# GITAM University III SEM Engineering Mathematics Lab Syllabus

B.Tech. (BT) III Semester

ENGINEERING MATHEMATICS-I

Course Code : EURBT301 Category : MT

Credits: 4 Hours : 4 per week

UNIT-I

Equations of a Plane, Straight Line and Sphere. Surface areas of overlapping spheres.

UNIT-II

Linear Algebra: Rank of a matrix, Eigen values and eigen vectors of a matrix, Cayley,

Hamilton theorem, Consistency of equations, Matrix inversion, Hermitian and Skew-

Hermitian forms, Unitary matrix.

UNIT-III

Differential Equations of First Order and Applications: Formation of differential

equations, solution of differential equation – Geometrical meaning, equations of the

first order and first degree, separable variables, Homogeneous equations, Linear

equations, Bernouli’s equation, Exact equations, equations reducible to exact

equations, Geometrical applications, Orthogonal trajectories.

UNIT-IV

Linear Differential Equations and Applications:

Higher order linear differential equation with constant coefficients. Cauchy’s and

Legendre’s linear equations. Simultaneous linear equations with constant coefficients.

UNIT-V

Laplace Transforms: Transforms of elementary functions, properties of Laplace

transforms, Existence conditions, Inverse transforms, Transforms of derivatives,

Transforms of integrals, multiplication by t, division by t, convolution theorem,

applications to Ordinary Differential Equations and simultaneous linear equations

with constant coefficients, unit, step function, unit impulse function and periodic

functions.

Text Books:

1. Theory of Matrices by Shantinarayan,

2. Higher Engineering Mathematics by Dr.B.S.Grewal.

3. Advanced Mathematics for Engineering Students Vol.2, by Narayanan,

Manikkavachakam Pillay and Ramanaiah.

Reference Books:

1. Higher Engineering Mathematics by Dr.M.K.Venkataraman.

2. Advance Engineering Mathematics by Erwin Kreyszig.

3. Engineering Mathematics by P.P.Gupta.

4. A Text book on Engineering Mathematics by N.P.Bali.