Course Objectives:

To learn

• Types of matrices and their properties.
• Concept of a rank of the matrix and applying this concept to know the consistency and solving the system of linear equations.
• Concept of Eigen values and eigenvectors and to reduce the quadratic form to canonical form.
• Concept of Sequence.
• Concept of nature of the series.
• Geometrical approach to the mean value theorems and their application to the mathematical problems
• Evaluation of surface areas and volumes of revolutions of curves.
• Evaluation of improper integrals using Beta and Gamma functions.
• Partial differentiation, concept of total derivative
• Finding maxima and minima of function of two and three variables.

Course Outcomes:

• After learning the contents of this paper the student must be able to
• Write the matrix representation of a set of linear equations and to analyse the solution of the system of equations
• Find the Eigen values and Eigen vectors
• Reduce the quadratic form to canonical form using orthogonal transformations.
• Analyse the nature of sequence and series.
• Solve the applications on the mean value theorems.
• Evaluate the improper integrals using Beta and Gamma functions
• Find the extreme values of functions of two variables with/ without constraints.

Text Books:

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition, 2010
2. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley & Sons, 2006.
3. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9thEdition,Pearson, Reprint, 2002.

References:

1. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint, 2008.
2. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11thReprint, 2010.

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