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# MA3151 Syllabus Matrix and Calculus Regulation 2021 Anna University

## MA3151 Syllabus Matrix and Calculus

COURSE OBJECTIVES:
􀁸 To develop the use of matrix algebra techniques that is needed by engineers for practical applications.
􀁸 To familiarize the students with differential calculus.
􀁸 To familiarize the student with functions of several variables. This is needed in many branches of engineering.
􀁸 To make the students understand various techniques of integration.
􀁸 To acquaint the student with mathematical tools needed in evaluating multiple integrals and their applications.

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 DIFFERENTIAL CALCULUS  MA3151 Syllabus Matrix and Calculus
Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules (sum, product, quotient, chain rules) – Implicit differentiation – Logarithmic differentiation – Applications :
Maxima and Minima of functions of one variable.

UNIT – III FUNCTIONS OF SEVERAL VARIABLES MA3151 Syllabus Matrix and Calculus

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of
two variables – Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.

UNIT – IV INTEGRAL CALCULUS MA3151 Syllabus Matrix and Calculus

Definite and Indefinite integrals – Substitution rule – Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial
fraction, Integration of irrational functions – Improper integrals – Applications : Hydrostatic force and pressure, moments and centres of mass.

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.

TOTAL: 60 PERIODS

COURSE OUTCOMES:

At the end of the course the students will be able to
􀁸 Use the matrix algebra methods for solving practical problems.
􀁸 Apply differential calculus tools in solving various application problems.
􀁸 Able to use differential calculus ideas on several variable functions.
􀁸 Apply different methods of integration in solving practical problems.
􀁸 Apply multiple integral ideas in solving areas, volumes and other practical problems.

### TEXT BOOKS: MA3151 Syllabus Matrix and Calculus

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].

REFERENCES : MA3151 Syllabus Matrix and Calculus

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.

 Subject name Matrix and Calculus Subject Code MA3151 Semester 1 Regulation 2021 Regulation

MA3151 Syllabus Matrix and Calculus

MA3151 Notes Matrix and Calculus

MA3151 Important Questions Matrix and Calculus

MA3151 Question Bank Matrix and Calculus

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