Module 1
Vector differential calculus: Differentiation of vector functions- scalar and vector fields- gradient – divergence and curl of a vector function – their physical meaning – directional derivative – scalar potential- conservative field – identities – simple problems.
Vector differential calculus: Differentiation of vector functions- scalar and vector fields- gradient – divergence and curl of a vector function – their physical meaning – directional derivative – scalar potential- conservative field – identities – simple problems.
Module2
Vector integral calculus: Line- surface and volume integrals- work done by a force along a path- application of Green’s theorem- Stoke’s theorem and Gauss divergence theorem.
Vector integral calculus: Line- surface and volume integrals- work done by a force along a path- application of Green’s theorem- Stoke’s theorem and Gauss divergence theorem.
Module 3
Function of complex variable: Definition of analytic function and singular points- derivation of C.R. equations in Cartesian co-ordinates- harmonic and orthogonal properties- construction of analytic function given real or imaginary parts- complex potential- conformal transformation of functions like Zn, ez, 1/z, Sin z, z + k2/z – bilinear transformation- cross ratio- invariant property- simple problems.
Function of complex variable: Definition of analytic function and singular points- derivation of C.R. equations in Cartesian co-ordinates- harmonic and orthogonal properties- construction of analytic function given real or imaginary parts- complex potential- conformal transformation of functions like Zn, ez, 1/z, Sin z, z + k2/z – bilinear transformation- cross ratio- invariant property- simple problems.
Module 4
Finite differences: meaning of ?, , E, µ, d – interpolation using Newton’s forward and backward formula- central differences- problems using Stirlings formula- Lagrange’s formula and Newton’s divided difference formula for unequal intervals.
Finite differences: meaning of ?, , E, µ, d – interpolation using Newton’s forward and backward formula- central differences- problems using Stirlings formula- Lagrange’s formula and Newton’s divided difference formula for unequal intervals.
Module 5
Difference Calculus: Numerical differentiation using forward and backward differences. Numerical integration- Newton-Cote’s formula- trapezoidal rule- Simpson’s 1/3rd and 3/8th rule- simple problems- difference equations – solutions of difference equations.
Difference Calculus: Numerical differentiation using forward and backward differences. Numerical integration- Newton-Cote’s formula- trapezoidal rule- Simpson’s 1/3rd and 3/8th rule- simple problems- difference equations – solutions of difference equations.
mgu university b.tech syllabus
References
1. Advanced Engg. Mathematics: Erwin Kreyzing- Wiley Eastern. Pub.
2. Higher Engg. Mathematics: B. S. Grewal- Khanna publishers.
3. Numerical methods in Science and Engineering: M K Venkataraman- National Pub.
4. Numerical methods: S Balachandra Rao- University Press.
5. Advanced Engineering Mathematics: Michael D Greenberg- PHI.
6. Theory and Problems of Vector analysis: Murray Spiegel- Schaum’s- Mc Graw Hill.
2. Higher Engg. Mathematics: B. S. Grewal- Khanna publishers.
3. Numerical methods in Science and Engineering: M K Venkataraman- National Pub.
4. Numerical methods: S Balachandra Rao- University Press.
5. Advanced Engineering Mathematics: Michael D Greenberg- PHI.
6. Theory and Problems of Vector analysis: Murray Spiegel- Schaum’s- Mc Graw Hill.