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

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2021 Scheme M2 Notes – ADVANCED CALCULUS AND NUMERICAL METHODS (Download👇)

Syllabus Copy

21MAT21 SYLLABUS

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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.

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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.

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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.

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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.

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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.

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