Preview Partial Differential Equations

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Maths.Engineering Platform Walkthrough

1. Formation of PDE's by elimination of arbitrary constants

1.1 Introduction

1.2 Formation of Partial Differential Equations

1.3 Solved Problem 1

1.4 Solved Problem 2

1.5 Solved Problem 3

1.6 Solved Problem 4

1.7 Solved Problem 5

1.8 Solved Problem 6

1.9 Solved Problem 7

1.10 Solved Problem 8

1.11 Solved Problem 9

1.12 Solved Problem 10

1.13 Solved Problem 11

1.14 Solved Problem 12

1.15 Exercise

2. Formation of PDE's by elimination of arbitrary functions

2.1 Introduction

2.2 Solved Problem 1

2.3 Solved Problem 2

2.4 Solved Problem 3

2.5 Solved Problem 4

2.6 Solved Problem 5

2.7 Solved Problem 6

2.8 Solved Problem 7

2.9 Solved Problem 8

2.10 Solved Problem 9

2.11 Solved Problem 10

2.12 Solved Problem 11

2.13 Solved Problem 12

2.14 Exercise

3. Solutions of standard first order partial differential equations

3.1 Introduction

3.2 Type I

3.3 Type II

3.4 Type III

3.5 Type IV

3.6 Type V

3.7 Type VI

3.8 Solved Problem 1

3.9 Solved Problem 2

3.10 Solved Problem 3

3.11 Solved Problem 4

3.12 Solved Problem 5

3.13 Solved Problem 6

3.14 Solved Problem 7

3.15 Solved Problem 8

3.16 Solved Problem 9

3.17 Solved Problem 10

3.18 Solved Problem 11

3.19 Solved Problem 12

3.20 Solved Problem 13

3.21 Solved Problem 14

3.22 Solved Problem 15

3.23 Solved Problem 16

3.24 Solved Problem 17

3.25 Solved Problem 18

3.26 Solved Problem 19

3.27 Solved Problem 20

3.28 Solved Problem 21

3.29 Solved Problem 22

3.30 Solved Problem 23

3.31 Solved Problem 24

3.32 Solved Problem 25

3.33 Solved Problem 26

3.34 Solved Problem 27

3.35 Exercise

4. First Order Linear(Lagrange's) Equation

4.1 Introduction

4.2 Linear partial differential equation of the first order

4.3 Solved Problem 1

4.5 Solved Problem 3

4.7 Solved Problem 5

4.8 Solved Problem 6

4.9 Solved Problem 7

4.10 Solved Problem 8

4.11 Solved Problem 9

4.12 Solved Problem 10

4.13 Solved Problem 11

4.14 Solved Problem 12

4.15 Solved Problem 13

4.16 Exercise

5. Higher Order Partial Differential Equation

5.1 Introduction

5.2 Solved Problem 1

5.3 Solved Problem 2

5.4 Solved Problem 3

5.5 Solved Problem 4

5.6 Solved Problem 5

5.7 Solved Problem 6

5.8 Solved Problem 7

5.9 Solved Problem 8

5.10 Solved Problem 9

5.11 Solved Problem 10

5.12 Solved Problem 11

5.13 Solved Problem 12

5.14 Solved Problem 13

5.15 Solved Problem 14

5.16 Solved Problem 15

5.17 Solved Problem 16

5.18 Solved Problem 17

5.19 Solved Problem 18

5.20 Exercise

6. Complementary Function for a Non-homogenous Linear Equation

6.1 Introduction

6.2 Solved Problem 1

6.3 Solved Problem 2

6.4 Solved Problem 3

6.5 Solved Problem 4

6.6 Solved Problem 5

6.7 Solved Problem 6

6.8 Solved Problem 7

6.9 Solved Problem 8

6.9 Solved Problem 9

6.9 Solved Problem 10

6.10 Exercise

7. Classification of second order PDE

7.1 Introduction

7.2 Solved Problem 1

7.3 Solved Problem 2

7.4 Solved Problem 3

7.5 Solved Problem 4

7.6 Solved Problem 5

7.7 Solved Problem 6

7.8 Solved Problem 7

7.9 Solved Problem 8

7.10 Solved Problem 9

7.11 Solved Problem 10

7.12 Exercise

8. Method of separation of variables

8.1 Introduction

8.2 Solved Problem 1

8.3 Solved Problem 2

8.4 Solved Problem 3

8.5 Solved Problem 4

8.6 Solved Problem 5

8.7 Solved Problem 6

8.8 Solved Problem 7

8.9 Solved Problem 8

8.10 Exercise

9. Solutions of One dimensional wave equation

9.1 Introduction

9.2 Tranasverse vibration of a stretched string - one dimesional wave equation

9.3 Transmission line equations

9.4 Variable separable solutions of the wave

9.5 Choice of proper solution

9.6 Solution of a damped vibrating string equation

9.7 Problems on vibrating string with non-zero initial velocity

9.8 Solved Problem 1

9.9 Solved Problem 2

9.10 Solved Problem 3

9.11 Solved Problem 4

9.12 Solved Problem 5

9.13 Solved Problem 6

9.14 Solved Problem 7

9.15 Solved Problem 8

9.16 Solved Problem 9

9.17 Solved Problem 10

9.18 Solved Problem 11

9.19 Solved Problem 12

9.20 Exercise

10. Solutions of One dimensional Heat equation

10.1 Introduction

10.2 Equation of variable heat flow in one dimension

10.3 Variable separable solutions of the heat equation

10.4 Choice of proper solution

10.5 One dimensional heat equation

10.6 Solved Problem 1

10.7 Solved Problem 2

10.8 Solved Problem 3

10.9 Solved Problem 4

10.10 Solved Problem 5

10.11 Solved Problem 6

10.12 Solved Problem 7

10.13 Solved Problem 8

10.14 Exercise

Preview - Partial Differential Equations