18MATDIP31 ADDITIONAL MATHEMATICS – I syllabus for EC



A d v e r t i s e m e n t

Module-1 Complex Trigonometry 0 hours

Complex Trigonometry:

Complex Numbers: Definitions and properties. Modulus and amplitude of a complex number, Argand’s diagram, De-Moivre’s theorem (without proof).

 

Vector Algebra:

Scalar and vectors. Addition and subtraction and multiplication of vectors- Dot and Cross products, problems.

Module-2 Differential Calculus 0 hours

Differential Calculus:

Review of successive differentiation-illustrative examples. Maclaurin’s series expansions-Illustrative examples. Partial Differentiation: Euler’s theorem-problems on first order derivatives only. Total derivatives-differentiation of composite functions. Jacobians of order two-Problems.

Module-3 Vector Differentiation 0 hours

Vector Differentiation:

Differentiation of vector functions. Velocity and acceleration of a particle moving on a space curve. Scalar and vector point functions. Gradient, Divergence, Curl-simple problems. Solenoidal and irrotational vector fields-Problems.

Module-4 Integral Calculus 0 hours

Integral Calculus:

Review of elementary integral calculus. Reduction formulae for sinn, cosnx (with proof) and sinm xcosnx (without proof) and evaluation of these with standard limits-Examples. Double and triple integrals-Simple examples.

Module-5 Ordinary differential equations (ODE’s) 0 hours

Ordinary differential equations (ODE’s)

Introduction-solutions of first order and first-degree differential equations: exact, linear differential equations. Equations reducible to exact and Bernoulli’s equation.

 

Course Outcomes:

At the end of the course the student will be able to:

• CO1: Apply concepts of complex numbers and vector algebra to analyze the problems arising in related area.

• CO2: Use derivatives and partial derivatives to calculate rate of change of multivariate functions.

• CO3: Analyze position, velocity and acceleration in two and three dimensions of vector valued functions.

• CO4: Learn techniques of integration including the evaluation of double and triple integrals.

• CO5: Identify and solve first order ordinary differential equations.

 

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.

• Each full question will be for 20 marks.

• There will be two full questions (with a maximum of four sub- questions) from each module.

• Each full question will have sub- question covering all the topics under a module.

• The students will have to answer five full questions, selecting one full question from each module.

 

Textbook

1 Higher Engineering Mathematics B. S. Grewal Khanna Publishers 43rd Edition, 2015

 

Reference Books

1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2015

2 Engineering Mathematics N. P .Bali and Manish Goyal Laxmi Publishers 7th Edition, 2007

3 Engineering Mathematics Vol. I Rohit Khurana Cengage Learning 1 st Edition, 2015

Last Updated: Tuesday, January 24, 2023