Branch: Common Semester
Maclaurin's and Taylor's theorem, Partial differentiation, Euler's theorem and its application in approximation and errors, Maxima and minima of two variables, Tangents and Normals; Subtangent and Subnormal, Curvature: Radius of curvature, Center of Curvature (Cartesian and polar coordinates).
Definite Integral as limit of a sum, Application in summation of series, Double and Triple integral, Change of order of integration, Beta and Gamma functions, Length of the curves, Volumes and surfaces using double and triple integral.
Ordinary differential equations of first order linear and higher degree, Linear higher order differential equation with constant coefficients, Homogeneous linear differential equation, Simultaneous linear differential equations.
Rank of matrix, Solution of simultaneous equation by elementary transformation, Consistency of equation, Eigen Values and Eigen Vectors, Cayley-Hamilton theorem and its application to find the inverse.
Algebra of logic, Boolean algebra, Principle of Duality, Basic theorems, Boolean expressions and function. Graph Theory: Graphs, Sub graphs, degree and distance, Tree, Cycles and Network. Elementary concept of Fuzzy logic.
Reference Books: -
1. Higher Engineering Mathematics. by B.V. Ramana, TMH
2. Higher Engineering Mathematics- By B.S. Grewal.
3. Matrix Operations- Bronson, Schaum Series TMH
4. Calculus- Ayres, Schaum series, TMH
5. Engineering Mathematics- By K.A. Laxminarayan, Vikas Pub. House Pvt Ltd. New Delhi.
6. Advanced Engineering mathematics by Erwin Kreyszig, John Willy & sons.
7. Advanced Engineering Mathematics- Wylie and Barrett, TMH