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Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Vector Differential Calculus Grad, Div,

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Presentation on theme: "Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Vector Differential Calculus Grad, Div,"— Presentation transcript:

1 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Vector Differential Calculus Grad, Div, Curl Text Chapter 9 Emphasis Sections: 9.4, 9.7-9.9

2 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 364-365

3 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 365

4 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 366 (1)

5 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 366 (2)

6 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 367 (1)

7 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 367 (2)

8 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 368 (1)

9 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 368 (2a) Continued

10 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 368 (2b)

11 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 369

12 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 371 (1)

13 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 371 (2)

14 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 371 (3)

15 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 372 (1)

16 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 372 (2)

17 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 373

18 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 374a Continued We use

19 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 374b

20 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 375

21 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 377 (1a) Continued

22 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 377 (1b)

23 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 377 (2)

24 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 378 (1)

25 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 378 (2)

26 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 379 (1)

27 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 379 (2a) Continued

28 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 379 (2b)

29 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 380a Continued

30 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 370b

31 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 381 (1a) Continued

32 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 381 (1b)

33 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 381 (2a) Continued

34 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 381 (2b)

35 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 382

36 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 384a

37 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 384b

38 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 387a

39 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 387b Continued

40 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 387C

41 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 388 (1) Rules:

42 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 388 (2)

43 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 389

44 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 390

45 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 391

46 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 392 (1)

47 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 392 (2a) Continued

48 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 392 (2b) Continued

49 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 392 (2c)

50 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 393

51 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 394-395

52 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 395

53 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 395-396a Continued

54 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 395-396b

55 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 396-397a Continued

56 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 396-397b

57 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 401 (1)

58 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 401 (2)

59 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 403

60 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 404 (1) Cylindrical Coordinates k j i z x y r  z

61 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 404-405 (2a) Continued

62 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 404-405 (2b)

63 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 405

64 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 406

65 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 406-407

66 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 407 Continued

67 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 407 Continued

68 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 410a Continued

69 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 410b

70 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 411 (1) Cylindrical Coordinates

71 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 411 (2)

72 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 412-413a Continued

73 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 412-413b Continued

74 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 412-413c Continued

75 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 412-413d Continued

76 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 412-413e

77 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 414

78 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 414-415b Continued

79 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 414-415b

80 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 415

81 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 416

82 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Page 417-419a Continued

83 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419b Continued

84 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419c Continued

85 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419d Continued

86 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419e Continued

87 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419g Continued

88 Advanced Engineering Mathematics by Erwin Kreyszig Copyright  2007 John Wiley & Sons, Inc. All rights reserved. Pages 417-419h


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