The second semester syllabus for B.E, MA2161 Mathematics - II for Anna university chennai.This is to common for all the branches
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UNIT I Ordinary DIFFERENTIAL EQUATIONS 12
Higher order linear dif ferential EQUATIONS with constant coefficients - Method ofvariation of parameters - Cauchy's and Legendre's LINEAR EQUATIONS - SimultaneousLINEAR EQUATIONS first order with constant coefficients.
UNIT II, Vector Calculus 12
The Gradient Divergence and Curl - Directional derivative - irrotational and solenoidalvector fields - Vector integration - Green's theorem in a plane, Gauss divergencetheorem and Stokes' theorem (excluding proofs) - Simple applications involvingCubes and rectangular parallelpipeds.
UNIT III Analytic FUNCTIONS 12
Functions of a complex variable - Analytic functions - Necessary Conditions, the Cauchy- Riemann equation and Sufficient Conditions (excluding proofs) - Harmonic andOrthogonal properties of analytic function - Harmonic conjugate - Construction ofAnalytic functions - Conformal mapping: w = z + c, cz, 1 / z, and Bilinear Transformation.
UNIT IV COMPLEX INTEGRATION 12
Complex integration - S tatement and applications of Cauchy's integral theorem andCauchy's integral f ormula - Taylor and Laurent expansions - Singular points -Residues - Residue theorem - Application of residue theorem to Evaluate the lineintegrals - Unit circle and semi-circular contour (excluding poles is the boundaries).
UNIT V LAPLACE Transform 12
Laplace Transform - Conditions for Existence - Transform of elementary functions -Basic properties - Transform of derivatives and integrals - Transform of unit stepfunction and impulse functions - Transform of periodic functions.Definition of the inverse Laplace transform as contour integral - convolution theorem(Excluding proof) - Initial and Final value theorems - Solution of linear ODE ofUsing the second order with constant coefficients by Laplace transformation techniques.
TOTAL: 60 PERIOD
TEXT BOOK:
1.RDBali N. P and Manish Goyal, "Text Book of Engineering Mathematics", 3Edition, Laxmi Publications (P) LTD., (2008).
2.T h Grewal. B.S, "Higher Engineering Mathematics", 40Edition, KhannaPublications, Delhi (2007).
References:
1.BV Ramana, "Higher Engineering Mathematics", Tata McGraw Hill PublishingCompany in New Delhi, (2007)
2. Glyn James, "Advanced Engineering Mathematics", 3Edition, PearsonEducation, (2007).
3. Erwin Kreyszig, "Advanced Engineering Mathematics", 7Edition, Wiley,India, (2007).RD4th Jain RK and Iyengar SRK, "Advanced Engineering Mathematics", 3Edition, Narosa Publishing House Pvt. Ltd.., (2007)
To download this
click here
UNIT I Ordinary DIFFERENTIAL EQUATIONS 12
Higher order linear dif ferential EQUATIONS with constant coefficients - Method ofvariation of parameters - Cauchy's and Legendre's LINEAR EQUATIONS - SimultaneousLINEAR EQUATIONS first order with constant coefficients.
UNIT II, Vector Calculus 12
The Gradient Divergence and Curl - Directional derivative - irrotational and solenoidalvector fields - Vector integration - Green's theorem in a plane, Gauss divergencetheorem and Stokes' theorem (excluding proofs) - Simple applications involvingCubes and rectangular parallelpipeds.
UNIT III Analytic FUNCTIONS 12
Functions of a complex variable - Analytic functions - Necessary Conditions, the Cauchy- Riemann equation and Sufficient Conditions (excluding proofs) - Harmonic andOrthogonal properties of analytic function - Harmonic conjugate - Construction ofAnalytic functions - Conformal mapping: w = z + c, cz, 1 / z, and Bilinear Transformation.
UNIT IV COMPLEX INTEGRATION 12
Complex integration - S tatement and applications of Cauchy's integral theorem andCauchy's integral f ormula - Taylor and Laurent expansions - Singular points -Residues - Residue theorem - Application of residue theorem to Evaluate the lineintegrals - Unit circle and semi-circular contour (excluding poles is the boundaries).
UNIT V LAPLACE Transform 12
Laplace Transform - Conditions for Existence - Transform of elementary functions -Basic properties - Transform of derivatives and integrals - Transform of unit stepfunction and impulse functions - Transform of periodic functions.Definition of the inverse Laplace transform as contour integral - convolution theorem(Excluding proof) - Initial and Final value theorems - Solution of linear ODE ofUsing the second order with constant coefficients by Laplace transformation techniques.
TOTAL: 60 PERIOD
TEXT BOOK:
1.RDBali N. P and Manish Goyal, "Text Book of Engineering Mathematics", 3Edition, Laxmi Publications (P) LTD., (2008).
2.T h Grewal. B.S, "Higher Engineering Mathematics", 40Edition, KhannaPublications, Delhi (2007).
References:
1.BV Ramana, "Higher Engineering Mathematics", Tata McGraw Hill PublishingCompany in New Delhi, (2007)
2. Glyn James, "Advanced Engineering Mathematics", 3Edition, PearsonEducation, (2007).
3. Erwin Kreyszig, "Advanced Engineering Mathematics", 7Edition, Wiley,India, (2007).RD4th Jain RK and Iyengar SRK, "Advanced Engineering Mathematics", 3Edition, Narosa Publishing House Pvt. Ltd.., (2007)
To download this
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