(Common to all branches except Biotechnology and Agricultural engineering
branches)

**UNIT I = Differential Calculus-I**

- Determination of nth derivative of standard functions-illustrative examples*.
- Leibnitz’s theorem (without proof) and problems.
- Taylor’s and Maclaurin’s series for one variable (without proof).
- Differential coefficient of length of arc (concept and formulae without proof).
- Curvature – Cartesian formula for radius of curvature, centre of curvature.
- Asymptotes for cartesian coordinates only. Curve tracing (cartesian & polar coordinates), simple problems.

Note:*in the case of illustrative examples, questions are not to be set.

**UNIT II = Differential Calculus-II**

- Partial Differentiation. Euler’s theorem. Change of variables.
- Jacobians.
- Approximation of errors.
- Expansion of functions of several variables (without proof).
- Extrema function of several variables.
- Lagrange’s Method of Multipliers (simple problems only).
- Envelopes. Evolutes.

**UNIT III = Multiple Integrals**

- Double Integral.
- Triple Integral.
- Change of Order of Integration.
- Change of Variables.
- Application of double and triple integrals to area and volume.
- Beta and Gamma functions.
- Dirichlet’s integral and application.

**UNIT IV = Vector Calculus**

- Vector differentiation, Vector point function.
- Gradient, divergence and curl of a vector point function and their physical interpretation.
- Vector integration: Line, surface and volume integrals.
- Statement of Green’s, Stoke’s and Gauss divergence theorems (without proof) and problems.

**UNIT V = Matrices**

- Elementary row and column transformation rank of a matrix.
- Linear dependence, consistency of linear system of equations and their solution.
- Characteristic equation .Cayley-Hamilton theorem. Eigen values and Eigen vectors, diagonalization.
- Complex and unitary matrices.
- Application of matrices to engineering problems

**Text Books:-**

- B. V. Ramana, Higher Engineering Mathematics, Tata Mc Graw-Hill Publishing Company Ltd., 2008.
- B. S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
- Babu Ram , Engineering Mathematics, Pearson.

**Reference Books:-**

- E.Kreyszig, Advance Engineering Mathematics, John Wiley & Sons,2005.
- Peter V. O’Neil, Advance Engineering Mathematics, Thomson (Cengage)Learning,2007.
- Maurice D. Weir, Joel Hass, Frank R.Giordano, Thomas, Calculus, Eleventh Edition ,Pearson.
- R. K. Jain & S. R. K. Iyenger , Advance Engineering Mathematics , Narosa Publishing -House, 2002.

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