Ordinary and Partial Differential Equation

Description

Author : Ravendra Kumar . As Per B.Sc. / B.A. Mathematics Generic Elective syllabus of 2nd Semester (Dibrugarh) & 3rd Semester (Gauhati) under various Indian Universities

Content in Details

1. Differential Equation of First Order and First Degree 08 – 69
1.1. Introduction 08-09
1.2. Ordinary and partial differential equation 09-09
1.3. Order of the differential equation 09-09
1.4. Degree of the differential equation 09-09
1.5. Formation of a differential equation 09-14
1.6. Solution of differential equation of first order and first degree 14-15
1.7. Method of separation variable 15-20
1.8. Homogeneous differential equation 20-26
1.9. Equation reducible to homogeneous form 26-34
1.10. Linear differential equation 34-42
1.11. Bernoulli’s equation 42-48
1.12.Exact differential equation 48-54
1.13. Integrating factor 54-57
1.14. Rule for finding integrating factor 57-66
1.15. Change of Variable .66-69
2. Differential Equation of First Order and Higher Degree 70 – 86
2.1. Equation solvable for P 70-75
2.2. Equation solvable for Y 75-76
2.3. Equation solvable for X 76-83
2.4. Clairaut equation 83-86
3. The Wronskian 87 – 106
3.1. Definition 87-883.2. Linear combination of the function 88-88
3.3. Linear dependent set of function 88-88
3.4. Linear independent set of function 88-88
3.5. Application 88-106
4. Solution of Differential Equation by Reducing it’s Order 107 – 138
4.1. Complete solution of second order in term of known integral 107-120
4.2. Removal of first derivative (Transformation to the normal form) 120-129
4.3. Change of independent variable 129-138
5. Method of Variation of Parameter 139 – 153
6. Linear Homogeneous Equation with Constant Coefficient 154 – 188
6.1. Solution of differential equation 154-161
6.2. Particular integral 161-162
6.3. Particular integral for some cases 162-188
7. Homogeneous Linear Equation (Cauchy-Euler’s Equation) 189 – 201
7.1. Cauchy-euler’s equation 189-191
7.2. Determination of complementery function (C.F.) 191-191
7.3. Particular integral of the function (P.I.) 191-199
7.4. Equation reducible to homogeneous linear form 199-201
8. Simultaneous Differential Equation 202 – 218
8.1. Introduction 202-212
8.2. Simultaneous equation of the form 212-218
9. Total Differential Equation 219 – 240
9.1. Pfaffian differential form 219-219
9.2. Pfaffian differential equation 219-219
9.3. Pfaffian differential equation in three variable (Total d.e.) 219-224
9.4. Condition of exactness 224-238
9.5. When the equation is not integrable 238                                                                                                                                10. Partial Differential Equation of First Degree 241 – 255
10.1.Definition 241-241
10.2. Order of partial differential equation 241-242
10.3. Degree of partial differential equation 242-242
10.4. Linear partial differential equation 242-243
10.5.Nonlinear partial differential equation 243-243
10.6. Formation of partial differential equation 243-254
10.7.Solution of partial differential equation 254-255
11. Lagrange’s Method 256 – 276
11.1. Lagrange’s equation 256-256
11.2. General solution of Lagrange’s equation 256-257
11.3. Linear partial differential equation with n independent variable 257-270
11.4. Integral surface passes through the given point 270-276
12. Nonlinear Partial Differential Equation of First Order 277 – 298
12.1. Introduction 277-277
12.2.Standard form I 277-283
12.3.Standard form II 283-289
12.4.Standard form III 289-294
12.5.Standard form IV 294-298
13. Charpit’s Method 299 – 312
13.1. Introduction 299-299
13.2. Charpit’s auxiliarly equation 299-312
14. Classification of Second Order Partial Differential Equation 313 – 320
14.1. Linear partial differential equation of second order in independent variable 313-314                                                    14.2. Classification of linear partial differential equation of second order in two independent variable. 314-320