INTUITION MATTERS! - Applied Calculus for Engineers-Complete
4.4 (226 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,091 students enrolled

INTUITION MATTERS! - Applied Calculus for Engineers-Complete

Calculus + Engineering + PID: Functions, Limits, Derivatives, Vectors, differential equations, integrals: BEST CALCULUS
4.4 (226 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,091 students enrolled
Created by Mark Misin
Last updated 7/2020
English
English [Auto]
Current price: $139.99 Original price: $199.99 Discount: 30% off
5 hours left at this price!
30-Day Money-Back Guarantee
This course includes
  • 35 hours on-demand video
  • 3 articles
  • 3 downloadable resources
  • Full lifetime access
  • Access on mobile and TV
  • Assignments
  • Certificate of Completion
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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:

  1. Single variable functions

  2. Trigonometric functions

  3. Multidimensional functions

  4. Limits

  5. Derivatives - single variable

  6. Vectors

  7. Transformations

  8. Parametric Equations

  9. Multivariable Calculus

  10. Single variable integrals

  11. Multivariable integrals

  12. Calculus in Control Engineering (PID controller & magnetic train simulation)

  13. Introduction to Differential Equations

  14. 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
Course content
Expand all 223 lectures 34:58:06
+ Single variable functions
29 lectures 03:26:19
The Simulation Python codes
01:23
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 - 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
+ Trigonometric functions
18 lectures 01:53:05
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
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
3 lectures 33:06
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
09:16
What is a function and what is not - multidimensional functions
11:08
+ Limits
9 lectures 01:11:34
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
23 lectures 04:17:07
SIM: Earth, Mars, Moon - solution
03:46
Derivatives - What are they - multidimensional point of view
07:33
Practice your derivative intuition - exercises
10:53
In this assignment, you need to prove that the derivative of sin(theta) with respect to theta equals cos(theta) using the formal definition of a derivative.
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
Welcome! :) I would like to give you a small challenge to solve. This assignment will cover the first 5 sections.
Motion of a Projectile (The Crazy Motorcyclist)
4 questions
+ Vectors
28 lectures 03:58:00
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
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
00:51
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
+ Transformations
6 lectures 44:29
3D Cartesian VS Cylindrical VS Spherical coordinate systems - what are they
07:37
Apply 3 dimensional coordinate systems - when to use what
07:08
Going from Polar to Cartesian
06:15
Going from Cartesian to Polar
03:20
Going between 3 dimensional coordinate systems - how to switch between them
09:47
+ Parametric Equations
29 lectures 04:39:42
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
MEGA Application - Python simulation of different 3D spiral trajectories
07:57
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 - 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 arm's 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
This is an imagination exercise! You have your initial spiral. You have 5 questions. After each question, the shape of the spiral changes. Here is the important thing. When you move to the next question, then you have to take the spiral that you got from your previous question and start from there.
Spiral - Final shape
1 question
+ Multivariable Calculus
19 lectures 04:33:49
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 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
19 lectures 04:40:18
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
In this project, after having completed the integral section, you have to compute the length of the spiral trajectory in meters as time goes from 0 to 10 seconds.
Spiral trajectory length
1 question