๐Ÿ“˜ M2

ORDINARY DIFFERENTIAL EQUATIONS AND VECTOR CALCULUS

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MA201 Unit 1 First Order Ode

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MA201 Unit 3 Laplace Transforms

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MA201 Unit 4 Vector Differentiation

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MA201 Unit 5 Vector Integration

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Syllabus Overview

UNIT 1 First Order ODE

First Order ODE

  • Exact differential equations
  • Equations reducible to exact differential equations
  • Linear and Bernoulliโ€™s equations
  • Orthogonal Trajectories (only in Cartesian Coordinates)
  • Applications: Newtonโ€™s law of cooling, Law of natural growth and decay

UNIT 2 Ordinary Differential Equations of Higher Order

Ordinary Differential Equations of Higher Order

  • Second order linear differential equations with constant coefficients
  • Non-Homogeneous terms of the type ๐‘’^๐‘Ž๐‘ฅ, sin ๐‘Ž๐‘ฅ, cos ๐‘Ž๐‘ฅ, polynomials in ๐‘ฅ, ๐‘’^๐‘Ž๐‘ฅV(๐‘ฅ) and ๐‘ฅV(๐‘ฅ)
  • Method of variation of parameters
  • Equations reducible to linear ODE with constant coefficients: Legendreโ€™s equation, Cauchy-Euler equation
  • Applications: Electric Circuits

UNIT 3 Laplace transforms

Laplace transforms

  • Laplace Transform of standard functions
  • First shifting theorem
  • Second shifting theorem
  • Unit step function
  • Dirac delta function
  • Laplace transforms of functions when they are multiplied and divided by โ€˜tโ€™
  • Laplace transforms of derivatives and integrals of function
  • Evaluation of integrals by Laplace transforms
  • Laplace transform of periodic functions
  • Inverse Laplace transform by different methods
  • Convolution theorem (without proof)
  • Applications: solving Initial value problems by Laplace Transform method

UNIT 4 Vector Differentiation

Vector Differentiation

  • Vector point functions and scalar point functions
  • Gradient, Divergence and Curl
  • Directional derivatives
  • Tangent plane and normal line
  • Vector Identities
  • Scalar potential functions
  • Solenoidal and Irrotational vectors

UNIT 5 Vector Integration

Vector Integration

  • Line, Surface and Volume Integrals
  • Theorems of Green, Gauss and Stokes (without proofs) and their applications
ORDINARY DIFFERENTIAL EQUATIONS AND VECTOR CALCULUS Notes