engineering mathematics ii
ADVANCED CALCULUS AND NUMERICAL METHOD (18MAT21)
VTU Engineering Mathematics-2 Advanced calculus and numerical methods aims to prepare the students:
- To familiarize the important tools of vector calculus, ordinary/partial differential equations and power series required to analyze the engineering problems.
- To apply the knowledge of interpolation/extrapolation and numerical integration technique whenever analytical methods fail or very complicated, to offer solutions.
Here you can Download VTU study material such as Textbooks, Notes, Previous year Question papers. Download Engineering mathematics-2 Notes below.
Vector Differentiation: Scalar and vector fields. Gradient, directional derivative; curl and divergence-physical interpretation; solenoidal and irrotational vector fields- Illustrative problems.
Vector Integration: Line integrals, Theorems of Green, Gauss and Stokes (without proof). Applications to work done by a force and flux.
Differential Equations of higher-order:- Second order linear ODE’s with constant coefficients-Inverse differential operators, method of variation of parameters; Cauchy’s and Legendre homogeneous equations. Applications to oscillations of a spring and L-C-R circuits.
Partial Differential Equations(PDE’s):- Formation of PDE’s by elimination of arbitrary constants and functions. Solution of non-homogeneous PDE by direct integration. Homogeneous PDEs involving derivatives with respect to one independent variable only. Solution of Lagrange’s linear PDE. Derivation of one-dimensional heat and wave equations and solutions by the method of separation of variables.
Infinite Series:- Series of positive terms- convergence and divergence. Cauchy’s root test and D’Alembert’s ratio test(without proof)- Illustrative examples.
Power Series solutions:- Series solution of Bessel’s differential equation leading to Jn(x)- Bessel’s function of first kind-orthogonality. Series solution of Legendre’s differential equation leading to Pn(x)-Legendre polynomials. Rodrigue’s formula (without proof), problems.
Numerical Methods: Finite differences. Interpolation/extrapolation using Newton’s forward and backward difference formulae, Newton’s divided difference and Lagrange’s formulae (All formulae without proof). Solution of polynomial and transcendental equations — Newton-Raphson and Regula-Falsi methods( only formulae)- Illustrative examples.
Numerical integration: Simpson’s (1/3)” and (3/8)” rules, Weddle’s rule (without proof) —Problems.