Solutions to Differential Equations and Calculus of Variations by N. Gupta

Contents:

SECTION I
1.    Series Solution of Differential Equations
2.    Legendre Equation
3.    Bessel Equation
4.    Hypergeometric Equation
5.    Sturm-Liouville Problems

SECTION II
6.    Laplace Transforms
7.    Inverse Laplace Transforms
8.    Solution of Integral Equations Using Laplace Transformation
9.    Solution of Systems of Differential Equations Using the Laplace Transformation

SECTION III
10.  Partial Differential Equations
11.  Partial Differential Equations of the First Order
       (Equations Linear in p and q)
12.  Partial Differential Equations of the First Order
       (Equations Non-linear in p and q)
13.  Homogeneous Linear Partial Differential Equations with Constant Coefficients
14.  Non-homogeneous Linear Partial Differential Equations with Constant Coefficients
15.  Partial Differential Equations Reducible to Equations with Constant Coefficients
16.  Monge's Methods

SECTION IV
17.  Variational Problems with Fixed Boundaries
18.  Variational Problems with Moving Boundaries
19.  Sufficient Conditions for an Extremum