Calculus MTH 250 Lecture 27 Previous Lectures Summary

Calculus (MTH 250) Lecture 27

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

Today’s Lecture • Recalls • Simple polar regions • Double integrals in polar coordinates • Finding area using polar double integrals • Changing coordinates in integrals • Introduction to line integrals

Racalls

Racalls

Racalls

Racalls

Racalls

Racalls Theorem: Def.

Racalls Theorem

Simple polar regions

Simple polar regions

Double integrals in polar coordinates

Double integrals in polar coordinates

Double integrals in polar coordinates

Double integrals in polar coordinates

Double integrals in polar coordinates

Double integrals in polar coordinates

Double integrals in polar coordinates

Finding area using polar double integrals

Changing coordinates in integrals

Changing coordinates in integrals

Changing coordinates in integrals

Changing coordinates in integrals

Changing coordinates in integrals

Changing coordinates in integrals

Introduction to line integrals

Introduction to line integrals

Introduction to line integrals

Introduction to line integrals

Introduction to line integrals

Introduction to line integrals

Lecture Summary • Recalls • Simple polar regions • Double integrals in polar coordinates • Finding area using polar double integrals • Changing coordinates in integrals • Introduction to line integrals