Objective:
To impart the knowledge of related mathematics and essential for solving engineering problems.
Course Contents:
Differential calculus and applications:
Successive differentiation: Standard results, use of partial fractions; Leibnitz’s theorem.
Expansions and indeterminate forms: Maclaurin’s and Taylor’s series: indeterminate forms and reducible to these forms.
Physical applications of differentiation: Related rates: approximate calculations, relative and percentage errors, increasing and decreasing functions, maximal & minima, practical problems.
Geometrical applications of differentiation: curvature of Cartesian curves, concavity, convexity, point of inflexion, asymptotes, curve teaching of important Cartesian, polar and parametric curves.
Partial Differentiation: Functions of two or more variables, partial derivatives, homogeneous functions- Eller’s theorem, error and approximations, maximal and minima of functions of two variables.
Integral calculus and its applications:
Revision of standard formulae, methods of integration, areas of Cartesian and polar curve, lengths of curves, volumes of revolution and surfaces of revolution.
Multiple integrals: Double integration in Cartesian and polar coordinates, change of order of integration, change from Cartesian to polar coordinates, application to area, mess of a plate and volume, Triple integral and volume as triple integral.
Ordinary linear differential equations:
Ordinary differential equations of first order and first degree, variable separable, homogeneous, linear, exact and equations reducible to these forms. Applications to orthogonal trajectories, Linear differential equations with constant coefficients rulers for finding complimentary function and particular integrals. Applications to practical problems.
Reference books:
1 Elementary Engineering Mathematics. - By B. S. Grewal.
2 Textbook on Engineering Maths Vol-1. - By Wartikar & Wartikar.
3. Engineering Mathematics I - By G.V. Kumbhojkar.
Evaluation:
Internal 60 %
Class
assignments/tutorials, Class attendance, Tests, Class interactions, and any
laboratory work if required
etc.)
Final 40 %
(Written Exam)
