(MTH 250) Lecture 26 Calculus. Previous Lecture’s Summary Recalls Introduction to double integrals Iterated integrals Theorem of Fubini Properties of.

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Presentation transcript:

(MTH 250) Lecture 26 Calculus

Previous Lecture’s Summary Recalls Introduction to double integrals Iterated integrals Theorem of Fubini Properties of double integrals Integrals over non-rectangular regions Reversing the order of integration

Today’s Lecture Recalls Polar Coordinates Rectangular Coordinates. Cylindrical Coordinates Spherical Coordinates Equations of Surfaces Conversion of Coordinate Systems Directional Derivatives Gradients.

Recalls

Recalls

Definition : Recalls

Theorem: Recalls

Definition: Recalls

Properties of double integrals Theorem:

Polar coordinates

Rectangular coordinates

Cylindrical coordinates

Spherical coordinates

Equations of surfaces

Conversion of Coordinate systems

Directional Derivatives

Theorem: Directional Derivatives

Gradient Definition: Remark:

Gradient Properties:

Gradient

Gradient

Gradient

Gradient Theorem: Remark:

Gradient

Gradient

Lecture Summary Polar Coordinates Rectangular Coordinates. Cylindrical Coordinates Spherical Coordinates Equations of Surfaces Conversion of Coordinate Systems Directional Derivatives Gradients.