RTU 1st Year 2nd Sem B.Tech. Syllabus Engineering Mathematics II

202 ENGINEERING MATHEMATICS-II

Unit 1

Coordinate Geometry of Three Dimensions: Equation of a sphere, Intersection of a sphere and a
plane, tangent plane, Intersection of two spheres, orthogonality of two spheres, Right circular
cone. Right circular cylinder.

Unit 2

Matrices: Rank of a matrix, Rank of matrix by reducing to normal forms, Consistency of systems
of linear simultaneous equations and its solution, Eigen values and Eigen vectors, CayleyR.
Hamilton theorem (without proof), Diagonalization of matrix.

Unit 3

Vector Calculus: Scalar and vector field, differentiation & integration of vector functions,
Gradient, Divergence, Curl and Differential Operator, Line, Surface and volume Integrals.

Unit 4

Application of Vector Calculus: Green’s Theorem in a Plane, Gauss’s and Stoke’s Theorem
(without proof) and their Applications.
Fourier Series: Expansion of simple functions in Fourier Series, half range Fourier sine and
cosine series, change of interval. Harmonic Analysis.

Unit 5

Differential Equations: Series Solutions of Second Order Linear Differential Equations with
Variable Coefficients (Complementary Functions only), Partial Differential Equations of First
Order : Lagrange’s Form, Standard Forms, Charpit’s Method .