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INTUITION MATTERS! Applied Calculus for Engineers - Part 1
Section 1: Single Variable Functions
Functions - what are they - high school review 1 (9:40)
Functions - what are they - high school review 2 (10:13)
SIM: Straight line functions in motion (3:26)
Intro to (Linux & macOS Terminal) & (Windows Command Prompt) (12:50)
Python installation instructions - Ubuntu (6:45)
Python installation instructions - Windows 10 (6:34)
Python installation instructions - macOS (8:04)
Codes for the Python animations in this course
Practice functions - airplane homework (9:12)
Abstract World VS Real World - 1 (5:54)
Abstract World VS Real World - 2 (5:44)
Straight line functions - How to manipulate them (10:32)
Inverse functions - what are they and how to find them (8:05)
Find inverse functions - example (5:15)
Parabolic functions - How to manipulate them (12:26)
Cubic functions - How to manipulate them (6:39)
SIM: Car race exercise - who will win the race? (1:03)
SIM: Car race exercise - who will win the race - SOLUTION (2:46)
What is a function, what is not - 1 (8:53)
What is a function, what is not - 2 (6:25)
Inverse function of a parabola - how to find it (6:09)
Inverse function of a cubic function- how to find it (7:01)
Functions in general form - how to manipulate them (10:49)
SIM: General functions in motion (5:39)
Piecewise defined functions - how to form them (10:27)
How to shift functions (8:35)
How to do function operations (12:07)
Practice function operations (8:34)
Quadratic function roots - How to get them 1 (11:00)
Quadratic function roots - How to get them 2 (7:55)
Which terms dominate in functions (7:23)
SIM: 3 airplane race - who wins, and when? (1:19)
Section 2: Trigonometric functions
Pi number and circumference of a circle - what are they and how to get them (13:27)
Radians VS Degrees & how to get the arc length of a circle (11:39)
Sine function - where does it come from (12:54)
Cosine and tangent function - where do they come from (8:14)
Inverse of trigonometric functions - how to get them (10:28)
Practice trigonometric functions - exercises (4:43)
Abstract VS Real - Aerospace Engineering example (13:41)
SIM: Avoid the crash - exercise (3:50)
SIM: Avoid the crash - solution 1 (1:48)
SIM: Avoid the crash - solution 2 (4:35)
SIM: Avoid the crash - solution 3 (2:53)
SIM: Avoid the crash - solution 4 (6:41)
SIM: Avoid the crash - solution 5 (5:15)
SIM: Avoid the crash - solution 6 (1:56)
SIM: Avoid the crash - solution 7 (3:56)
SIM: Avoid the crash - solution 8 (1:08)
SIM: Avoid the crash - solution 9 (4:56)
SIM: Avoid the crash - solution 10 (1:01)
Section 3: Multidimensional functions
2 variable function - how to apply it to a simple airplane example (12:42)
3 variable function - how to apply it to a simple airplane example (9:16)
What is a function and what is not - multidimensional functions (11:08)
Section 4: Limits
Variable equaling VS approaching something - what's the difference (12:04)
Variable approaching infinity - what happens (8:02)
Smart financial decision using limits - how to do it (11:08)
Manipulate trigonometric functions in different ways - how (11:03)
Model a wave with a trigonometric function - how (12:19)
Get from a sine to a cosine function - exercise (3:16)
Practice limits on a trigonometric function - does the limit exist? (4:34)
SIM: Limit simulation (3:05)
SIM: sin_limit simulation (6:03)
Section 5: Derivatives - single variable
Derivatives - what are they - falling sphere example 1 (13:02)
Where does the equation Hi - 5*t^2 come from?
Derivatives - what are they - falling sphere example 2 (11:05)
Derivatives - what are they - falling sphere example 3 (14:42)
SIM: Earth, Mars, Moon - exercise (3:27)
SIM: Earth, Mars, Moon - solution (3:46)
Derivatives - What are they - multidimensional point of view (7:33)
Practice your derivative intuition - exercises (10:53)
Prove that d(sin(theta))/d(theta)=cos(theta) - instructions
Prove that d(sin(theta))/d(theta)=cos(theta) - solutions
chain rule - how to apply it to a multi link problem - water pipe example 1 (11:20)
chain rule - how to apply it to a multi link problem - water pipe example 2 (15:58)
Differential operators - What are they and how to apply them (10:18)
Multilevel derivatives - double, triple, quadruple (7:35)
Derivative rules - shortcuts 1 (7:15)
Derivative rules - shortcuts 2 (12:32)
Implicit VS Explicit functions - chain rule - water pipe example (14:07)
Derivative rules - BIG exercise (14:59)
Trigonometric function derivatives - how to take them 1 (11:15)
Trigonometric function derivatives - how to take them 2 (9:38)
Minimize the material used to produce a can - how to apply derivatives 1 (14:20)
Minimize the material used to produce a can - how to apply derivatives 2 (9:01)
Minimize the material used to produce a can - how to apply derivatives 3 (16:39)
Exponential functions - what are they - how to manipulate them (10:08)
Logarithmic functions & log scale - what are they & derivatives (13:25)
Maximize your profit - how to apply derivatives for that (14:09)
Motion of a Projectile (The Crazy Motorcyclist)
Motion of a Projectile (The Crazy Motorcyclist) - Solution
Practice your derivative intuition - exercises
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