The Complete 18MAT21  Advanced Calculus and Numerical Methods  Maths Notes
 4.9

2018 Scheme  Chemistry Department
 Created by AcquireHowTo
 5 Modules
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.
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...What You’ll Learn
Vector Calculus: Vector Differentiation: Scalar and vector fields. Gradient, directional derivative; curl and divergencephysical 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)
Differential Equations of higherorder: Second order linear ODE's with constant coefficientsInverse differential operators, method of variation of parameters; Cauchy's and Legendre homogeneous equations. Applications to oscillations of spring and LCR circuits.
(RBT Levels: L1, L2 & L3)
Partial Differential Equations(PDE's): Formation of PDE by elimination of arbitrary constants and functions. Solution of nonhomogeneous PDE by direct integration. Homogeneous PDEs involve derivatives with respect to one independent variable only. Solution of Lagrange's linear PDE. Derivation of onedimensional heat and wave equations and solutions by the method of separation of variables.
(RBT Levels: L1, L2 & L3)
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 kindorthogonality. Series solution of Legendre's differential equation leading to Pn(x)Legendre polynomials. Rodrigue's formula (without proof), problems.
(RBT Levels: L1 & L2)
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 — NewtonRaphson and RegulaFalsi methods( only formulae) Illustrative examples.
Numerical integration: Simpson's (1/3)" and (3/8)" rules, Weddle's rule
(RBT Levels: L1, L2 & L3)
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...Course Curriculum & Downloads Module Wise
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