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Engineering Mathematics – I (NAS-103)

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Syllabus of Engineering Mathematics – I (NAS-103)

Unit – 1: Differential Calculus – I
Leibnitz’s theorem, Partial derivatives, Euler’s theorem for homogeneous functions, Total derivatives,
Change of variables, Curve tracing: Cartesian and Polar coordinates.
Unit – 2: Differential Calculus – II
Taylor’s and Maclaurin’s Theorems, Expansion of function of several variables, Jacobian, Approximation
of errors, Extrema of functions of several variables, Lagrange’s method of multipliers ( Simple
applications).
Unit – 3: Linear Algebra
Inverse of a matrix by elementary transformations, Rank of a matrix ( Echelon & Normal form), Linear
dependence, Consistency of linear system of equations and their solution,. Characteristic equation,
Eigen values and eigen vectors, Cayley-Hamilton Theorem,A brief introduction to Vector
Spaces,Subspaces. Rank & Nullity. Linear transformations.
Unit – 4: Multiple Integrals
Double and triple integrals, Change of order of integration, Change of variables, Application of
integration to lengths, Volumes and Surface areas – Cartesian and Polar coordinates. Beta and Gamma
functions, Dirichlet’s integral and applications.
Unit – 5: Vector Calculus
Point function, Gradient,Divergence and Curl and their physical interpretations, Vector identities,
Directional derivatives. Line,Surface and Volume integrals, Applications of Green’s, Stoke’s and Gauss
divergence theorems (without proofs),
Text Books:
1. E. Kreyszig :Advanced Engineering Mathematics-Volume-I,JohnWiley & Sons
2. B. V. Ramana, Higher Engineering Mathematics, Tata Mc Graw- Hill Publishing
Company Ltd.
3. R.K.Jain & S.R.K. Iyenger, Advance Engineering Mathematics, Narosa
Publishing House.
Reference Books:
1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers.
2. Peter V. O’ Neil, Advanced Engineering Mathematics, Thomas ( Cengage) Learning.
3. Thomas & Finley, Calculus, Narosa Publishing House
4. Rukmangadachari, Engineering Mathematics – I, Pearson Education.

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