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)

...

Course Faq

Announcement

AcquireHowTo

Admin 1 year ago

Upcomming Updates of the AcquireHowTo

  • -- CGPA/SGPA Calculator with University Filter.
  • -- Student Projects Guide and Download.
  • -- 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.

2nd
Semester
4769
Total Views

2th Sem Chemistry Department VTU Notes
Full lifetime access
10+ downloadable resources
Assignments
Question Papers