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Students - University students of Science and Engineering will practically improve their intuitive understanding of Calculus concepts
- You’ll learn to apply Calculus concepts in real-life situations, and start making more sense of what you’ve already learned about Calculus at university or college (your studies will become much easier and clearer from now on!)
- If you’re already using Calculus as a scientist or engineer, you’ll be able to apply it better in your work after filling the gaps you might have, so you can accelerate your successful career
- You’ll get a solid mathematical basis that you can use anywhere in your work or studies

32h 8m

02:31

3:23:16

Abstract World VS Real World part 1

06:23

Abstract World VS Real World part 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?

01:04

SIM: Car race exercise - who will win the race - SOLUTION

02:46

What is a function, what is not part 1

08:53

What is a function, what is not part 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 part 1

11:00

Quadratic function roots - How to get them part 2

07:55

Which terms dominate in functions

07:23

SIM: 3 airplane race - who wins, and when?

01:19

1:49:21

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

04:43

Abstract VS Real - Aerospace Engineering example

13:41

SIM: Avoid the crash - exercise

00:00

SIM: Avoid the crash - solution 1

01:49

SIM: Avoid the crash - solution 2

04:35

SIM: Avoid the crash - solution 3

02:54

SIM: Avoid the crash - solution 4

06:42

SIM: Avoid the crash - solution 5

05:16

SIM: Avoid the crash - solution 6

01:57

SIM: Avoid the crash - solution 7

03:56

SIM: Avoid the crash - solution 8

01:08

SIM: Avoid the crash - solution 9

04:57

SIM: Avoid the crash - solution 10

01:01

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

1:11:35

Variable equaling VS approaching something - what's 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

Limit approaching 0

03:05

Sin limit

06:04

4:17:08

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

Earth, Mars, Moon - acceleration exercise

03:28

Earth, Mars, Moon - acceleration 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 part 1

07:15

Derivative rules - shortcuts part 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 part 1

11:15

Trigonometric function derivatives - how to take them part 2

09:38

Minimize the material used to produce a can - how to apply derivatives part 1

14:20

Minimize the material used to produce a can - how to apply derivatives part 2

09:01

Minimize the material used to produce a can - how to apply derivatives part 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

4:17:12

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 (Corrected)

05:34

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 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

51:28

2D Cartesian VS Polar coordinate systems - what are they

10:22

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

4:39:48

Intro into Parametric Equations - Intuition

07:32

MEGA Application - Landing Airplane in 2D

07:03

SIM: MEGA Application - Landing airplane

03:23

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 - Sinusoidal trajectory airplane

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 - Spiral 1

02:45

SIM: MEGA Application - Spiral 2

01:35

SIM: MEGA Application - Spiral 3

03:07

SIM: MEGA Application - Spiral 4

02:39

SIM: MEGA Application - Spiral 5

01:15

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 arm's trajectory

07:29

SIM: MEGA Application - Robot 1

04:28

SIM: MEGA Application - Robot 2

03:24

3D Rotational matrix - how to derive it part 1

18:19

3D Rotational matrix - how to derive it part 2

11:05

3D Rotational matrix - how to derive it part 3

12:50

4:33:49

Implicit functions - what are they and how to graph them

13:22

Implicit function derivatives - how to take them

11:42

Expanding function dimensions part 1

06:40

Expanding function dimensions part 2

06:28

Machine Learning example - how to apply multidimensionality

16:50

Partial derivatives - intro part 1

15:06

Partial derivatives - intro part 2

14:51

Partial derivatives - intro part 3

13:47

Higher dimensional partial derivatives & its graph

12:57

Airplane example - Chain rule in parametric equations - partial derivatives part 1

06:37

Airplane example - Chain rule in parametric equations - partial derivatives part 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 part 1

16:57

Taylor Series - what is it and how to formulate it part 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

4:40:18

Discrete VS Continuous functions - what's the difference

10:44

Intro to Integrals - The area of the wall calculation part 1

10:30

Intro to Integrals - The area of the wall calculation part 2

14:36

Integrals - what's the meaning of it part 1

11:56

Integrals - what's the meaning of it part 2

13:10

Integrals - what's the meaning of it part 3

13:42

Integrals - what's the meaning of it part 4

17:47

Indefinite Integrals VS Definite Integrals - what's the difference

15:02

Definite Integrals - Area of the wall calculation part 1

22:04

Definite Integrals - Area of the wall calculation part 2

12:40

Improper Integrals - made intuitive

20:42

Definite Integrals - formal definition

20:41

Area of a circle & initial conditions - integrals applied lecture

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 part 1

16:19

Curve length calculation - integrals applied part 2

10:26

Spiral length calculation in 3D - integrals applied

12:31

1:14:36

Multivariable integrals - intuition part 1

16:55

Multivariable integrals - intuition part 2

17:31

Multivariable integrals - intuition part 3

09:54

Triple Integrals - intuition

07:50

Quadruple Integrals - intuition

06:26

Mass calculation with varying density - applied tripple integrals

16:00

28:51

Differential Equations - intuition & different representations part 1

16:09

Differential Equations - intuition & different representations part 2

12:42

05:45

Wave representation in time & frequency domain

05:45

I want to help you master Calculus for engineers. There are two ways to learn Calculus: you can memorize all of its functions and actions that you can do with it, or you can understand it from the essence. The first method provides you with the knowledge that will dissipate once you stop using it. The second method will equip you with an ability to apply the potential of Calculus for engineers, even in situations that you haven’t learned anywhere. Because you will know how it works, so you’ll never forget how you may benefit from it in any given situation. My goal is to prepare you as a master of Calculus who understands it thoroughly and then can use it intuitively. Does it sound good? Then join in, and let’s get down to learning stuff!

First and foremost, I can’t stress enough how important it is to understand Calculus for engineers. So, once again, in this Calculus online course, you’re going to focus on the essence of it, and not just memorize a set of functions. I know there are many online courses you can choose from, and the delivery of information will vary greatly. My promise is that I can make Calculus a second nature for you. This Calculus online course is going to be both informative and practical – and fun.

I’ve used my Python skills to develop many simulations to back up my explanations. I’ve invested a lot of my time to bring a fantastic added visual value for my students. You know why? Because it’s fun! It’s fun to see how maths work. I can guarantee that no other course on Calculus does that. I’m sure it will aid you in your quest to learn Calculus easily to the level of using it intuitively. I’m an Aerospace & Robotics engineer, and in my exciting and long career, I’ve witnessed that in science and engineering, everything is based on Calculus. So I hope my experience will help you a lot!

In my lectures, I’ll often start with a practical problem or question. I’ll test your thinking by asking you to solve the problem (with a paused video), and then we’ll carry on together to see my way of addressing those multiple problems. There’s a lot of value in getting stuck with a task, so I strongly encourage you to pause the video and do stuff on your own. That’s how I approach teaching, guys.

Among a massive number of topics that we’re going to cover (after all, it’s going to be a 31+ hours Calculus online course), I think the most valuable things that you’ll learn are these:

- I’ll help you to improve your understanding of Calculus drastically. Yes, we’ll work on vector Calculus and Multivariable Calculus, but eventually, these topics will blend to achieve this primary goal.
- You’ll learn Calculus easily and apply it in real-life situations. This Calculus for engineers course will help you understand all the other input that you’ve received on Calculus before.
- I want you to experience as few Calculus limits as possible. We’ll work on filling the gaps you might have from your work with Calculus if you’ve already been using vector Calculus, multivariable Calculus, but haven’t experienced its full potential.
- Also, I’ll guide you to learn Calculus easily for designing a PID controller. I’ll explain what PID is and all the backstage information about it. Plus, I’ll share the code.

So, lots and lots of benefits – you only need to be hungry enough to devour everything this Calculus online course has to offer!

You’ll be trained to apply Calculus in real life to a level not seen in other courses. You’ll find out about Calculus limits, however few, too, so you can genuinely make use of it in any situation. Let’s get started: learn Calculus easily!

- Basic understanding in algebra
- Willingness to learn and experiment

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Mark Misin is an Aerospace & Robotics Engineer with a broad scope of interest. He’s set on a mission to elevate humanity’s knowledge, skills, and general love for science and engineering. How does he do it?

Mark firmly believes that online education has an enormous potential to reach many people on Earth because it’s easily scalable. In such way, quality education is becoming affordable and accessible to numbers hardly ever imagined. Mark believes that great teachers can change the lives of millions of people. Learners get the opportunity to stay out of poverty and create a better living environment for themselves.

On BitDegree, Mark Misin is offering a chance to get a comprehensive course of Applied Calculus for Engineering. Mark’s approach is to develop students’ skills to such a level when they can understand Calculus intuitively and learn to apply it. His course should drastically improve your intuitive understanding of the concepts of Calculus.

Mark Misin’s teaching approach is of benefit to many different professionals or college students as he presents essential information in a more simplified way. He focuses on applying Calculus at realistic work, which helps to accelerate students’ success making careers in the real world. Join in to improve your general mathematical, engineering skills, and tap into a wealth of practical case studies offered by Mark!

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