**CHHATTISGARH SWAMI VIVEKANAND TECHNICAL UNIVERSITY**

**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**

**Matrices**

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.