBOOKS:<\/strong>
1. Advanced Engineering Mathematics by Kreyszig, John Wiley & Sons.
2. Higher Engineering Mathematics by Dr. B.S. Grewal, Khanna Publishers.<\/p>\n\n\n\nREFERENCES:<\/strong><\/p>\n\n\n\n
1. Mathematical Methods by T.K.V. Iyengar, B.Krishna Gandhi & Others, S. Chand.<\/span><\/p>\n\n\n\n
2. Introductory Methods by Numerical Analysis by S.S. Sastry, PHI Learning Pvt. Ltd.<\/span><\/p>\n\n\n\n
3. Mathematical Methods by G.Shankar Rao, I.K. International Publications, N.Delhi
4. Advanced Engineering Mathematics with MATLAB, Dean G. Duffy, 3rd Edi, 2013, CRC Press Taylor & Francis Group.
5. Mathematics for Engineers and Scientists, Alan Jeffrey, 6ht Edi, 2013, Chapman & Hall\/ CRC
6. Advanced Engineering Mathematics, Michael Greenberg, Second Edition. Person Education
7 Mathematics for Engineers By K.B.Datta And M.A S.Srinivas,Cengage Publications<\/p>\n\n\n\nOutcomes<\/strong>: From a given discrete data, one will be able to predict the value of the data at an intermediate point and by curve fitting, can find the most appropriate formula for a guessed relation of the data variables. This method of analysis data helps engineers to understand the system for better interpretation and decision making.<\/p>\n\n\n\n
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- After studying this unit, one will be able to find a root of a given equation and will be able to find a<\/li>\n\n\n\n
- numerical solution for a given differential equation. Helps in describing the system by an ODE, if possible. Also, suggests finding the solution as a first approximation.<\/li>\n\n\n\n
- One will be able to find the expansion of a given function by Fourier series and Fourier Transform of the function.<\/li>\n\n\n\n
- Helps in phase transformation, Phase change and attenuation of coefficients in acoustics.<\/li>\n\n\n\n
- After studying this unit, one will be able to find a corresponding Partial Differential Equation for an unknown function with many independent variables and to find their solution.<\/li>\n\n\n\n
- Most of the problems in physical and engineering applications, problems are highly non-linear and hence expressing them as PDEs\u2019. Hence understanding the nature of the equation and finding a suitable solution is very much essential.<\/li>\n\n\n\n
- After studying this unit, one will be able to evaluate multiple integrals (line, surface, volume integrals) and convert line integrals to area integrals and surface integrals to volume integrals.<\/li>\n\n\n\n
- It is an essential requirement for an engineer to understand the behavior of the physical system.<\/li>\n<\/ul>\n\n\n\n
Download the iStudy App for all syllabus and other updates.<\/a>
<\/a><\/h4>\n\n\n\nFor more information about all JNTU updates please stay connected to us on FB and don\u2019t hesitate to ask any questions in the comment.<\/p>\n\n\n\n