Calculus MTH 250 Lecture 25 Previous Lectures Summary

Previous Lecture’s Summary • Differentiability of multivariable functions • Differentials & linear approximations •

Today’s Lecture • Recalls • Introduction to double integrals • Iterated integrals • Theorem

Recalls Definition (Total differential):

Recalls Definition (chain rules) for partial derivatives:

Introduction to double integrals Definition: The sum in the limit is called the Riemann

Integrals on non-rectangular regions Definition:

Lecture Summary • Introduction to double integrals • Iterated integrals • Theorem of Fubini

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Calculus (MTH 250) Lecture 25

Previous Lecture’s Summary • Differentiability of multivariable functions • Differentials & linear approximations • Chain rules for partial differentiation • Implicit differentiation • Extrema of multivariable functions

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

Recalls

Recalls Definition (Total differential):

Recalls

Recalls Definition (chain rules) for partial derivatives:

Recalls

Recalls Theorem: Definitions:

Recalls

Introduction to double integrals

Introduction to double integrals Definition: The sum in the limit is called the Riemann sum.

Introduction to double integrals

Iterated integrals Definition:

Iterated integrals

Theorem of Fubini Theorem:

Theorem of Fubini

Properties of double integrals Theorem:

Integrals on non-rectangular regions Definition:

Integrals on non rectangular regions

Properties of double integrals Theorem:

Properties of double integrals

Reversing the order of integration

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