Syllabus Engineering Mathematics - III (2403111/2393111/2413111/2043111/2033111) (Mechanical / Mechanical & Automation / Mechatronics / Automobile / Automation and Robotics) Theory Term work Pract / Oral Total Internal Assessment End Sem Exam Exam Duration (in Hrs) Test 1 Test 2 Total 20 20 40 60 02 hrs 25 - 125 Module Detailed Content 1 Module : Laplace Transform 1.1 Definition of Laplace transform, Condition of Existence of Laplace transform, Laplace Transform (L) of Standard Functions like πππ‘, π ππ(ππ‘), πππ (ππ‘), π ππβ(ππ‘), πππ β(ππ‘) and π‘π , π€βπππ π ο³ 0. 1.2 Properties of Laplace Transform : Linearity, First Shifting theorem, change of scale Property, multiplication by t, Division by t, Laplace Transform of integrals (Properties without proof). 1.3 Evaluation of integrals by using Laplace Transformation. (Chapter - 1) 2 Module : Inverse Laplace Transform 2.1 Inverse Laplace Transform, Linearity property, use of standard formulae to find inverse Laplace Transform, finding Inverse Laplace transform using derivative. 2.2 Partial fractions method & first shift property to find inverse Laplace transform. 2.3 Inverse Laplace transform using Convolution theorem (without proof). (Chapter - 2) 3 Module : Fourier Series 3.1 Dirichletβs conditions, Definition of Fourier series. Fourier series of periodic functions with period 2Ο and 2l (No questions should be ask on split function). 3.2 Fourier series of even and odd functions. (No question should be asked on split function). 3.3 Half range Sine and Cosine Series. (Chapter - 3) 4 Module : Complex Variables 4.1 Function f(z) of complex variable, limit, continuity and differentiability of f(z), Analytic function, necessary and sufficient conditions for f(z) to be analytic (without proof), Cauchy-Riemann equations in cartesian coordinates (without proof). 4.2 Milne-Thomson method to determine analytic function f(z) when real part (u) or Imaginary part (v) is given. 4.3 Harmonic function, Harmonic conjugate. (Chapter - 4) 5 Module : Matrices 5.1 Characteristic equation, Eigen values and Eigen vectors, Properties of Eigen values and Eigen vectors. (No theorems / proof). 5.2 Cayley-Hamilton theorem (without proof) : Application to find the inverse of the given square matrix and to determine the given higher degree polynomial matrix. 5.3 Similarity of matrices, Diagonalization of matrices. (Chapter - 5) 6 Module : Numerical methods for PDE 6.1 Introduction of Partial Differential equations, method of separation of variables, Vibrations of string, Analytical method for one dimensional heat equations. (only problems). 6.2 Crank Nicholson method. 6.3 Bender Schmidt method. (Chapter - 6)
