MA 9315 APPLIED MATHEMATICS FOR THERMAL ENGINEERS SYLLABUS | ANNA UNIVERSITY ME ENERGY ENGINEERING 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER ME ENERGY 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 9315 APPLIED MATHEMATICS FOR THERMAL ENGINEERS L T P C
3 1 0 4
UNIT I APPLICATIONS OF FOURIER TRANSFORM 9
Fourier Transform methods – one-dimensional heat conduction problems in infinite
and semi-infinite rod – Laplace Equation – Poisson Equation.
UNIT II CALCULUS OF VARIATIONS 9
Concept of variation and its properties – Euler’s equation – Functionals 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 III CONFORMAL MAPPING AND APPLICATIONS 9
The Schwarz- Christoffel transformation – Transformation of boundaries in
parametric form – Physical applications:Fluid flow and heat flow problems.
UNIT IV FINITE DIFFERENCE METHODS FOR
PARABOLIC EQUATIONS 9
One dimensional parabolic equation – Explicit and Crank-Nicolson Schemes –
Thomas Algorithm – Weighted average approximation – Dirichlet and Neumann
conditions – Two dimensional parabolic equations – ADI method.
UNIT V FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS 9
Solutions of Laplace and Poisson equations in a rectangular region – Finite
difference in polar coordinates – Formulae for derivatives near a curved boundary
while using a square mesh.
L +T: 45+15 = 60PERIODS
REFERENCES:
1. Mitchell A.R. and Griffith D.F., The Finite difference method in partial differential
equations, John Wiley and sons, New York (1980).
2. Sankara Rao, K., Introduction to Partial Differential Equations, Prentice Hall of
India Pvt. Ltd., New Delhi (1997).
3. Gupta, A.S., Calculus of Variations with Applications, Prentice Hall of India Pvt.
Ltd., New Delhi (1997).
4. Spiegel, M.R., Theory and Problems of Complex Variables and its Application
(Schaum’s Outline Series), McGraw Hill Book Co., Singapore (1981).
5. Andrews, L.C. and Shivamoggi, B.K., Integral Transforms for Engineers, Prentice
Hall of India Pvt. Ltd., New Delhi (2003).
6. Elsgolts, L., Differential Equations and the Calculus of Variations, MIR Publishers,
Moscow (1973).
7. Mathews, J.H. and Howell, R.W., Complex Analysis for Mathematics and
Engineering, Narosa Publishing House, New Delhi (1997).
8. Morton, K.W. and Mayers, D.F. Numerical solution of partial differential
equations, Cambridge University press, Cambridge (2002).
9. Jain, M. K., Iyengar, S. R. K. and Jain, R. K. “ Computational Methods for Partial
Differential Equations”, New Age International (P) Ltd., 2003.
MA 9315 APPLIED MATHEMATICS FOR THERMAL ENGINEERS L T P C
3 1 0 4
UNIT I APPLICATIONS OF FOURIER TRANSFORM 9
Fourier Transform methods – one-dimensional heat conduction problems in infinite
and semi-infinite rod – Laplace Equation – Poisson Equation.
UNIT II CALCULUS OF VARIATIONS 9
Concept of variation and its properties – Euler’s equation – Functionals 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 III CONFORMAL MAPPING AND APPLICATIONS 9
The Schwarz- Christoffel transformation – Transformation of boundaries in
parametric form – Physical applications:Fluid flow and heat flow problems.
UNIT IV FINITE DIFFERENCE METHODS FOR
PARABOLIC EQUATIONS 9
One dimensional parabolic equation – Explicit and Crank-Nicolson Schemes –
Thomas Algorithm – Weighted average approximation – Dirichlet and Neumann
conditions – Two dimensional parabolic equations – ADI method.
UNIT V FINITE DIFFERENCE METHODS FOR ELLIPTIC EQUATIONS 9
Solutions of Laplace and Poisson equations in a rectangular region – Finite
difference in polar coordinates – Formulae for derivatives near a curved boundary
while using a square mesh.
L +T: 45+15 = 60PERIODS
REFERENCES:
1. Mitchell A.R. and Griffith D.F., The Finite difference method in partial differential
equations, John Wiley and sons, New York (1980).
2. Sankara Rao, K., Introduction to Partial Differential Equations, Prentice Hall of
India Pvt. Ltd., New Delhi (1997).
3. Gupta, A.S., Calculus of Variations with Applications, Prentice Hall of India Pvt.
Ltd., New Delhi (1997).
4. Spiegel, M.R., Theory and Problems of Complex Variables and its Application
(Schaum’s Outline Series), McGraw Hill Book Co., Singapore (1981).
5. Andrews, L.C. and Shivamoggi, B.K., Integral Transforms for Engineers, Prentice
Hall of India Pvt. Ltd., New Delhi (2003).
6. Elsgolts, L., Differential Equations and the Calculus of Variations, MIR Publishers,
Moscow (1973).
7. Mathews, J.H. and Howell, R.W., Complex Analysis for Mathematics and
Engineering, Narosa Publishing House, New Delhi (1997).
8. Morton, K.W. and Mayers, D.F. Numerical solution of partial differential
equations, Cambridge University press, Cambridge (2002).
9. Jain, M. K., Iyengar, S. R. K. and Jain, R. K. “ Computational Methods for Partial
Differential Equations”, New Age International (P) Ltd., 2003.
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