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21MAT21 ADVANCED CALCULUS AND NUMERICAL METHODS
| 21MAT21 M2 VTU NOTES |
| Attribute | Details |
|---|---|
| Course Code | 21MAT21 |
| CIE Marks | 50 |
| Teaching Hours/Week (L:T:P:S) | 2:2:0:0 |
| SEE Marks | 50 |
| Total Hours of Pedagogy | 40 |
| Total Marks | 100 |
| Credits | 03 |
| Exam Hours | 03 |
2021 Scheme M2 Notes – ADVANCED CALCULUS AND NUMERICAL METHODS (Download👇)
21MAT21 SYLLABUS
MODULE 1
Integral Calculus
Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by change
of order of integration, changing into polar coordinates. Applications to find: Area and Volume by
double integral. Problems.
Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions.
Problems.
MODULE 2
Vector Calculus
Vector Differentiation: Scalar and vector fields. Gradient, directional derivative, curl and
divergence – physical interpretation, solenoidal and irrotational vector fields. Problems.
Vector Integration: Line integrals, Surface integrals. Applications to work done by a force and flux.
Statement of Green’s theorem and Stoke’s theorem. Problems.
MODULE 3
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 derivative with respect to one independent variable only. Solution of Lagrange’s linear PDE. Derivation of one-dimensional heat equation and wave equation.
MODULE 4
Numerical Methods -1
Solution of polynomial and transcendental equations: Regula-Falsi and Newton-Raphson methods (only formulae). Problems.
Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae without proof). Problems.
Numerical integration: Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems.
MODULE 5
Numerical Methods -2
Numerical Solution of Ordinary Differential Equations (ODE’s):
Numerical Solution of Ordinary Differential Equations (ODE’s): Numerical solution of ordinary differential equations of first order and first degree: Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order, Milne’s predictor-corrector formula (No derivations of formulae). Problems.
