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PART-II

Each question should be from one unit and the last question can be a combination of two or more units. Each question should have 3 sub questions: A,B & C

A will be from the main text: 5 marks B from non-detailed text: 3 marks

C on grammar and Vocabulary: 6 marks






I Year - II Semester



MATHEMATICS-III

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Course Objectives:


  1. The course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course.

  2. The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.

  3. Understand the most basic numerical methods to solve simultaneous linear equations.



Course Outcomes: At the end of the Course, Student will be able to:


  1. Determine rank, Eigenvalues and Eigen vectors of a given matrix and solve simultaneous linear equations.

  2. Solve simultaneous linear equations numerically using various matrix methods.

  3. Determine double integral over a region and triple integral over a volume.

  4. Calculate gradient of a scalar function, divergence and curl of a vector function. Determine line, surface and volume integrals. Apply Green, Stokes and Gauss divergence theorems to calculate line, surface and volume integrals.



UNIT I: Linear systems of equations:

Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination - Gauss Jordon- Gauss Jacobi and Gauss Seidal methods.Applications: Finding the current in electrical circuits.



UNIT II: Eigen values - Eigen vectors and Quadratic forms:

Eigen values - Eigen vectors– Properties – Cayley-Hamilton theorem - Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form – Rank - Positive, negative and semi definite - Index – Signature.

Applications: Free vibration of a two-mass system.

UNIT III: Multiple integrals:

Curve tracing: Cartesian, Polar and Parametric forms.

Multiple integrals: Double and triple integrals – Change of variables – Change of order of integration. Applications: Finding Areas and Volumes.

UNIT IV: Special functions:

Beta and Gamma functions- Properties - Relation between Beta and Gamma functions- Evaluation of improper integrals.

Applications: Evaluation of integrals.

UNIT V: Vector Differentiation:

Gradient- Divergence- Curl - Laplacian and second order operators -Vector identities. Applications: Equation of continuity, potential surfaces




UNIT VI: Vector Integration:


Line integral – Work done – Potential function – Area- Surface and volume integrals Vector integral theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and related problems.

Applications: Work done, Force.



Text Books:


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

  2. N.P.Bali, Engineering Mathematics, Lakshmi Publications.

Reference Books:


  1. Greenberg, Advanced Engineering Mathematics, 2nd edition, Pearson edn

  2. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India

  3. Peter O’Neil, Advanced Engineering Mathematics,7th edition, Cengage Learning.

  4. D.W. Jordan and T.Smith, Mathematical Techniques, Oxford University Press.

  5. Srimanta Pal, Subodh C.Bhunia, Engineering Mathematics, Oxford University Press.

  6. Dass H.K., Rajnish Verma. Er., Higher Engineering Mathematics, S. Chand Co. Pvt. Ltd, Delhi.



I Year - II Semester




APPLIED CHEMISTRY

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(Common to EEE, ECE, CSE, IT, EIE, E.Com.E, )

Knowledge of basic concepts of Chemistry for Engineering students will help them as professional engineers later in design and material selection, as well as utilizing the available resources.



Learning Objectives:


    • Plastics are nowadays used in household appliances; also they are used as composites (FRP) in aerospace industries (Unit I).

    • Fuels as a source of energy are a basic need of any industry, particularly industries like thermal power stations, steel industry, fertilizer industry etc., and hence they are introduced (Unit II).

    • The basics for the construction of galvanic cells as well as some of the sensors used in instruments are introduced. Also if corrosion is to be controlled, one has to understand the mechanism of corrosion which itself is explained by electrochemical theory (Unit III).

    • With the increase in demand, a wide variety of materials are coming up; some of them have excellent engineering properties and a few of these materials are introduced (Unit IV).

    • Understanding of crystal structures will help to understand the conductivity, semiconductors and superconductors. Magnetic properties are also studied (Unit V).

    • With the increase in demand for power and also with depleting sources of fossil fuels, the demand for alternative sources of fuels is increasing. Some of the prospective fuel sources are introduced (Unit VI).


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