Anna University Syllabus Regulation 21 (B.TECH Sem-1) MATRICES AND CALCULUS

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     MA3151                                            MATRICES  AND  CALCULUS                      L T P C 3 1 0 4

COURSE OBJECTIVES: 

 

•       To develop the use of matrix algebra techniques that are 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 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.

 

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:

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:

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.

 

 

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