Calculus MTH 250 Lecture 23 Previous Lectures Summary

Calculus (MTH 250) Lecture 23

Previous Lecture’s Summary • Direction cosines • Scalar triple product • Parametric equations of lines • Vector equations of planes • Vector-valued functions • Limits, continuity & differentiability • Integration

Today’s Lecture • Recalls • Multivariable functions • Limits along smooth curves • Limits of multivariable functions • Continuity of multivariable functions • Partial differentiation

Recalls

Recalls

Recalls

Recalls

Recalls

Recalls

Recalls

Multivariable functions

Multivariable functions

Multivariable functions

Multivariable functions

Limits along smooth curves

Limits along smooth curves

Limits along smooth curves

Limits of multivariable functions

Limits of multivariable functions

Limits of multivariable functions Definition (formal):

Limits of multivariable functions Example: Find Solution:

Limits of multivariable functions Theorem:

Continuity of multivariable functions Def: Theorem:

Continuity of multivariable functions

Continuity of multivariable functions Limit & continuity in 3 D:

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Partial differentiation

Lecture Summary • Recalls • Multivariable functions • Limits along smooth curves • Limits of multivariable functions • Continuity of multivariable functions • Partial differentiation