CSVTU Syllabus Applied Mathematics I

Courses of Study and Scheme of Examination of B.E. First Year (2012-13)
Semester: Ist Branch: Common to All Branches
Subject: Applied Mathematics-I Code: 300114 (14)

Unit – I
Rank & inverse by elementary transformation; system of linear equations; eigen values & eigen vectors; Caley-Hamilton Theorem.
Unit – II
Differential Calculus
Successive differentiation, Leibnitz’s theorem; expansion of functions in Taylor’s & Maclaurin’s series; tracing of simple curves.
Unit – III
Integral Calculus
Reduction formula, application of integration to rectification, quadrature, volume of revolution, centre of gravity & moment of inertia.
Unit – IV
Partial Differentiation
Partial derivatives, Euler’s theorem on homogeneous functions, maxima & minima of functions of two variables, Lagrange’s method of undetermined multipliers, Jacobians; differentiation under the integral sign.
Unit – V
Ordinary Differential Equations & Applications
Exact differential equations, reducible to exact form; first order differential equations (non-linear); application to simple electrical circuits & heat flow.
Name of the Text Books:
1. Higher Engg. Mathematics by B. S. Grewal (38th edition)- Khanna Publishers.
2. Advanced Engg. Mathematics by Erwin Kreyszig (8th edition)- John Wiley & Sons.
Name of the Reference Books:
1. Differential Calculus by Gorakh Prasad – Pothishala Private Limited.
2. Integral Calculus by Gorakh Prasad – Pothishala Private Limited.
3. Advanced Engg. Mathematics by R. K. Jain & S. R. K. Iyengar Narosa Publishing House.
4. Applied Mathematics by P. N. Wartikar & J. N. Wartikar, Vol. (I&II) – Pune Vidyarthi Griha Prakashan, Pune.
5. Applied Mathematics for Engineers & Physicists by Louis A. Pipes – McGraw Hill.

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