UNIT I ORDINARY DIFFERENTIAL EQUATIONS
Higher order linear differential equations with constant coefficients – Method of variation of
parameters – Cauchy’s and Legendre’s linear equations – Simultaneous first order linear equations
with constant coefficients.
UNIT II VECTOR CALCULUS
Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector fields –
Vector integration – Green’s theorem in a plane, Gauss divergence theorem and stokes’ theorem
(excluding proofs) – Simple applications involving cubes and rectangular parallelpipeds.
UNIT III ANALYTIC FUNCTIONS
Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy – Riemann
equation and Sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of
analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.
UNIT IV COMPLEX INTEGRATION
Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s
integral formula – Taylor and Laurent expansions – Singular points – Residues – Residue theorem –
Application of residue theorem to evaluate real integrals – Unit circle and semi-circular
contour(excluding poles on boundaries).
UNIT V LAPLACE TRANSFORM
Laplace transform – Conditions for existence – Transform of elementary functions – Basic properties
– Transform of derivatives and integrals – Transform of unit step function and impulse functions –
Transform of periodic functions.
Definition of Inverse Laplace transform as contour integral – Convolution theorem (excluding proof) –
Initial and Final value theorems – Solution of linear ODE of second order with constant coefficients
using Laplace transformation techniques.
TOTAL : 60 PERIODS
TEXT BOOK:
1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3rd Edition, Laxmi Publications (p) Ltd., (2008).
2. Grewal. B.S, “Higher Engineering Mathematics”, 40th Edition, Khanna Publications, Delhi, (2007).
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company,
New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 3rd Edition, Pearson Education, (2007).
3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7th Edition, Wiley India, (2007).
4. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3rdEdition, Narosa
Publishing House Pvt. Ltd., (2007).
Higher order linear differential equations with constant coefficients – Method of variation of
parameters – Cauchy’s and Legendre’s linear equations – Simultaneous first order linear equations
with constant coefficients.
UNIT II VECTOR CALCULUS
Gradient Divergence and Curl – Directional derivative – Irrotational and solenoidal vector fields –
Vector integration – Green’s theorem in a plane, Gauss divergence theorem and stokes’ theorem
(excluding proofs) – Simple applications involving cubes and rectangular parallelpipeds.
UNIT III ANALYTIC FUNCTIONS
Functions of a complex variable – Analytic functions – Necessary conditions, Cauchy – Riemann
equation and Sufficient conditions (excluding proofs) – Harmonic and orthogonal properties of
analytic function – Harmonic conjugate – Construction of analytic functions – Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.
UNIT IV COMPLEX INTEGRATION
Complex integration – Statement and applications of Cauchy’s integral theorem and Cauchy’s
integral formula – Taylor and Laurent expansions – Singular points – Residues – Residue theorem –
Application of residue theorem to evaluate real integrals – Unit circle and semi-circular
contour(excluding poles on boundaries).
UNIT V LAPLACE TRANSFORM
Laplace transform – Conditions for existence – Transform of elementary functions – Basic properties
– Transform of derivatives and integrals – Transform of unit step function and impulse functions –
Transform of periodic functions.
Definition of Inverse Laplace transform as contour integral – Convolution theorem (excluding proof) –
Initial and Final value theorems – Solution of linear ODE of second order with constant coefficients
using Laplace transformation techniques.
TOTAL : 60 PERIODS
TEXT BOOK:
1. Bali N. P and Manish Goyal, “Text book of Engineering Mathematics”, 3rd Edition, Laxmi Publications (p) Ltd., (2008).
2. Grewal. B.S, “Higher Engineering Mathematics”, 40th Edition, Khanna Publications, Delhi, (2007).
REFERENCES:
1. Ramana B.V, “Higher Engineering Mathematics”,Tata McGraw Hill Publishing Company,
New Delhi, (2007).
2. Glyn James, “Advanced Engineering Mathematics”, 3rd Edition, Pearson Education, (2007).
3. Erwin Kreyszig, “Advanced Engineering Mathematics”, 7th Edition, Wiley India, (2007).
4. Jain R.K and Iyengar S.R.K, “Advanced Engineering Mathematics”, 3rdEdition, Narosa
Publishing House Pvt. Ltd., (2007).
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