Class Work : 50 marks 

Exam : 100 marks

Section A 

Vector Calculus: Differentiation of vectors, scalar and vector point functions. Gradient of a scalar field and directional derivative, divergence and curl of a vector field and their physical interpretations. Integration of vectors, line integral, surface integral, volume integral, Green, Stoke’s and Gauss theorems (without proof) and their applications.   

Section B 

Ordinary Differential Equations and Applications: Exact differential equations, equations reducible to exact differential equations. Applications of differential equations of first order & first degree to simple electric circuits, Newton’s law of cooling, heat flow and orthogonal trajectories, linear differential equations of second and higher order. Complete solution, complementary function and particular integral, method of variation of parameters to find particular integral, Cauchy’s and Legendre’s linear equations, simultaneous linear equations with constant co-efficients. Applications of linear differential equations to simple pendulum, oscillatory electric circuits. 

Section C 

Laplace Transforms and its Applications: Laplace transforms of elementary functions, properties of Laplace transforms, existence conditions, transforms of derivatives, transforms of integrals, multiplication by t, division by t. Evaluation of integrals by Laplace transforms. Laplace transform of unit step function, unit impulse function and periodic function. Inverse transforms, convolution theorem, application to linear differential equations and simultaneous linear differential equations with constant coefficients and applications to integral equations. n 

Section D 

Partial Differential Equations and Its Applications: Formation of partial differential equations, Lagrange’s linear partial differential equation, first order non-linear partial differential equation, Charpit’s method. Method of separation of variables and its applications to wave equation, one dimensional heat equation and two-dimensional heat flow (steady state solutions only).

Text Books: 

1. Advanced Engineering Mathematics: E. Kreyszig 

2 .Calculus and Analytic Geometry: G. B. Thomas, R. L. Finney 

3. Higher Engineering Mathematics: B. S. Grewal 

Reference Books 

1. Higher Engineering Mathematics: B. V. Ramana 

2. Differential and Integral Calculus: Piskunov 

3. Advanced Engineering Mathematics: Jain and Iyenger 

Note: 

Examiner will set 9 questions in total, with two questions from each section and one question covering all sections which will be Q.1. This Q.1 is compulsory and of short answer type. Each question carries equal mark (20 marks). Students have to attempt 5 questions in total.