Double integration (Cartesian co-ordinates) – Change of order of integration – Applications of double integral (Area) – Triple Integration (Cartesian co-ordinates) – Applications: Volume as triple integrals and solids of revolution.
Gradient of a scalar field. Directional derivative – Divergence of a vector field – Curl of a vector field –Solenoidal and Irrotational of a vector – Greens Theorem, Gauss Divergence Theorem and Stoke’s Theorem (statements only).
Derivatives of f(z) -Analytic function – Cauchy-Riemann Equations- Harmonic function– Harmonic conjugate – Construction of an Analytic function - Conformal Mapping- Conformality of w= z + c, cz, 1/z, Mobius transformations – Application to flow problems.
Cauchy’s integral theorem – Cauchy’s integral formula – Taylor’s series – Laurent’s series – singularities –– Residues – Cauchy Residue theorem .
Conditions – Transforms of elementary functions – Properties - Transform of derivatives and integrals – Unit step function (Heaviside function) –Dirac’s Delta function – Laplace transform of periodic functions – Inverse Laplace transforms - Convolution theorem – Partial fraction method - Applications to solution of linear ordinary differential equations of second order with constant coefficients.
Reference Book:
1.Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, John Wiley & Sons, 2018. 2. G.B.Thomas, Calculus, 12th Edition, Pearson Education India, 2015. 3. T. Veerarajan, Engineering Mathematics, 3rd Edition, Tata McGraw-Hill, 2011 4.James stewart,Calculus,7th Edition,Cengage Learning,2012 5. Ramana, B.V., Higher Engineering Mathematics, Tata McGraw Hill, 2017
Text Book:
1.B.S. Grewal, Higher Engineering Mathematics, 43rd Edition, Khanna Publishers, 2015. 2. Bali N. P and Manish Goyal, “A Text book of Engineering Mathematics”, Eighth Edition, Laxmi Publications Pvt Ltd.,2011..