# 21MAT21 Advanced Calculus and Numerical Methods VTU Notes

### 21MAT21 Advanced Calculus and Numerical Methods VTU Notes and Question Papers

Here you can download the 2021 Scheme First Year VTU Notes and Question Papers of 21MAT21 Advanced Calculus and Numerical Methods.

### Module 1: Multiple Integrals, Beta and Gamma functions

This module covers, “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 a double integral. Problems.”

### Module 2: Vector Differentiation and Vector Integration

This module covers, “Scalar and vector fields. Gradient, directional derivative, curl and divergence physical interpretation, solenoidal and irrotational vector fields. Line integrals, Surface integrals.”

### Module 3: Partial Differential Equations (PDE’s)

This module covers, “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.”

### Module 4: Numerical methods -1 and Numerical integration

This module covers, “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.”

### Module 5: Numerical Solution of Ordinary Differential Equations (ODE’s)

The module covers, “Numerical solution of ordinary differential equations of the first order and first degree: Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth-order, Milne’s predictor-corrector formula.”

Module wise Notes of 21MAT21 Advanced Calculus and Numerical Methods

M1, M2, M3, M4, M5 (Uploaded Soon)

VTU Semester End Exam and Model Question Papers