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08.101 ENGINEERING MATHEMATICS- I
L-T-P : 2-1-0 Credits: 6
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.
