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Engineering Mathematics

The University of New South Wales, , Prof. Chris Tisdell

Updated On 02 Feb, 19

Overview

Contents:
Vector Revision - Intro to curves and vector functions - Limits of vector functions - Calculus of vector functions - Calculus of vector functions tutorial - Vector functions of one variable tutorial - Vector functions tutorial - Intro to functions of two variables - Partial derivatives-2 variable functions: graphs + limits tutorial - Multivariable chain rule and differentiability - Chain rule: partial derivative of $arctan (y/x)$ w.r.t. $x$ - Chain rule: identity involving partial derivatives - Chain rule & partial derivatives - Partial derivatives and PDEs tutorial - Multivariable chain rule tutorial - Gradient and directional derivative - Gradient of a function - Tutorial on gradient and tangent plane - Directional derivative of $f(x,y)$ - Gradient & directional derivative tutorial - Tangent plane approximation and error estimation - Partial derivatives and error estimation - Multivariable Taylor Polynomials - Taylor polynomials: functions of two variables - Differentiation under integral signs: Leibniz rule - Leibniz' rule: Integration via differentiation under integral sign

Evaluating challenging integrals via differentiation: Leibniz rule - Critical points of functions. Chris Tisdell UNSW Sydney - Second derivative test: two variables. Chris Tisdell UNSW Sydney - How to find critical points of functions - Critical points + 2nd derivative test: Multivariable calculus - Critical points + 2nd derivative test: Multivariable calculus - How to find and classify critical points of functions - Lagrange multipliers - Lagrange multipliers: Extreme values of a function subject to a constraint - Lagrange multipliers example - Lagrange multiplier example: Minimizing a function subject to a constraint - 2nd derivative test, max / min and Lagrange multipliers tutorial - Lagrange multipliers: 2 constraints-Intro to vector fields - What is the divergence - Divergence + Vector fields - Divergence of a vector field: Vector Calculus - What is the curl? Chris Tisdell UNSW Sydney - Curl of a vector field (ex. no.1): Vector Calculus - Line integrals - Integration over curves - Path integral (scalar line integral) from vector calculus

Includes

Lecture 9: Partial derivatives. Chris Tisdell UNSW Sydney

4.1 ( 11 )


Lecture Details

We introduce the concept of partial derivatives and show how to compute them. Plenty of examples are discussed and presented including an example where the mixed derivates do not commute.

Ratings

5.0


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Comments
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Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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