MA 9111 MATHEMATICS – I L T P C
(Common to all branches of B.E. / B.Tech. Programmes) 3 1 0 4
AIM:
To make available the basic concepts of engineering mathematics, to prepare the
student for new concepts to be introduced in the subsequent semesters and to provide
the necessary mathematical skills that are needed in modeling physical processes by an
engineer.
OBJECTIVES:
To develop the use of matrix algebra techniques this is needed by engineers for
practical applications.
To make the student knowledgeable in the area of infinite series and their
convergence so that he/ she will be familiar with limitations of using infinite series
approximations for solutions arising in mathematical modeling
To familiarize the student with functions of several variables which is needed in
many branches of engineering
To introduce the concepts of improper integrals, Gamma, Beta and Error
functions which are needed in engineering applications
To acquaint the student with mathematical tools needed in evaluating multiple
integrals and their usage
UNIT I MATRICES 9+3
Characteristic equation – Eigenvalues and Eigenvectors of a real matrix – Properties of
eigenvalues and eigenvectors – Cayley-Hamilton Theorem – Diagonalization of
matrices – Reduction of a quadratic form to canonical form by orthogonal transformation
– Nature of quadratic forms.
UNIT II INFINITE SERIES 9+3
Sequences – Convergence of series – General properties – Series of positive terms –
Tests of convergence (Comparison test, Integral test, Comparison of ratios and
D’Alembert’s ratio test) – Alternating series – Series of positive and negative terms –
Absolute and conditional convergence – Power Series – Convergence of exponential,
logarithmic and Binomial Series.
UNIT III FUNCTIONS OF SEVERAL VARIABLES 9+3
Limit and Continuity – Partial derivatives – Homogeneous functions and Euler’s theorem
– Total derivative – Differentiation of implicit functions – Change of variables – Jacobians
– Partial differentiation of implicit functions – Taylor’s series for functions of two variables
– Errors and approximations – Maxima and minima of functions of two variables –
Lagrange’s method of undetermined multipliers.
UNIT IV IMPROPER INTEGRALS 9+3
Improper integrals of the first and second kind and their convergence – Evaluation of
integrals involving a parameter by Leibnitz rule – Beta and Gamma functions –
Properties – Evaluation of integrals using Beta and Gamma functions – Error functions.
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 – Area of a curved surface.
L: 45, T: 15, TOTAL : 60 PERIODS
TEXT BOOKS
1. Grewal B.S., Higher Engineering Mathematics (40
th
Edition), Khanna Publishers,
Delhi (2007).
2. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill Co. Ltd., New
Delhi (2007).
REFERENCES
1. Jain R.K. and Iyengar S.R.K., Advanced Engineering Mathematics (3rd Edition), Narosa Publications, Delhi (2007).
2. Bali N., Goyal M. and Watkins C., Advanced Engineering Mathematics (7 th Edition), Firewall Media, New Delhi (2007).
3. Greenberg M.D., Advanced Engineering Mathematics (2nd Edition), Pearson
Education, New Delhi (1998).
(Common to all branches of B.E. / B.Tech. Programmes) 3 1 0 4
AIM:
To make available the basic concepts of engineering mathematics, to prepare the
student for new concepts to be introduced in the subsequent semesters and to provide
the necessary mathematical skills that are needed in modeling physical processes by an
engineer.
OBJECTIVES:
To develop the use of matrix algebra techniques this is needed by engineers for
practical applications.
To make the student knowledgeable in the area of infinite series and their
convergence so that he/ she will be familiar with limitations of using infinite series
approximations for solutions arising in mathematical modeling
To familiarize the student with functions of several variables which is needed in
many branches of engineering
To introduce the concepts of improper integrals, Gamma, Beta and Error
functions which are needed in engineering applications
To acquaint the student with mathematical tools needed in evaluating multiple
integrals and their usage
UNIT I MATRICES 9+3
Characteristic equation – Eigenvalues and Eigenvectors of a real matrix – Properties of
eigenvalues and eigenvectors – Cayley-Hamilton Theorem – Diagonalization of
matrices – Reduction of a quadratic form to canonical form by orthogonal transformation
– Nature of quadratic forms.
UNIT II INFINITE SERIES 9+3
Sequences – Convergence of series – General properties – Series of positive terms –
Tests of convergence (Comparison test, Integral test, Comparison of ratios and
D’Alembert’s ratio test) – Alternating series – Series of positive and negative terms –
Absolute and conditional convergence – Power Series – Convergence of exponential,
logarithmic and Binomial Series.
UNIT III FUNCTIONS OF SEVERAL VARIABLES 9+3
Limit and Continuity – Partial derivatives – Homogeneous functions and Euler’s theorem
– Total derivative – Differentiation of implicit functions – Change of variables – Jacobians
– Partial differentiation of implicit functions – Taylor’s series for functions of two variables
– Errors and approximations – Maxima and minima of functions of two variables –
Lagrange’s method of undetermined multipliers.
UNIT IV IMPROPER INTEGRALS 9+3
Improper integrals of the first and second kind and their convergence – Evaluation of
integrals involving a parameter by Leibnitz rule – Beta and Gamma functions –
Properties – Evaluation of integrals using Beta and Gamma functions – Error functions.
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 – Area of a curved surface.
L: 45, T: 15, TOTAL : 60 PERIODS
TEXT BOOKS
1. Grewal B.S., Higher Engineering Mathematics (40
th
Edition), Khanna Publishers,
Delhi (2007).
2. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill Co. Ltd., New
Delhi (2007).
REFERENCES
1. Jain R.K. and Iyengar S.R.K., Advanced Engineering Mathematics (3rd Edition), Narosa Publications, Delhi (2007).
2. Bali N., Goyal M. and Watkins C., Advanced Engineering Mathematics (7 th Edition), Firewall Media, New Delhi (2007).
3. Greenberg M.D., Advanced Engineering Mathematics (2nd Edition), Pearson
Education, New Delhi (1998).
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