2K6 EN101: ENGINEERING MATHEMATICS I

Module I: Ordinary differential equations (16 hours)
A brief review of the method of solutions first order equations – Separable, homogeneous and linear types – Exact equations – Orthogonal trajectories – General linear second order equations – homogeneous linear equation of the second order with constant coefficients – Fundamental system of solutions – Method of variation of parameters – Cauchy’s equation.
Module II: Laplace transforms (17 hours)
Gamma and Beta functions – Definition and simple properties – Laplace transform – Inverse transform – Laplace transform of derivatives and integrals – Shifting theorems – Differentiation and integration of transforms – Transforms of unit step function and impulse function – Transforms of periodic functions – Solutions of ordinary differential equations using Laplace transforms.
Module III: Vector differential calculus (18 hours)
Functions of more than one variable – Idea of partial differentiation – Euler’s theorem for homogeneous functions – Chain rule of partial differentiation – Application in errors and approximations. Vector function of single variable – Differentiation of vector functions – Scalar and vector fields – Gradient of a scalar field – Divergence and curl of vector fields – Their physical meanings – Relation between the vector differential operators.
Module IV: Fourier series and harmonic analysis (15 hours)
Periodic functions – Trigonometric series – Euler formulae – Even and odd functions – Functions having arbitrary period – Half range expansions – Numerical method for determining Fourier coefficients – Harmonic analysis

Reference Books:
1. Piskunov N. , Differential and Integral calculus, MIR Publishers
2. Wylie C. R. , Advanced Engineering Mathematics, McGraw – Hill
3. B. S Grewal. , Higher Engineering Mathematics, Khanna publishers
4. Kreyszig E. , Advanced Engineering Mathematics, Wiley Eastern
5. Thomas G,B. , Calculus and Analytic Geometry, Addison Wesley
6. Spigel. , Vector analysis, Schume series, Mc Grawhill
7. Sastry S. S. Engineering Mathematics, Prentice Hall of India