INTUITION MATTERS! Applied Calculus in Engineering: Complete

About Course

I have NEVER believed in simply memorizing things. Your greatest asset in life is time. If you study something, you invest your time in it. If you memorize it, soon you will forget it – that is not a great investment. But if you truly understand something, that stays with you for good – it can serve you for a long time.

This course will give you strong intuition and understanding in Calculus, and you will be trained to apply it in real life. It will stay in your head for good – this is a GREAT investment! Watch some of my free preview videos, enroll in my course, and I will make Calculus second nature to you – that is a promise!

These are the topics that the course covers:

Single variable functions
Trigonometric functions
Multidimensional functions
Limits
Derivatives – single variable
Vectors
Transformations
Parametric Equations
Multivariable Calculus
Single variable integrals
Multivariable integrals
Introduction to Differential Equations & waves in time and frequency domain
Calculus in Control Engineering (PID controller & magnetic train simulation)

Most sections contain a small number of free preview videos for you to check out.

The great thing about this course is that it prepares you for pretty much all the other Engineering and Science courses, because Calculus is the basis of everything in this world.

Good luck!

Course Content

Single variable functions

Functions – what are they – high school review 1

09:40
Functions – what are they – high school review 2

10:15
SIM Straight line functions in motion

03:31
Practice functions – airplane homework

09:12
Abstract World VS Real World – 1

05:54
Abstract World VS Real World – 2

05:44
Straight line functions – How to manipulate them

10:32
Inverse functions – what are they and how to find them

08:05
Find inverse functions – example

05:15
Parabolic functions – How to manipulate them

12:26
Cubic functions – How to manipulate them

06:13
SIM Car race exercise – who will win the race

01:03
SIM Car race exercise – who will win the race – SOLUTION

02:46
What is a function what is not – 1

08:53
What is a function what is not – 2

06:25
Inverse function of a parabola – how to find it

06:09
Inverse function of a cubic function- how to find it

07:01
Functions in general form – how to manipulate them

10:49
SIM General functions in motion

05:39
Piecewise defined functions – how to form them

10:27
How to shift functions

08:35
How to do function operations

12:07
Practice function operations

08:34
Quadratic function roots – How to get them 1

11:00
Quadratic function roots – How to get them 2

07:55
Which terms dominate in functions

07:23
SIM 3 airplane race – who wins and when

01:19
Follow-up

02:06
Follow-up

02:06
Course Material Download Link

00:00

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

08:14
Inverse of trigonometric functions – how to get them

10:28
Practice trigonometric functions – exercises

04:04
SIM Avoid the crash – exercise

03:50
SIM Avoid the crash – solution 1

01:48
SIM Avoid the crash – solution 2

04:35
SIM Avoid the crash – solution 3

02:53
SIM Avoid the crash – solution 4

06:41
SIM Avoid the crash – solution 5

05:15
SIM Avoid the crash – solution 6

01:56
SIM Avoid the crash – solution 7

03:56
SIM Avoid the crash – solution 8

01:08
SIM Avoid the crash – solution 9

04:56
SIM Avoid the crash – solution 10

01:01

Multidimensional functions

Limits

Variable equaling VS approaching something – whats the difference

12:04
Variable approaching infinity – what happens

08:02
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

03:16
Practice limits on a trigonometric function – does the limit exist

04:34
SIM Limit simulation

03:05
SIM sin_limit simulation

06:03

Derivatives – single variable

Derivatives – what are they – falling sphere example 1

13:02
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

03:27
SIM Earth Mars Moon – solution

03:46
Derivatives – What are they – multidimensional point of view

07:33
Practice your derivative intuition – exercises

10:53
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

07:35
Derivative rules – shortcuts 1

07:15
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

09:38
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

09:01
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

Vectors

Vectors in 2 dimensions – what are they

09:55
Vectors in multiple dimensions – what are they

15:35
Vector terminology and disclaimers

06:30
Vector independence – intuition

10:27
Dot product – what is it and how to use it to prove vector independence

10:41
Vector magnitude – what is it

11:38
Vector components – exercise

06:07
Vector operations – how do they work

04:45
Apply the dot product – Forces on a box example

06:50
Cross product intuition- what is it

07:18
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

06:38
MEGA Application – Water tank example 2

09:47
MEGA Application – Water tank example 3

11:23
CORRECTION MEGA Application – Water tank example 3

05:01
MEGA Application – Water tank example 4

12:33
CORRECTION MEGA Application – Water tank example 4

02:25
MEGA Application – Water tank example 5

05:33
SIM MEGA Application – Water tank example – Complete

02:09
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

00:50
MEGA Application – Water tank massflow- use derivatives to get it

15:57
Distance VS Position vectors – whats the difference

16:14
Displacement VS Velocity VS Acceleration vectors – whats the difference

14:29
Graph Displacement Velocity Acceleration vectors

08:31
Acceleration vector – intuition

07:42
Vector derivatives – how do they work

02:31

Transformations

Parametric Equations

Intro into Parametric Equations – Intuition

07:32
MEGA Application – Landing Airplane in 2D

07:03
SIM MEGA Application Landing simulation

03:22
MEGA Application – Airplane flying in an oscillatory way (in 2D)

11:25
MEGA Application – Airplanes velocity and acceleration in 2D

18:09
SIM MEGA Application – Sin trajectory simulation

05:31
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

07:28
MEGA Application – Airplane flying in a spiral in 3D

14:47
MEGA Application – Python simulation of different 3D spiral trajectories

07:57
SIM MEGA Application – 3D trajectories – simulation 1

02:44
SIM MEGA Application – 3D trajectories – simulation 2

01:35
SIM MEGA Application – 3D trajectories – simulation 3

03:06
SIM MEGA Application – 3D trajectories – simulation 4

02:38
SIM MEGA Application – 3D trajectories – simulation 5

01:14
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

08:43
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

09:26
MEGA Application – 2 joint robot – Python simulation of the arms trajectory

07:29
SIM MEGA Application – 2 joint robot – simulation 1

04:27
SIM MEGA Application – 2 joint robot – simulation 2

03:24
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

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

06:40
Expanding function dimensions 2

06:28
Machine Learning example – how to apply multidimensionality

16:50
Partial derivatives – intro 1

15:06
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

06:37
Airplane example – Chain rule in parametric equations – partial derivatives 2

09:46
Multilevel partial derivatives – how to take them

15:17
Gradient – what is it and how to find it

07:33
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

Single variable integrals

Discrete VS Continuous functions – whats the difference

10:44
Intro to Integrals – The area of the wall calculation 1

10:30
Intro to Integrals – The area of the wall calculation 2

14:36
Integrals – whats the meaning of it 1

11:56
Integrals – whats the meaning of it 2

13:10
Integrals – whats the meaning of it 3

13:42
Integrals – whats the meaning of it 4

17:47
Indefinite Integrals VS Definite Integrals – whats the difference

15:02
Definite Integrals – Area of the wall calculation 1

22:04
Definite Integrals – Area of the wall calculation 2

12:40
Improper Integrals – made intuitive

20:42
Definite Integrals – formal definition

20:41
Area of a circle initial conditions – integrals applied

13:29
Area of a circle – 2nd approach – integrals applied

13:58
Volume of a solid – integrals applied

15:58
Integration by parts – where it comes from and how to apply it

14:03
Curve length calculation – integrals applied 1

16:19
Curve length calculation – integrals applied 2

10:26
Spiral length calculation in 3D – integrals applied

12:31

Multivariable integrals

Calculus in Control Engineering – PID controller

Systems controllers – intro 1

07:58
Systems controllers – intro 2

06:53
Systems controllers – intro 3

07:55
SIM Systems controllers – intro 4

02:58
Proportional Controller 1

05:05
Proportional Controller 2

01:51
Proportional Controller 3

13:04
Proportional Controller 4

13:30
Proportional Controller 5

08:37
SIM Proportional Controller 6

02:35
SIM Proportional Controller 7

02:41
PID 1

06:52
PID 2

11:33
PID 3

11:10
PID 4

02:06
PID 5

05:07
PID 6

08:21
PID 7

06:02
PID 8

13:14
PID 9

07:45
PID 10

10:20
PID 11

05:04
PID 12

02:00
PID 13

04:46
PID 14

06:37
PID 15

17:02
PID 16

14:29
PID 17

02:37

Introduction to Differential Equations

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About Course

What Will You Learn?

Course Content

Single variable functions

Functions – what are they – high school review 1

Functions – what are they – high school review 2

SIM Straight line functions in motion

Practice functions – airplane homework

Abstract World VS Real World – 1

Abstract World VS Real World – 2

Straight line functions – How to manipulate them

Inverse functions – what are they and how to find them

Find inverse functions – example

Parabolic functions – How to manipulate them

Cubic functions – How to manipulate them

SIM Car race exercise – who will win the race

SIM Car race exercise – who will win the race – SOLUTION

What is a function what is not – 1

What is a function what is not – 2

Inverse function of a parabola – how to find it

Inverse function of a cubic function- how to find it

Functions in general form – how to manipulate them

SIM General functions in motion

Piecewise defined functions – how to form them

How to shift functions

How to do function operations

Practice function operations

Quadratic function roots – How to get them 1

Quadratic function roots – How to get them 2

Which terms dominate in functions

SIM 3 airplane race – who wins and when

Follow-up

Follow-up

Course Material Download Link

Trigonometric functions

Pi number and circumference of a circle – what are they and how to get them

Radians VS Degrees how to get the arc length of a circle

Sine function – where does it come from

Cosine and tangent function – where do they come from

Inverse of trigonometric functions – how to get them

Practice trigonometric functions – exercises

SIM Avoid the crash – exercise

SIM Avoid the crash – solution 1

SIM Avoid the crash – solution 2

SIM Avoid the crash – solution 3

SIM Avoid the crash – solution 4

SIM Avoid the crash – solution 5

SIM Avoid the crash – solution 6

SIM Avoid the crash – solution 7

SIM Avoid the crash – solution 8

SIM Avoid the crash – solution 9

SIM Avoid the crash – solution 10

Multidimensional functions

2 variable function – how to apply it to a simple airplane example

3 variable function – how to apply it to a simple airplane example

What is a function and what is not – multidimensional functions

Limits

Variable equaling VS approaching something – whats the difference

Variable approaching infinity – what happens

Smart financial decision using limits – how to do it

Manipulate trigonometric functions in different ways – how

Model a wave with a trigonometric function – how

Get from a sine to a cosine function – exercise

Practice limits on a trigonometric function – does the limit exist

SIM Limit simulation

SIM sin_limit simulation

Derivatives – single variable

Derivatives – what are they – falling sphere example 1

Derivatives – what are they – falling sphere example 2

Derivatives – what are they – falling sphere example 3

SIM Earth Mars Moon – exercise

SIM Earth Mars Moon – solution

Derivatives – What are they – multidimensional point of view

Practice your derivative intuition – exercises

chain rule – how to apply it to a multi link problem – water pipe example 1

chain rule – how to apply it to a multi link problem – water pipe example 2

Differential operators – What are they and how to apply them

Multilevel derivatives – double triple quadruple

Derivative rules – shortcuts 1

Derivative rules – shortcuts 2