INTUITION MATTERS! - Applied Calculus for Engineers-Complete
4.5 (62 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.
595 students enrolled

INTUITION MATTERS! - Applied Calculus for Engineers-Complete

If you want to understand Calculus intuitively and have a strong skill in applying it, then this course is for you!
4.5 (62 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.
595 students enrolled
Created by Mark Misin
Last updated 10/2018
English
English [Auto-generated]
Current price: $9.99 Original price: $199.99 Discount: 95% off
30-Day Money-Back Guarantee
This course includes
  • 30.5 hours on-demand video
  • Full lifetime access
  • Access on mobile and TV
  • Assignments
  • Certificate of Completion
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What you'll learn
  • Science and Engineering students will drastically improve their intuitive understanding and the feel for all the hard to understand concepts taught in Calculus at universities. That will simplify their Calculus studies at colleges greatly.
  • Science and Engineering students will also have an advanced skill to apply Calculus concepts to real life situations and in other technical courses that are heavily dependent on Calculus. This course will give a foundation that makes other courses much more understandable, intuitive, and enjoyable for them.

  • For working Scientists and Engineers, this course will course will close any gaps they might have from their university years. After this course, they will be able to better apply Calculus to their work, which can accelerate their success in their careers.

  • People in other careers that also need mathematics (finance, econometrics, math enthusiasts, etc.), this course will give them a very strong mathematical basis that they will benefit from in their work.
Requirements
  • Addition, Subtraction, Multiplication, Division
  • very basic algebra
Description

Dear Students,

Welcome to the course! I am very happy to transfer my knowledge to you.

WHY should you take this course? Fair question!

In Science & Engineering, literally EVERYTHING is based on Calculus. From Mechanical & Aerospace to Electrical & Computer to ARTIFICIAL INTELLIGENCE & MACHINE LEARNING and many more.

If you REALLY understand Calculus and you are trained to APPLY it to REAL LIFE problems, learning and understanding more advanced material will be much EASIER. Your life will be much EASIER!

In my course, I WILL DELIVER just that. I WILL make you understand Calculus INTUITIVELY & in terms of APPLICATION. Just give it a shot!

In the lectures, I will often propose a problem or ask a question and then I will ask you to pause the video and solve the problem yourself. I strongly encourage you to ALWAYS try solving the problem first. If you get stuck, you can unpause the video and see how I had solved that problem. However, there is a BIG difference between going straight to the solution or first trying to solve it yourself, getting stuck, and then going to the solution. In the latter case, your understanding of the concept will be so much greater.

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. Introduction to Differential Equations

  13. 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
  • Any person whose life is connected to numbers (for example: finance, econometrics, math enthusiasts, etc.)
Course content
Expand all 157 lectures 30:20:22
+ Single variable functions
22 lectures 03:08:34
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
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
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
+ Trigonometric functions
7 lectures 01:15:06
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
+ 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
7 lectures 01:02:26
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
+ Derivatives - single variable
21 lectures 04:09:54
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
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
25 lectures 04:10:10
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
MEGA Application - Water tank example 2
09:47
MEGA Application - Water tank example 3
11:23
MEGA Application - Water tank example 4
12:33
MEGA Application - Water tank example 5
08:58
MEGA Application - Water tank example - exercise 1
11:10
MEGA Application - Water tank example - exercise 2
11:11
MEGA Application - Water tank massflow- 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
Graph Displacement, Velocity, & Acceleration vectors
08:31
Acceleration vector - intuition
07:42
Vector derivatives - how do they work
02:31
+ Transformations
5 lectures 51:28
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 Polar to Cartesian and back - how to switch between them
16:34
Going between 3 dimensional coordinate systems - how to switch between them
09:47
+ Parametric Equations
19 lectures 04:04:13
MEGA Application - Airplane flying in an oscillatory way (in 2D)
11:25
MEGA Application - Airplane's velocity and acceleration in 2D
18:09
MEGA Application - Airplane doing circles in 2D - Cartesian & Polar coordinates
16:29
MEGA Application - Airplane doing circles in 2D - Velocity & Acceleration
17:41
MEGA Application - Airplane flying in a spiral in 3D
14:47
MEGA Application - Python simulation of different 3D spiral trajectories
07:57
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
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
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