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AOE 5104 Class 3 9

Unnumbered slides contain comments that I inserted and are not part of Professor's Devenport's original presentation. . 3. Last Class

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AOE 5104 Class 3 9

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    1. AOE 5104 Class 3 9/2/08 Online presentations for today’s class: Vector Algebra and Calculus 1 and 2 Vector Algebra and Calculus Crib Homework 1 due 9/4 Study group assignments have been made and are online. Recitations will be Mondays @ 5:30pm (with Nathan Alexander) Tuesdays @ 5pm (with Chris Rock) Locations TBA Which recitation you attend depends on which study group you belong to and is listed with the study group assignments

    3. 3 Last Class… Vectors, inherent property of direction Algebra Volumetric flow rate through an area Taking components, eqn. of a streamline Triple products, A.BxC, Ax(BxC) Coordinate systems Class 3. 8/29/06 Assignments: Online Presentation “Vector Algebra and Calculus 2” Homework 1, due 9/5/06 Vector Algebra and calculus crib on course web site Study groupsClass 3. 8/29/06 Assignments: Online Presentation “Vector Algebra and Calculus 2” Homework 1, due 9/5/06 Vector Algebra and calculus crib on course web site Study groups

    4. 4 Cylindrical Coordinates

    5. 5 Spherical Coordinates

    7. 7

    8. 8 Class Exercise Using cylindrical coordinates (r, ?, z) Gravity exerts a force per unit mass of 9.8m/s2 on the flow which at (1,0,1) is in the radial direction. Write down the component representation of this force at (1,0,1) b) (1,?,1) c) (1,?/2,0) d) (0,?/2,0)

    9. Vector Algebra in Components

    10. 3. Vector Calculus Fluid particle: Differentially Small Piece of the Fluid Material

    11. Class 3. 8/29/06 Assignments: Online Presentation “Vector Algebra and Calculus 2” Homework 1, due 9/5/06 Vector Algebra and calculus crib on course web site Study groups Class 3. 8/29/06 Assignments: Online Presentation “Vector Algebra and Calculus 2” Homework 1, due 9/5/06 Vector Algebra and calculus crib on course web site Study groups

    12. Concept of Differential Change In a Vector. The Vector Field.

    13. 13 Change in Unit Vectors – Cylindrical System

    14. 14 Change in Unit Vectors – Spherical System

    15. 15 Example

    16. 16 Vector Calculus w.r.t. Time Since any vector may be decomposed into scalar components, calculus w.r.t. time, only involves scalar calculus of the components

    17. 17 High Speed Flow Past an Axisymmetric Object

    19. 19 Integral Calculus With Respect to Space

    20. 20

    21. 21 Integral Calculus With Respect to Space

    22. 22

    23. 23 Differential Calculus w.r.t. Space Definitions of div, grad and curl

    27. 27 Gradient

    28. 28 Gradient Component of gradient is the partial derivative in the direction of that component Fourier´s Law of Heat Conduction

    30. 30 Differential form of the Gradient

    34. 34

    35. 35 Divergence

    36. 36

    37. 37

    38. 38 Curl

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