# NIT Jalandhar

# 1st year Syllabus

# All Subject

MA-101 Mathematics-I [3 1 0 4]

Formation of ordinary differential equations, solution of first order differential equations by separation of variables, homogeneous equations, exact differential equations, equations reducible to exact form by integrating factors, equations of the first order and higher degree, Clairaut’s equation.

Linear differential equations with constant coefficients, Cauchy’s homogeneous linear equation,

Legendre’s linear equation, simultaneous linear equations with constant coefficients.

Fourier series of periodic functions, even and odd functions, half range expansions and Fourier series of different wave forms, complex form of Fourier series and practical harmonic analysis.

Laplace transforms of various standard functions, properties of Laplace transforms and inverse Laplace transforms, Convolution theorem, Laplace transforms of unit step function, imulse function and periodic functions, application to solution of ordinary differential equations with constant coefficients and simultaneous differential equations.

Z-transform and difference equations, elementary properties of z-transform, Convolution theorem, formation of difference equations using z-transform.

Fourier transforms, Fourier integral theorem, Fourier sine, cosine integrals and transforms, Fourier transforms of derivatives of a function, convolution theorem, Parseval’s identity.

Books Recommended:

1. E Kreyszig, “Advanced Engineering Mathematics”, 8

th

Ed., John Wiley, Singapore (2001).

2. R K Jain and S R K lyengar, “Advanced Engineering Mathematics”, 2

nd

Ed., Narosa Publishing

House, New Delhi (2003).

3. B S Grewal, “Higher Engineering mathematics”, Thirty-fifth edition, Khanna Publishers,

DelhiMA-102 Mathematics-II [3 1 0 4]

Linear dependence of vectors and rank of matrices, linear transformations and inverse of matrices, reduction to normal form, bilinear form and quadratic form, consistency and solution of linear algebraic system of equations, eigen values, eigen vectors and their applications to system of ordinary differential equations, Cayley Hamilton theorem, orthogonal, unitary, hermitian and similar matrices. Differential calculus of functions of several variables, partial differentiation, homogeneous functions and Euler’s theorem, Taylor’s and Maclaurin’s series, Taylor’s theorem for functions of two variables, functions of several variables, Lagrange’s method of multipliers.

Double and triple integrals, change of order of integration, change of variables, applications to

evaluation of area, surface area and volume. Scalar, and vector fields, differentiation of vectors, velocity and acceleration, vector differential operators Del, Gradient, Divergence and Curl and their physical interpretations, formulae involving these operators, line, surface and volume integrals, solenoidal and irrotational vectors, Green’s theorem, Gauss divergence theorem, Stoke’s theorem and their applications. Formulation and classification of partial differential equations, solution of first order linear equations, standard forms of non-linear equations, Charpit’s method, linear equations with constant coefficients, non-homogenous linear equations, Monge’s method for non-homogenous equations of second order, separation of variables method for solution of heat, wave and Laplace equation.

Books Recommended:

1. E Kreyszig, “Advanced Engineering Mathematics”, 8

th

Ed., John Wiley,Singapore (2001).

2. R K Jain and S R K lyengar, “Advanced Engineering Mathematics”, 2

nd

Ed., Narosa

Publishing House, New Delhi (2003).

3. I A N Sneddon, “Elements of Partial Differential Equations”, Tata McGraw Hill, Delhi

(1974).

4. B S Grewal, “Higher Engineering Mathematics”, Thirty-fifth edition, Khanna Publishers,

Delhi.