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4th December 2019, 02:24 PM
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| Re: Kerala University Syllabus for BTECH
The syllabus of B. Tech (Bachelor of Technology) Mechanical Engineering Degree Course offered by University of Kerala is as follows: 08.103 ENGINEERING MATHEMATICS- I MODULE- 1 Applications of differentiation:– Definition of Hyperbolic functions and their derivatives- Successive differentiation- Leibnitz’ Theorem(without proof)- Curvature Radius of curvature- centre of curvature- Evolute ( Cartesian ,polar and parametric forms) Partial differentiation and applications:- Partial derivatives- Euler’s theorem on homogeneous functions- Total derivatives- Jacobians- Errors and approximations Taylor’s series (one and two variables) - Maxima and minima of functions of two variables - Lagrange’s method- Leibnitz rule on differentiation under integral sign. Vector differentiation and applications :- Scalar and vector functions differentiation of vector functions-Velocity and acceleration- Scalar and vector fields Operator∇ - Gradient- Physical interpretation of gradient- Directional derivative Divergence- Curl- Identities involving ∇ (no proof) - Irrotational and solenoidal fields – Scalar potential. MODULE-II Laplace transforms:- Transforms of elementary functions - shifting property Inverse transforms- Transforms of derivatives and integrals- Transform functions multiplied by t and divided by t - Convolution theorem(without proof)-Transforms of unit step function, unit impulse function and periodic functions-second shifiting theorem- Solution of ordinary differential equations with constant coefficients using Laplace transforms. Differential Equations and Applications:- Linear differential equations with constant coefficients- Method of variation of parameters - Cauchy and Legendre equations –Simultaneous linear equations with constant coefficients- Application to orthogonal trajectories (cartisian form only). MODULE-III Matrices:-Rank of a matrix- Elementary transformations- Equivalent matrices Inverse of a matrix by gauss-Jordan method- Echelon form and normal form- Linear dependence and independence of vectors- Consistency- Solution of a system linear equations-Non homogeneous and homogeneous equations- Eigen values and eigen vectors – Properties of eigen values and eigen vectors- Cayley Hamilton theorem(no proof)- Diagonalisation- Quadratic forms- Reduction to canonical forms-Nature of quadratic forms-Definiteness, rank, signature and index. REFERENCES 1. Kreyszig; Advanced Engineering Mathematics, 8th edition, Wiley Eastern. 2. Peter O’ Neil ; Advanced Engineering Mathematics, Thomson 3. B.S.Grewal ; Higher Engineering Mathematics, Khanna Publishers 4. B.V.Ramana; Higher Engineering Mathematics, Tata Mc Graw Hill, 2006 5. Michel D Greenberg; Advanced Engineering Mathematics, Pearson International 6. Sureshan J, Nazarudeen and Royson; Engineering Mathematics I, Zenith Publications Syllabus B. Tech Mechanical Engineering University of Kerala     |