MA3151 MC SYLLABUS
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| Regulation | 2021 |
| Subject Code | MA3151 |
| Subject Name | MATRICES AND CALCULUS |
| Semester | I |
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 9+3
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 9+3
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 9+3
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 9+3
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 9+3
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
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 :
- Kreyszig.E, “Advanced Engineering Mathematics”, John Wiley and Sons, 10th Edition, New Delhi, 2016.
- Grewal.B.S., “Higher Engineering Mathematics”, Khanna Publishers, New Delhi, 44th Edition, 2018.
- 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 :
- Anton. H, Bivens. I and Davis. S, ” Calculus “, Wiley, 10th Edition, 2016
- Bali. N., Goyal. M. and Watkins. C., “Advanced Engineering Mathematics”, Firewall
Media (An imprint of Lakshmi Publications Pvt., Ltd.,), New Delhi, 7th Edition, 2009. - Jain. R.K. and Iyengar. S.R.K., “Advanced Engineering Mathematics”, Narosa
Publications, New Delhi, 5th Edition, 2016. - Narayanan. S. and Manicavachagom Pillai. T. K.,“Calculus” Volume I and II,
S. Viswanathan Publishers Pvt. Ltd., Chennai, 2009. - Ramana. B.V., “Higher Engineering Mathematics”, McGraw Hill Education Pvt. Ltd, New Delhi, 2016.
- Srimantha Pal and Bhunia. S.C, ” Engineering Mathematics ” Oxford University Press, 2015.
- Thomas. G. B., Hass. J, and Weir. M.D, ” Thomas Calculus “, 14th Edition, Pearson India, 2018.
MA3151 Matrices and Calculus Useful Links :
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| MA3151 Matrices and Calculus Question Bank | Click here |
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