DIFFERENTIAL EQUATIONS AND VECTOR CALCULUS
UNIT I
ORDINARY DIFFERENTIAL EQUATIONS OF THE FIRST ORDER
LDE of the first order:- Solution of Exact Linear and Bernoulli equations
- Modeling Newton’s law of cooling
- Growth and decay models
- Modeling of R-L circuit
UNIT II
ORDINARY DIFFERENTIAL EQUATIONS OF HIGHER ORDER
LDE with constant coefficients:
- Complementary function
- over damping
- under damping and critical damping of a system
- Particular integrals for f(x) of the form where the method of variation of parameters
LDE with variable coefficients:
- Cauchy’s homogeneous equation
- Legendre’s homogeneous equations
UNIT III
MULTIPLE INTEGRALS
Double integrals:
- Evaluation of Double Integrals
- change of order of integration (only Cartesian form)
- change of variables (Cartesian and polar coordinates)
Triple Integrals:
- Evaluation of triple integrals
- Change of variables (Cartesian to Spherical and Cylindrical polar coordinates)
Applications:
- Area using the double integral
- Volume of a solid using the double and triple integral
- Mass, Center of mass and Center of gravity using double and triple integrals
UNIT IV
VECTOR DIFFERENTIATION AND LINE INTEGRATION
Vector differentiation:
- Scalar and vector point functions
- Concepts of gradient
- divergence and curl of functions in cartesian framework
- solenoidal field
- irrotational field
- scalar potential
Vector line integration:
- Evaluation of the line integral
- concept of work done by a force field
- Conservative fields
UNIT V
SURFACE INTEGRATION AND VECTOR INTEGRAL THEOREMS
Surface integration:
- Evaluation of surface and volume integrals
- flux across a surface
Vector integral theorems:
- Green’s theorems
- Gauss theorems
- Stokes theorems (without proof) and their applications
Notes
Unit 1 ==> Unit1_notes.pdf
Unit 2 => Unit2_notes.pdf
GRIET_Notes 👉👉 CLICK HERE
Previous papers 👉👉 CLICK HERE
