### Lecture 1: Vector Revision

##### Lecture Details :

Free ebook: http://tinyurl.com/EngMathYTA review of vectors for those beginning vector calculus and several variable calculus. Such problems involving vectors are seen in first year university mathematics, physics and engineering.

##### Course Description :

Vector Revision - Intro to curves and vector functions - Sketch graph of vector function: an example - How to sketch the graph of a vector function - hen do vector functions intersect - Intersection of vector functions example - Limits of vector functions - Limits of vector functions: an example - Calculus of vector functions - 1 variable - Derivatives of vector functions example - Cross product differentiation example - angent to curve of vector function example - Arc length of vector functions example - Intro to functions of two variables - Intersection of sphere and cone example - Limits of functions of two variables - Limit doesn't exist 2 variables example - Limits in polar co-ordinates example-2 variable functions: graphs + limits tutorial

How to compute partial derivatives - Product + Quotient rule formulas: Partial derivatives - Partial derivatives: 2nd order examples - Basic partial differentiation and PDE example - Partial derivatives - Partial derivatives + PDEs tutorial - Tangent plane & normal vector example - Multivariable chain rule and differentiability - Chain rule: partial derivative of $arctan (y/x)$ w.r.t. $x$ - Chain rule: identity involving partial derivatives - two variables - 2nd derivatives example - Advection PDE + chain rule - Multivariable chain rule tutorial - Chain rule: differentiate integral example - Differentiate under integral signs: Leibniz rule - Leibniz' rule: Integration via differentiation under integral sign - Evaluating challenging integrals via differentiation: Leibniz rule - Gradient and directional derivative - Gradient & directional derivative tutorial - Application of gradient: temperature example