# Download notes of Engineering Mathematics – I (NAS-103)

**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.