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INTUITION MATTERS! Applied Calculus for Engineers - Part 2
Section 1: Vectors
Vectors in 2 dimensions - what are they (9:55)
Vectors in multiple dimensions - what are they (15:35)
Vector terminology and disclaimers (6:30)
Vector magnitude - what is it (11:38)
Vector components - exercise (6:07)
Vector operations - how do they work (4:45)
Apply the dot product - Forces on a box example (6:50)
Cross product intuition- what is it (7:18)
Cross product - how to calculate it (13:00)
Apply the cross product - electron and magnetic field example (10:20)
MEGA Application - Water tank example 1 (6:38)
MEGA Application - Water tank example 2 (9:47)
MEGA Application - Water tank example 3 (11:23)
CORRECTION: MEGA Application - Water tank example 3 (5:01)
MEGA Application - Water tank example 4 (12:33)
CORRECTION: MEGA Application - Water tank example 4 (2:25)
MEGA Application - Water tank example 5 (5:33)
SIM: MEGA Application - Water tank example - Complete (1:54)
MEGA Application - Water tank example - exercise 1 (11:10)
MEGA Application - Water tank example - exercise 2 (11:11)
SIM: MEGA Application - Water tank example - exercise (0:50)
MEGA Application - Water tank mass flow- use derivatives to get it (15:57)
Distance VS Position vectors - what's the difference (16:14)
Displacement VS Velocity VS Acceleration vectors - what's the difference (14:29)
Average displacement, velocity, and acceleration vectors - clarification
Graph Displacement, Velocity, & Acceleration vectors (8:31)
Acceleration vector - intuition (7:42)
Vector derivatives - how do they work (2:31)
Section 2: Transformations
2D Cartesian VS Polar coordinate systems - what are they (10:22)
3D Cartesian VS Cylindrical VS Spherical coordinate systems - what are they (7:37)
Apply 3 dimensional coordinate systems - when to use what (7:08)
Going from Polar to Cartesian (6:15)
Going from Cartesian to Polar (3:20)
Going between 3 dimensional coordinate systems - how to switch between them (9:47)
Section 3: Parametric equations
Intro into Parametric Equations - Intuition (7:32)
MEGA Application - Landing Airplane in 2D (7:03)
SIM: MEGA Application: Landing simulation (3:22)
MEGA Application - Airplane flying in an oscillatory way (in 2D) (11:25)
MEGA Application - Airplane's velocity and acceleration in 2D (18:09)
SIM: MEGA Application - Sin trajectory simulation (5:31)
MEGA Application - Airplane doing circles in 2D - Cartesian & Polar coordinates (16:29)
MEGA Application - Airplane doing circles in 2D - Velocity & Acceleration (17:41)
SIM: MEGA Application - Circle simulation (7:28)
MEGA Application - Airplane flying in a spiral in 3D (14:47)
SIM: MEGA Application - 3D trajectories - simulation 1 (2:44)
SIM: MEGA Application - 3D trajectories - simulation 2 (1:35)
SIM: MEGA Application - 3D trajectories - simulation 3 (3:06)
SIM: MEGA Application - 3D trajectories - simulation 4 (2:38)
SIM: MEGA Application - 3D trajectories - simulation 5 (1:14)
MEGA Application - 2 joint robot - Angular position, velocity, and acceleration (19:00)
MEGA Application - 2 joint robot - 2 joints rotating simultaneously (10:03)
MEGA Application - 2 joint robot - assigning multiple reference frames (14:32)
MEGA Application - 2 joint robot - describing a point in two different frames (8:43)
MEGA Application - 2 joint robot - deriving a 2D rotational matrix (12:58)
MEGA Application - 2 joint robot - describing rotating and translating joints (18:45)
MEGA Application - 2 joint robot - joints rotating at different frequencies (9:26)
SIM: MEGA Application - 2 joint robot - simulation 1 (4:27)
SIM: MEGA Application - 2 joint robot - simulation 2 (3:24)
3D Rotational matrix - how to derive it 1 (18:19)
3D Rotational matrix - how to derive it 2 (11:05)
3D Rotational matrix - how to derive it 3 (12:50)
Exercise: Spiral - Final shape
Exercise: Spiral - Final shape - Solution
Section 4: Multivariable Calculus
Implicit functions - what are they and how to graph them (13:22)
Implicit function derivatives - how to take them (11:42)
Expanding function dimensions 1 (6:40)
Expanding function dimensions 2 (6:28)
Machine Learning example - how to apply multidimensionality (16:50)
Partial derivatives - intro 1 (10:36)
Partial derivatives - intro 2 (14:51)
Partial derivatives - intro 3 (13:47)
Higher dimensional partial derivatives & its graph (12:57)
Airplane example - Chain rule in parametric equations - partial derivatives 1 (6:37)
Airplane example - Chain rule in parametric equations - partial derivatives 2 (9:46)
Multilevel partial derivatives - how to take them (15:17)
Gradient - what is it and how to find it (7:33)
Taylor Series - what is it and how to formulate it 1 (16:57)
Taylor Series - what is it and how to formulate it 2 (19:42)
Linearization and Quadratic Approximation - what is it and how to do it (28:24)
Multidimensional linearization - practical exercise (22:44)
Multidimensional quadratic approximation - Hessian Matrix (16:46)
Representing a system mathematically, in vector-matrix form, and block diagrams (18:20)
Exercise: Spiral - Final shape - Solution
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