Unit I: Ordinary Differential Equations
Review of differential equations (order, degree, linear, nonlinear, implicit and explicit form of solution, general solutions, particular solution, singular solution). Exactness, nonexact equations reduce to exact form.
Part I: 1.1-1.9, 2.12-2.22
Equations of first order but of higher degree:
Equations solvable for dy/dx, y, x, equations in Clairaut’s form, equations reducible to Clairaut’s form.
Part I: 4.1-4.11
Unit II: Equations of Second order
Linear homogeneous differential equations with constant coefficients, Euler- Cauchy equation, Linear Nonhomogeneous Differential Equations: Wronskian, linear independence, Method of undetermined coefficients. Method of variation of parameters.
Part I:5.1-5.5, 6.1-6.3, 1.12,1.13, 5.26-5.27, 7.1-7.5
Unit III: Systems of first order linear equations
Conversion of nth order differential equation to n first order differential equations, homogeneous linear system with constant coefficients, fundamental matrices, complex eigen values, repeated eigenvalues. simultaneous linear differential equations with constant coefficients, simultaneous linear differential equations with variable coefficients
PART I: 8.1-8.3, 2.1- 2.7
Partial Differential Equations
Review of partial differential equations (order, degree, linear, nonlinear).
Formation of equations by eliminating arbitrary constants and arbitrary functions.
Solutions of partial differential equations: General, particular and complete integrals.Lagrange’s linear equation, Charpit’s method, Methods to solve the first order partial differential equations of the forms f(p,q) = 0, f(z,p,q) = 0, f1(x,p) = f2(y,q) and Clairut’s form z = px + qy + f(p,q) where p = dz/dx and q = dz/dy.
Part III: 1.1 – 1.5, 2.3-2.12, 3.1-3.2, 3.7-3.8, 3.10-3.18
Classification of partial differential equations of second order. Homogeneous linear partial differential equations with constant coefficient of higher order.Non-homogeneous linear partial differential equations of higher order.
Part III: 8.1, 4.1-4.12