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.
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.
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.
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.
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