MA3151: Matrices and Calculus syllabus for Env 2021 regulation

Matrices and Calculus detailed syllabus for Environmental Engineering (Env) for 2021 regulation curriculum has been taken from the Anna University official website and presented for the Env students. For course code, course name, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Environmental Engineering 1st Sem scheme and its subjects, do visit Env 1st Sem 2021 regulation scheme. The detailed syllabus of matrices and calculus is as follows.

Course Objectives:

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Unit I

MATRICES Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications : Stretching of an elastic membrane.

Unit II

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Unit III

FUNCTIONS OF SEVERAL VARIABLES Partial differentiation – Homogeneous functions and Eulers theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylors series for functions of two variables – Applications : Maxima and minima of functions of two variables and Lagranges method of undetermined multipliers.

Unit IV

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Unit V

MULTIPLE INTEGRALS Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals – Applications : Moments and centres of mass, moment of inertia.

Course Outcomes:

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Text Books:

1. Kreyszig.E, “Advanced Engineering Mathematics”, John Wiley and Sons, 10th Edition, New Delhi, 2016.
2. Grewal.B.S., Higher Engineering Mathematics, Khanna Publishers, New Delhi, 44th Edition, 2018.
3. James Stewart, “Calculus : Early Transcendentals”, Cengage Learning, 8th Edition, New Delhi, 2015. [For Units II & IV – Sections 1.1, 2.2, 2.3, 2.5, 2.7 (Tangents problems only), 2.8, 3.1 to 3.6, 3.11, 4.1, 4.3, 5.1 (Area problems only), 5.2, 5.3, 5.4 (excluding net change theorem), 5.5, 7.1 – 7.4 and 7.8 ].

Reference Books:

1. Anton. H, Bivens. I and Davis. S, ” Calculus “, Wiley, 10th Edition, 2016
2. Bali. N., Goyal. M. and Watkins. C., Advanced Engineering Mathematics, Firewall Media (An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009.
3. Jain. R.K. and Iyengar. S.R.K., Advanced Engineering Mathematics, Narosa Publications, New Delhi, 5th Edition, 2016.
4. Narayanan. S. and Manicavachagom Pillai. T. K.,Calculus” Volume I and II, S. Viswanathan Publishers Pvt. Ltd., Chennai, 2009.
5. Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi, 2016.
6. Srimantha Pal and Bhunia. S.C, ” Engineering Mathematics ” Oxford University Press, 2015.
7. Thomas. G. B., Hass. J, and Weir. M.D, ” Thomas Calculus “, 14th Edition, Pearson India, 2018.

For detailed syllabus of all other subjects of Environmental Engineering, 2021 regulation curriculum do visit Env 1st Sem subject syllabuses for 2021 regulation.

For all Environmental Engineering results, visit Anna University Env all semester results direct link.