VTU Notes

# The Complete 18MAT21 | Advanced Calculus and Numerical Methods - Maths Notes

• 4.9
• 2018 Scheme | Chemistry Department ### Description

Course Learning Objectives:

This course, Advanced Calculus and Numerical Methods (18MAT21) aim to prepare the students:

• To familiarize the important tools of vector calculus, ordinary/partial differential equations and power series are required to analyze the engineering problems.
• To apply the knowledge of interpolation/extrapolation and numerical integration techniques whenever analytical methods fail or are very complicated, to offer solutions.

...

...

### What You’ll Learn

MODULE-I

Vector Calculus:- 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.

(RBT Levels: L1 & L2)

MODULE-II

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 spring and L-C-R circuits.

(RBT Levels: L1, L2 & L3)

MODULE-III

Partial Differential Equations(PDE's):- Formation of PDE by elimination of arbitrary constants and functions. Solution of non-homogeneous PDE by direct integration. Homogeneous PDEs involve 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.

(RBT Levels: L1, L2 & L3)

MODULE-IV

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.

(RBT Levels: L1 & L2)

MODULE-V

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

(RBT Levels: L1, L2 & L3)

...

...

### Announcement #### Upcomming Updates of the AcquireHowTo

• -- CGPA/SGPA Calculator with University Filter.
• -- Article Publishing platform for different categories.
• -- Courses for students on different topics.
• -- Student Dashboard for AcquireHowTo Products.
• -- Online Portal to buy Minor Projects and Major Projects.
• -- Last year Exams Question paper .
• These all updates are comming soon on our portal. Once the updates roll out you will be notified.

1st
Semester
254
Total Views

1th Sem Chemistry Department VTU Notes