MA 9212 APPLIED MATHEMATICS SYLLABUS | ANNA UNIVERSITY ME STRUCTURAL ENGINEERING 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER ME STRUCTURAL ENGINEERING DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI,TIRUNELVELI,COIMBATORE), 2009 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009
MA 9212 APPLIED MATHEMATICS L T P C
3 1 0 4
OBJECTIVE:
To familiarize the students in the field of differential and elliptic equations to
solve boundary value problems associated with engineering applications.
To expose the students to variational formulation and numerical integration
techniques and their applications to obtain solutions for buckling, dynamic
response, heat and flow problems of one and two dimensional conditions.
UNIT I ONE DIMENSIONAL WAVE AND HEAT EQUATIONS 10+3
Laplace transform methods for one-dimensional wave equation – Displacements in a
long string – longitudinal vibration of an elastic bar – Fourier transform methods for onedimensional
heat conduction problems in infinite and semi-infinite rods.
UNIT II ELLIPTIC EQUATION 9+3
Laplace equation – Properties of harmonic functions – Solution of Laplace’s equation by
means of Fourier transforms in a half plane, in an infinite strip and in a semi-infinite strip
– Solution of Poisson equation by Fourier transform method.
UNIT III CALCULUS OF VARIATIONS 9+3
Concept of variation and its properties – Euler’s equation – Functional dependant on first
and higher order derivatives – Functionals dependant on functions of several
independent variables – Variational problems with moving boundaries –Direct methods –
Ritz and Kantorovich methods.
UNIT IV EIGEN VALUE PROBLEMS 9+3
Methods of solutions: Faddeev – Leverrier Method, Power Method with deflation –
Approximate Methods: Rayleigh – Ritz Method
UNIT V NUMERICAL INTEGRATION 8+3
Gaussian Quadrature – One and Two Dimensions – Gauss Hermite Quadrature – Monte
Carlo Method – Multiple Integration by using mapping function
TOTAL (L:30+T:15) : 45 PERIODS
REFERENCES:
1. Sankara Rao, K., “Introduction to Partial Differential Equations”, Prentice Hall of India
Pvt. Ltd., New Delhi, 1997.
2. Rajasekaran.S, “Numerical Methods in Science and Engineering A Practical
Approach”, A.H.Wheeler and Company Private Limited, 1986.
3. Gupta, A.S., “Calculus of Variations with Applications”, Prentice Hall of India Pvt.
Ltd., New Delhi, 1997.
4. Andrews, L.C. and Shivamoggi, B.K., “Integral Transforms for Engineers”, Prentice
Hall of India Pvt. Ltd., New Delhi, 2003.
MA 9212 APPLIED MATHEMATICS L T P C
3 1 0 4
OBJECTIVE:
To familiarize the students in the field of differential and elliptic equations to
solve boundary value problems associated with engineering applications.
To expose the students to variational formulation and numerical integration
techniques and their applications to obtain solutions for buckling, dynamic
response, heat and flow problems of one and two dimensional conditions.
UNIT I ONE DIMENSIONAL WAVE AND HEAT EQUATIONS 10+3
Laplace transform methods for one-dimensional wave equation – Displacements in a
long string – longitudinal vibration of an elastic bar – Fourier transform methods for onedimensional
heat conduction problems in infinite and semi-infinite rods.
UNIT II ELLIPTIC EQUATION 9+3
Laplace equation – Properties of harmonic functions – Solution of Laplace’s equation by
means of Fourier transforms in a half plane, in an infinite strip and in a semi-infinite strip
– Solution of Poisson equation by Fourier transform method.
UNIT III CALCULUS OF VARIATIONS 9+3
Concept of variation and its properties – Euler’s equation – Functional dependant on first
and higher order derivatives – Functionals dependant on functions of several
independent variables – Variational problems with moving boundaries –Direct methods –
Ritz and Kantorovich methods.
UNIT IV EIGEN VALUE PROBLEMS 9+3
Methods of solutions: Faddeev – Leverrier Method, Power Method with deflation –
Approximate Methods: Rayleigh – Ritz Method
UNIT V NUMERICAL INTEGRATION 8+3
Gaussian Quadrature – One and Two Dimensions – Gauss Hermite Quadrature – Monte
Carlo Method – Multiple Integration by using mapping function
TOTAL (L:30+T:15) : 45 PERIODS
REFERENCES:
1. Sankara Rao, K., “Introduction to Partial Differential Equations”, Prentice Hall of India
Pvt. Ltd., New Delhi, 1997.
2. Rajasekaran.S, “Numerical Methods in Science and Engineering A Practical
Approach”, A.H.Wheeler and Company Private Limited, 1986.
3. Gupta, A.S., “Calculus of Variations with Applications”, Prentice Hall of India Pvt.
Ltd., New Delhi, 1997.
4. Andrews, L.C. and Shivamoggi, B.K., “Integral Transforms for Engineers”, Prentice
Hall of India Pvt. Ltd., New Delhi, 2003.
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