### MMTU/MTU NOIDA B.Tech 1st Year Syllabus (AS 101 Engineering Mathematics – I) with Text & Reference Books

(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:-
1. B. V. Ramana, Higher Engineering Mathematics, Tata Mc Graw-Hill Publishing Company Ltd., 2008.
2. B. S. Grewal, Higher Engineering Mathematics, Khanna Publisher, 2005.
3. Babu Ram , Engineering Mathematics, Pearson.
Reference Books:-
1. E.Kreyszig, Advance Engineering Mathematics, John Wiley & Sons,2005.
2. Peter V. O’Neil, Advance Engineering Mathematics, Thomson (Cengage)Learning,2007.
3. Maurice D. Weir, Joel Hass, Frank R.Giordano, Thomas, Calculus, Eleventh Edition ,Pearson.
4. R. K. Jain & S. R. K. Iyenger , Advance Engineering Mathematics , Narosa Publishing -House, 2002.