[UR] Multivariable Calculus Wk.1-2 Recap, 2nd Semester FAST NUCES LHR

Timestamps:

Introduction Stuff
0:00 - Some Silly lil' Names
0:50 - Interior Points vs Boundary Points
2:11 - Interior VS Boundary, Finding Boundaries
3:50 - Closed vs Open Regions
4:37 - Level Curves

Limit Evaluation and Continuity
5:29 - Limits for Multivariable Functions
6:13 - Continuity of a Function
6:33 - Explaining the Substitution Method with Example
7:30 - Converting Expression from 2 Variables into 1
8:30 - Why k?
9:15 - We DONT Assume y to be Dependent on x
9:40 - Solving the Problem
10:01 - Limit Existence Requirement
11:02 - Another Limit Evaluation Problem
12:45 - The Teacher's Tip
13:24 - Summary for Those Who Have No Idea What Just happened
15:50 - Trying a Different Substitution in the same Question

Partial Derivatives
17:10 - Partial Derivatives Definition
17:40 - Solving Partial Derivatives Directly
18:50 - When to put dx and ∂x?
19:30 - 2nd Order Partial Derivatives
20:25 - Mixed Derivative Theorem
20:58 - Parametric Equations
22:10 - Chain Rule for Multivariable Parametrics
24:47 - Implicit Partial Differentiation

Directional Derivatives
25:42 - Directional Derivative
27:11 - Solving Directional Derivative by Definition
28:42 - Gradient Method