What you'll learn

You will develop very strong intuition & understanding in Calculus
You will learn how to apply Calculus in real life to the level not seen in other courses

Requirements

Addition, Subtraction, Multiplication, Division
very basic algebra

Description

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
Calculus in Control Engineering (PID controller & magnetic train simulation)
Introduction to Differential Equations
Extra Wisdom - waves in time and frequency domain

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

Good luck!

Who this course is for:

Science and Engineering students
Working Scientists and Engineers

Featured review

Sunil Raj

56 courses

11 reviews

a year ago

I don't leave a 5-star rating before completing a course; This was the course I was searching for months — 35 hours of premium content. Just as I expected, apart from the course, the course instructor is amiable and kind, I will purchase if he creates a few more courses in the future. Top-notch Delivery, People like him could change the old ways of the education system. I recommend this course to everyone.

15 sections • 225 lectures • 35h 21m total length

Preview09:40
Preview10:13
Preview03:26
Preview06:44
Preview06:52
The Simulation Python codes
00:42
Preview09:12
Abstract World VS Real World - 1
Preview05:54
Abstract World VS Real World - 2
Preview05:44
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
Preview01:03
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
Preview02:06

Pi number and circumference of a circle - what are they and how to get them
Preview13:27
Radians VS Degrees & how to get the arc length of a circle
Preview11:39
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
04:43
Abstract VS Real - Aerospace Engineering example
13:41
Preview03:50
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

Variable equaling VS approaching something - what's the difference
Preview12:04
Variable approaching infinity - what happens
Preview08:02
Smart financial decision using limits - how to do it
Preview11:08
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 - what are they - falling sphere example 1
Preview13:02
Preview00:24
Preview11:05
Preview14:42
Preview03:27
SIM: Earth, Mars, Moon - solution
03:46
Derivatives - What are they - multidimensional point of view
07:33
Practice your derivative intuition - exercises
10:53
Prove that d(sin(theta))/d(theta)=cos(theta)
1 question
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
Motion of a Projectile (The Crazy Motorcyclist)
4 questions

Vectors in 2 dimensions - what are they
Preview09:55
Vectors in multiple dimensions - what are they
15:35
Vector terminology and disclaimers
06:30
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
Preview10:20
Preview06:38
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
01:54
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
00:51
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
01:57
Graph Displacement, Velocity, & Acceleration vectors
08:31
Acceleration vector - intuition
07:42
Vector derivatives - how do they work
02:31

Preview07:32
Preview07:03
SIM: MEGA Application: Landing simulation
03:22
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
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
Preview02:44
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
Preview19:00
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
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
Spiral - Final shape
1 question

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
Preview15:06
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

Discrete VS Continuous functions - what's the difference
Preview10:44
Intro to Integrals - The area of the wall calculation 1
Preview10:30
Intro to Integrals - The area of the wall calculation 2
Preview14:36
Integrals - what's the meaning of it 1
11:56
Integrals - what's the meaning of it 2
13:10
Integrals - what's the meaning of it 3
13:42
Integrals - what's the meaning of it 4
17:47
Indefinite Integrals VS Definite Integrals - what's 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
Spiral trajectory length
1 question

Mark Misin

Aerospace & Robotics Engineer

4.5 Instructor Rating
437 Reviews
3,512 Students
3 Courses

The Mission: to elevate humanity's knowledge, skills and love for science & engineering

I think that online education is the future because of one single fact - it is easily scalable. One course of a single great teacher can reach millions of people and potentially transform their lives. If education is more scalable, it will be more affordable. More affordable and accessible education will give more people an opportunity to stay out of poverty and create a great life for themselves.

I am here to contribute to this movement.

This course includes:

INTUITION MATTERS! - Applied Calculus for Engineers-Complete

What you'll learn

Requirements

Description

Who this course is for:

Featured review

Course content

Instructor

This course includes:

INTUITION MATTERS! - Applied Calculus for Engineers-Complete

What you'll learn

Requirements

Description

Who this course is for:

Featured review

Course content

Single variable functions31 lectures • 3hr 39min

Trigonometric functions18 lectures • 1hr 53min

Multidimensional functions3 lectures • 33min

Limits9 lectures • 1hr 12min

Derivatives - single variable24 lectures • 4hr 18min

Vectors28 lectures • 3hr 58min

Transformations6 lectures • 44min

Parametric Equations27 lectures • 4hr 24min

Multivariable Calculus19 lectures • 4hr 34min

Single variable integrals19 lectures • 4hr 40min

Instructor