Recent Event Highlights: Lecture 15: Vector Calculus - Surface integrals + vector fields. Chris Tisdell UNSW., Lecture 13: Vector Calculus - What is a surface integral? (part 1) Chris Tisdell UNSW, Lecture 14: Vector Calculus - More on surface integrals. Chris Tisdell UNSW, Lecture 10: Vector Calculus: More on Green's Theorem. Chris Tisdell UNSW, Lecture 12: Vector calculus - Parametrised surfaces. Chris Tisdell UNSW, Lecture 9: Vector Calculus - What is Green's theorem? Chris Tisdell UNSW, and 49 more...
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This lecture discusses "surface integrals" of vector fields. In particular, we discover how to integrate vector fields over surfaces in 3D space and "flux" integrals. A few examples are presented to illustrate the ideas. Such concepts have important applications in fluid flow and electromagnetics. Surface integrals are seen in 2nd-year universiiy mathematics courses.
This lecture gently introduces the idea of a "surface integral" and illustrates how to integral functions over surfaces. The idea is a generalization of double integrals in the plane. The concept of surface integral has a number of important applications such as caculating surface area. In addition, surface integrals find use when calculating the mass of a surface like a cone or bowl. A number of examples are presented to illustrate the ideas. Such concepts are seen in 2nd-year university mathematics courses.
This lecture continues discussing "surface integrals" and further illustrates how to integral functions over surfaces. The idea is a generalization of double integrals in the plane. The concept of surface integral has a number of important applications in the field of engineering, for example, calculating the mass of a surface like a cone or bowl. A number of examples are presented to illustrate the ideas. Such concepts are seen in 2nd-year university mathematics courses.
This is the 2nd lecture on Green's theorem and it's use. In this lecture we explore some interesting applications of Green's theorem and present several examples. Also some proofs are discussed.
This lecture gently introduces the idea of parametrizing surfaces in space. The content is a prequel to integration over surfaces that sit in 3D. Many examples are discussed and a method to find tangent vectors and normal vectors to a given surface are presented.
This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, which gives the relationship between divergence and flux. Plenty of examples are presented.
This lecture discusses the "fundamental theorem of line integrals for gradient fields". The topic is motivated and the theorem is stated and proved. A number of examples are presented to illustrate the theory.
This lecture discusses the applications of line integrals, including calculating work; flux (flow) in the plane over curves; and also circulation around curves in the plane. A number of examples are presented to illustrate the theory. The fundamental theorem of line integrals may be thought of as one of the basic theorems of vector calculus.
This lecture discusses how to integrate vector fields over curves, better known as "line integrals". Dr Chris Tisdell defines the concept of a line integral and presents some examples on their calculation. Special attention is given to the applications of line integrals such as: calculating work done by a variable force on a particle moving over curved paths; fluid flow (flux) over closed curves; circulation and flow integrals. Plenty of examples are presented.
This lecture gently introduces the idea of a the "curl" of a vector field. The curl is one of the basic operations of vector calculus. Dr Chris Tisdell discusses the definition of the curl and how to compute it. Plently of examples are provided. A physical interpretation of the curl is also presented in terms of circulation density. Basically speaking, curl measures the tendency of a vecotr field to "swirl" around a point.
This video discusses the 'divergence' of a vector field. Divergence is one of the basic operations of vector calculus and, loosely speaking, may be thought of as a type of derivative in vector calculus. Dr Chris Tisdell introduces the idea of divergence, discusses some examples and also gives a physical interpretation of divergence in terms of 'flux density'.
This lecture gently introduces the idea of a vector field. Dr Chris Tisdell discusses the need for a vector field, plus presents many examples. This lecture is from a course of Vector Calculus, which is taught at UNSW, Sydney by Dr Chris Tisdell..
I discuss and solve a simple problem that involves the evaluation of a line integral. This particular line integral is in the differential form. The method used to solve this problem is one that involves a simple substitution. Such an example is seen in 2nd-year university mathematics.
I present a simple example where I compute the divergence of a given vector field. I give a rough interpretation of the physical meaning of divergence. Such an example is seen in 2nd year university mathematics courses.
I present a simple example where I compute the curl of a given vector field. I give a rough interpretation of the physical meaning of curl. Such an example is seen in 2nd year university mathematics courses.
I present and solve a simple example where the curl of a given vector field is sought. The curl is one of the basic operations of "vector calculus". Such and example is seen in 2nd year university mathematics. Such an example is seen in 2nd year university mathematics courses.
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I present an example where I calculate the line integral of a given vector function over a closed curve.. In particular, I the vector function is a $${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$ and the closed curve is the unit circle, oriented in the anticlockwise direction. I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics. Such an example is seen in second year university mathematics.
I discuss and solve an example involving a path integral (also known as a scalar line integral) from vector calculus. In particular, I integrate a given function over a helix in 3D-space, where the integration is with respect to arc length. Such concepts are seen in 2nd-year university mathematics and enjoy applications to engineering.
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...had algebra, geometry, analytical geometry, trigonometry, differential calculus, integral calculus, linear algebra, and vector calculus, I suggested to my wife that I might help him. An Attempt to Personally Help - Would you believe it? Pre-algebra was such...
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Lecture 31: Stokes' theorem. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 34: Final review. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 32: Stokes' theorem (cont.); review. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 30: Line integrals in space, curl, exactness and potentials. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 26: Spherical coordinates; surface area. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 33: Topological considerations; Maxwell's equations. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 28: Divergence theorem. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 25: Triple integrals in rectangular and cylindrical coordinates. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 27: Vector fields in 3D; surface integrals and flux. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 29: Divergence theorem (cont.): applications and proof. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 35: Final review (cont.). View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 07: Review. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 22: Green's theorem. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 23: Flux; normal form of Green's theorem. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 24: Simply connected regions; review View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 20: Path independence and conservative fields. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 19: Vector fields and line integrals in the plane. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 21: Gradient fields and potential functions. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 16: Double integrals. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 18: Change of variables. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 17: Double integrals in polar coordinates; applications. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 14: Non-independent variables. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 11: Differentials; chain rule. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 10: Second derivative test; boundaries and infinity. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 09: Max-min problems; least squares. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 15: Partial differential equations; review. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 13: Lagrange multipliers. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 08: Level curves; partial derivatives; tangent plane approximation. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 12: Gradient; directional derivative; tangent plane. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
Lecture 02: Determinants; cross product. View the complete course at: http://ocw.mit.edu/18-02F07 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu ...
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