INTUITION MATTERS! Applied Calculus in Engineering: Complete

Calculus + Engineering + PID: Functions, Limits, Derivatives, Vectors, differential equations, integrals: BEST CALCULUS

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Mark Misin Engineering Ltd

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33.5 giờ video

230 bài giảng

1 bài quiz

Truy cập vĩnh viễn

Học trên mọi thiết bị

Cập nhật: 07/06/2026

#Applied Mathematics #Calculus #Engineering Calculus #Python

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You will develop very strong intuition & understanding in Calculus

You will also receive very strong training in problem solving in Calculus

You will learn how to apply Calculus in real life to the level not seen in other courses

You will see how to apply Calculus in control systems by designing a PID controller

Yêu cầu

Addition, Subtraction, Multiplication, Division

very basic algebra

Đối tượng phù hợp

Science and Engineering students

Working Scientists and Engineers

Nội dung khóa học

15 phần • 230 bài giảng

1 Functions - what are they - high school review 1

2 Functions - what are they - high school review 2

3 SIM: Straight line functions in motion

4 Practice functions - airplane homework

5 Abstract World VS Real World - 1

6 Abstract World VS Real World - 2

7 Straight line functions - How to manipulate them

8 Inverse functions - what are they and how to find them

9 Find inverse functions - example

10 Parabolic functions - How to manipulate them

11 Cubic functions - How to manipulate them

12 SIM: Car race exercise - who will win the race?

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

14 What is a function, what is not - 1

15 What is a function, what is not - 2

16 Inverse function of a parabola - how to find it

17 Inverse function of a cubic function- how to find it

18 Functions in general form - how to manipulate them

19 SIM: General functions in motion

20 Piecewise defined functions - how to form them

21 How to shift functions

22 How to do function operations

23 Practice function operations

24 Quadratic function roots - How to get them 1

25 Quadratic function roots - How to get them 2

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

27 Follow-up

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

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

3 Sine function - where does it come from

4 Cosine and tangent function - where do they come from

5 Inverse of trigonometric functions - how to get them

6 Practice trigonometric functions - exercises

7 Abstract VS Real - Aerospace Engineering example

8 SIM: Avoid the crash - exercise

9 SIM: Avoid the crash - solution 1

10 SIM: Avoid the crash - solution 2

11 SIM: Avoid the crash - solution 3

12 SIM: Avoid the crash - solution 4

13 SIM: Avoid the crash - solution 5

14 SIM: Avoid the crash - solution 6

15 SIM: Avoid the crash - solution 7

16 SIM: Avoid the crash - solution 8

17 SIM: Avoid the crash - solution 9

18 SIM: Avoid the crash - solution 10

1 2 variable function - how to apply it to a simple airplane example

2 3 variable function - how to apply it to a simple airplane example

3 What is a function and what is not - multidimensional functions

1 Variable equaling VS approaching something - what's the difference

2 Variable approaching infinity - what happens

3 Smart financial decision using limits - how to do it

4 Manipulate trigonometric functions in different ways - how

5 Model a wave with a trigonometric function - how

6 Get from a sine to a cosine function - exercise

7 Practice limits on a trigonometric function - does the limit exist?

8 SIM: Limit simulation

9 SIM: sin_limit simulation

1 Derivatives - what are they - falling sphere example 1

2 Where does the the equation Hi-5*t^2 come from?

3 Derivatives - what are they - falling sphere example 2

4 Derivatives - what are they - falling sphere example 3

5 SIM: Earth, Mars, Moon - exercise

6 SIM: Earth, Mars, Moon - solution

7 Practice your derivative intuition - exercises

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

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

10 Differential operators - What are they and how to apply them

11 Multilevel derivatives - double, triple, quadruple

12 Derivative rules - shortcuts 1

13 Derivative rules - shortcuts 2

14 Implicit VS Explicit functions - chain rule - water pipe example

15 Derivative rules - BIG exercise

16 Trigonometric function derivatives - how to take them 1

17 Trigonometric function derivatives - how to take them 2

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

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

20 Minimize the material used to produce a can - how to apply derivatives 3

21 Exponential functions - what are they - how to manipulate them

22 Logarithmic functions & log scale - what are they & derivatives

23 Maximize your profit - how to apply derivatives for that

24 Practice trigonometry with this free online game

1 Vectors in 2 dimensions - what are they

2 Vectors in multiple dimensions - what are they

3 Vector terminology and disclaimers

4 Vector magnitude - what is it

5 Vector components - exercise

6 Vector operations - how do they work

7 Apply the dot product - Forces on a box example

8 Cross product intuition- what is it

9 Cross product - how to calculate it

10 Apply the cross product - electron and magnetic field example

11 MEGA Application - Water tank example 1

12 MEGA Application - Water tank example 2

13 MEGA Application - Water tank example 3

14 CORRECTION: MEGA Application - Water tank example 3

15 MEGA Application - Water tank example 4

16 CORRECTION: MEGA Application - Water tank example 4

17 MEGA Application - Water tank example 5

18 SIM: MEGA Application - Water tank example - Complete

19 MEGA Application - Water tank example - exercise 1

20 MEGA Application - Water tank example - exercise 2

21 SIM: MEGA Application - Water tank example - exercise

22 MEGA Application - Water tank mass flow- use derivatives to get it

23 Distance VS Position vectors - what's the difference

24 Displacement VS Velocity VS Acceleration vectors - what's the difference

25 Average displacement, velocity, and acceleration vectors - clarification

26 Graph Displacement, Velocity, & Acceleration vectors

27 Acceleration vector - intuition

28 Vector derivatives - how do they work

1 2D Cartesian VS Polar coordinate systems - what are they

2 3D Cartesian VS Cylindrical VS Spherical coordinate systems - what are they

3 Apply 3 dimensional coordinate systems - when to use what

4 Going from Polar to Cartesian

5 Going from Cartesian to Polar

6 Going between 3 dimensional coordinate systems - how to switch between them

1 Intro into Parametric Equations - Intuition

2 MEGA Application - Landing Airplane in 2D

3 SIM: MEGA Application: Landing simulation

4 MEGA Application - Airplane flying in an oscillatory way (in 2D)

5 MEGA Application - Airplane's velocity and acceleration in 2D

6 SIM: MEGA Application - Sin trajectory simulation

7 MEGA Application - Airplane doing circles in 2D - Cartesian & Polar coordinates

8 MEGA Application - Airplane doing circles in 2D - Velocity & Acceleration

9 SIM: MEGA Application - Circle simulation

10 MEGA Application - Airplane flying in a spiral in 3D

11 SIM: MEGA Application - 3D trajectories - simulation 1

12 SIM: MEGA Application - 3D trajectories - simulation 2

13 SIM: MEGA Application - 3D trajectories - simulation 3

14 SIM: MEGA Application - 3D trajectories - simulation 4

15 SIM: MEGA Application - 3D trajectories - simulation 5

16 MEGA Application - 2 joint robot - Angular position & velocity

17 MEGA Application - 2 joint robot - 2 joints rotating simultaneously

18 MEGA Application - 2 joint robot - assigning multiple reference frames

19 MEGA Application - 2 joint robot - describing a point in two different frames

20 MEGA Application - 2 joint robot - deriving a 2D rotational matrix

21 MEGA Application - 2 joint robot - describing rotating and translating joints

22 MEGA Application - 2 joint robot - joints rotating at different frequencies

23 SIM: MEGA Application - 2 joint robot - simulation 1

24 SIM: MEGA Application - 2 joint robot - simulation 2

25 3D Rotational matrix - how to derive it 1

26 3D Rotational matrix - how to derive it 2

27 3D Rotational matrix - how to derive it 3

1 Implicit functions - what are they and how to graph them

2 Implicit function derivatives - how to take them

3 Expanding function dimensions 1

4 Expanding function dimensions 2

5 Machine Learning example - how to apply multidimensionality

6 Partial derivatives - intro 1

7 Partial derivatives - intro 2

8 Partial derivatives - intro 3

9 Higher dimensional partial derivatives & its graph

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

11 Airplane example - Chain rule in parametric equations - partial derivatives 2

12 Multilevel partial derivatives - how to take them

13 Gradient - what is it and how to find it

14 Neural Networks + Calculus (Article recommendation)

15 Taylor Series - what is it and how to formulate it 1

16 Taylor Series - what is it and how to formulate it 2

17 Linearization and Quadratic Approximation - what is it and how to do it

18 Multidimensional linearization - practical exercise

19 Multidimensional quadratic approximation - Hessian Matrix

20 Representing a system mathematically, in vector-matrix form, and block diagrams

1 Discrete VS Continuous functions - what's the difference

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

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

4 Integrals - what's the meaning of it 1

5 Integrals - what's the meaning of it 2

6 Integrals - what's the meaning of it 3

7 Integrals - what's the meaning of it 4

8 Indefinite Integrals VS Definite Integrals - what's the difference

9 Definite Integrals - Area of the wall calculation 1

10 Definite Integrals - Area of the wall calculation 2

11 Improper Integrals - made intuitive

12 Definite Integrals - formal definition

13 Area of a circle & initial conditions - integrals applied

14 Area of a circle - 2nd approach - integrals applied

15 Volume of a solid - integrals applied

16 Integration by parts - where it comes from and how to apply it

17 Curve length calculation - integrals applied 1

18 Curve length calculation - integrals applied 2

19 Tính toán chiều dài đường xoắn ốc trong không gian 3D - ứng dụng tích phân

1 Tích phân nhiều biến - trực quan 1

2 Tích phân nhiều biến - trực quan 2

3 Tích phân nhiều biến - trực quan 3

4 Tích phân bội ba - trực quan

5 Tích phân bội bốn - trực quan

6 Tính toán khối lượng với mật độ thay đổi - ứng dụng tích phân bội ba

1 Phương trình Vi phân - trực quan & các cách biểu diễn khác nhau 1

2 Phương trình Vi phân - trực quan & các cách biểu diễn khác nhau 2

3 Biểu diễn sóng trong miền thời gian và miền tần số

1 Nhập môn Điều khiển - cách điều khiển hệ thống bằng bộ điều khiển 1

2 Nhập môn Điều khiển - cách điều khiển hệ thống bằng bộ điều khiển 2

3 Hệ thống Vòng hở VS Vòng kín

4 Điều khiển bể nước trong mô phỏng Python

5 Giới thiệu về bộ điều khiển tỷ lệ (P)

6 Mô hình hóa bể nước 1

7 Mô hình hóa bể nước 2

8 Tích phân số ứng dụng cho mô hình bể nước

9 Kết hợp toán học với cấu trúc điều khiển

10 Mô phỏng bể nước - bộ điều khiển tỷ lệ (P)

11 Giới thiệu về mô phỏng PID

12 PID: Mô hình hóa đoàn tàu với các lực tác dụng 1

13 PID: Mô hình hóa đoàn tàu với các lực tác dụng 2

14 PID: Chuyển từ đầu vào hệ thống sang đầu ra hệ thống bằng tích phân số

15 PID: Mô phỏng tàu từ tính - bộ điều khiển tỷ lệ (P)

16 PID: Giải thích hiện tượng vọt lố của bộ điều khiển tỷ lệ 1

17 PID: Giải thích hiện tượng vọt lố của bộ điều khiển tỷ lệ 2

18 PID: Giải thích hiện tượng vọt lố của bộ điều khiển tỷ lệ 3

19 PID: Giới thiệu về Điều khiển Đạo hàm (D)

20 PID: Hiệu chỉnh bộ điều khiển

21 PID: Bộ điều khiển tỷ lệ & đạo hàm & mô phỏng tàu từ tính trong Python

22 PID: Giới thiệu về Điều khiển Tích phân (I)

23 PID: Mô phỏng tàu từ tính bằng Python trên mặt phẳng nghiêng

24 PID: Mô hình toán học của đoàn tàu trên mặt phẳng nghiêng 1

25 PID: Mô hình toán học của đoàn tàu trên mặt phẳng nghiêng 2

26 PID: Kết hợp Điều khiển Tỷ lệ, Đạo hàm, Tích phân

27 PID: Mô phỏng tàu từ tính (mặt phẳng nghiêng & PID)

28 Giải thích mã lệnh tàu PID 1

29 Giải thích mã lệnh tàu PID 2

30 Giải thích mã lệnh tàu PID 3

31 Giới thiệu ngắn về công cụ tạo hoạt ảnh trong Python

32 PID: Giải thích nhanh mã lệnh & hoạt ảnh (bể nước)

33 Mã lệnh cho bộ điều khiển P & PID (Yêu cầu Python 3, Numpy & Matplotlib)

1 Giới thiệu về (Terminal trên Linux & macOS) & (Command Prompt trên Windows)

2 Hướng dẫn cài đặt Python

3 Cài đặt môi trường Python và các thư viện (Windows 11)

4 Cài đặt môi trường Python và các thư viện (Linux Ubuntu)

5 Cài đặt môi trường Python và các thư viện (macOS)

6 Các mã lệnh mô phỏng bằng Python

1 Bài giảng bổ sung

Giới thiệu khóa học

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!