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INTUITION MATTERS! Applied Calculus for Engineers - Part 1

Calculus + Engineering: Functions, Trigonometry, Limits, Derivatives: BEST CALCULUS

Instructed by Mark Misin

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  • You will develop very strong intuition & understanding in functions, limits and derivatives. You will learn how to apply Calculus in real life to the level not seen in other courses.

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!

These are the topics that the course covers:

  1. Single variable functions

  2. Trigonometric functions

  3. Multidimensional functions

  4. Limits

  5. Derivatives - single variable

I wish you good luck in learning!

Mark

  • basic algebra
  • Science and Engineering students, working scientists and engineers
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Section 1 : Single variable functions

  • Lecture 1 :
  • Functions - what are they - high school review 1 Preview
  • Lecture 2 :
  • Functions - what are they - high school review 2
  • Lecture 3 :
  • SIM: Straight line functions in motion
  • Lecture 4 :
  • Practice functions - airplane homework
  • Lecture 5 :
  • Abstract World VS Real World - 1
  • Lecture 6 :
  • Abstract World VS Real World - 2
  • Lecture 7 :
  • Straight line functions - How to manipulate them
  • Lecture 8 :
  • Inverse functions - what are they and how to find them
  • Lecture 9 :
  • Find inverse functions - example
  • Lecture 10 :
  • Parabolic functions - How to manipulate them
  • Lecture 11 :
  • Cubic functions - How to manipulate them
  • Lecture 12 :
  • SIM: Car race exercise - who will win the race?
  • Lecture 13 :
  • SIM: Car race exercise - who will win the race - SOLUTION
  • Lecture 14 :
  • What is a function, what is not - 1
  • Lecture 15 :
  • What is a function, what is not - 2
  • Lecture 16 :
  • Inverse function of a parabola - how to find it
  • Lecture 17 :
  • Inverse function of a cubic function- how to find it
  • Lecture 18 :
  • SIM: General functions in motion
  • Lecture 19 :
  • How to shift functions
  • Lecture 20 :
  • Practice function operations
  • Lecture 21 :
  • Quadratic function roots - How to get them 2
  • Lecture 22 :
  • Which terms dominate in functions
  • Lecture 23 :
  • SIM: 3 airplane race - who wins, and when?
  • Lecture 24 :
  • Quadratic function roots - How to get them 1
  • Lecture 25 :
  • How to do function operations
  • Lecture 26 :
  • Piecewise defined functions - how to form them
  • Lecture 27 :
  • Functions in general form - how to manipulate them
  • Lecture 28 :
  • Code Linux Installation Vehicle
  • Lecture 29 :
  • Code Windows Installation Vehicle

Section 2 : Trigonometric functions

  • Lecture 1 :
  • Pi number and circumference of a circle - what are they and how to get them
  • Lecture 2 :
  • Radians VS Degrees & how to get the arc length of a circle
  • Lecture 3 :
  • Sine function - where does it come from
  • Lecture 4 :
  • Cosine and tangent function - where do they come from
  • Lecture 5 :
  • Inverse of trigonometric functions - how to get them
  • Lecture 6 :
  • Practice trigonometric functions - exercises
  • Lecture 7 :
  • Abstract VS Real - Aerospace Engineering example
  • Lecture 8 :
  • SIM: Avoid the crash - exercise
  • Lecture 9 :
  • SIM: Avoid the crash - solution 1
  • Lecture 10 :
  • SIM: Avoid the crash - solution 2
  • Lecture 11 :
  • SIM: Avoid the crash - solution 3
  • Lecture 12 :
  • SIM: Avoid the crash - solution 4
  • Lecture 13 :
  • SIM: Avoid the crash - solution 5
  • Lecture 14 :
  • SIM: Avoid the crash - solution 6
  • Lecture 15 :
  • SIM: Avoid the crash - solution 7
  • Lecture 16 :
  • SIM: Avoid the crash - solution 8
  • Lecture 17 :
  • SIM: Avoid the crash - solution 9
  • Lecture 18 :
  • SIM: Avoid the crash - solution 10

Section 3 : Multidimensional functions

  • Lecture 1 :
  • 2 variable function - how to apply it to a simple airplane example
  • Lecture 2 :
  • 3 variable function - how to apply it to a simple airplane example
  • Lecture 3 :
  • What is a function and what is not - multidimensional functions

Section 4 : Limits

  • Lecture 1 :
  • Variable equaling VS approaching something - what's the difference
  • Lecture 2 :
  • Variable approaching infinity - what happens
  • Lecture 3 :
  • Smart financial decision using limits - how to do it
  • Lecture 4 :
  • Manipulate trigonometric functions in different ways - how
  • Lecture 5 :
  • Model a wave with a trigonometric function - how
  • Lecture 6 :
  • Get from a sine to a cosine function - exercise
  • Lecture 7 :
  • Practice limits on a trigonometric function - does the limit exist?
  • Lecture 8 :
  • SIM: Limit simulation
  • Lecture 9 :
  • SIM: sin_limit simulation

Section 5 : Derivatives - single variable

  • Lecture 1 :
  • Derivatives - what are they - falling sphere example 1
  • Lecture 2 :
  • Derivatives - what are they - falling sphere example 2
  • Lecture 3 :
  • Derivatives - what are they - falling sphere example 3
  • Lecture 4 :
  • SIM: Earth, Mars, Moon - exercise
  • Lecture 5 :
  • SIM: Earth, Mars, Moon - solution
  • Lecture 6 :
  • Derivatives - What are they - multidimensional point of view
  • Lecture 7 :
  • Practice your derivative intuition - exercises
  • Lecture 8 :
  • Chain rule - how to apply it to a multi link problem - water pipe example 1
  • Lecture 9 :
  • Chain rule - how to apply it to a multi link problem - water pipe example 2
  • Lecture 10 :
  • Differential operators - What are they and how to apply them
  • Lecture 11 :
  • Multilevel derivatives - double, triple, quadruple
  • Lecture 12 :
  • Derivative rules - shortcuts 1
  • Lecture 13 :
  • Derivative rules - shortcuts 2
  • Lecture 14 :
  • Implicit VS Explicit functions - chain rule - water pipe example
  • Lecture 15 :
  • Derivative rules - BIG exercise
  • Lecture 16 :
  • Trigonometric function derivatives - how to take them 1
  • Lecture 17 :
  • Trigonometric function derivatives - how to take them 2
  • Lecture 18 :
  • Minimize the material used to produce a can - how to apply derivatives 1
  • Lecture 19 :
  • Minimize the material used to produce a can - how to apply derivatives 2
  • Lecture 20 :
  • Minimize the material used to produce a can - how to apply derivatives 3
  • Lecture 21 :
  • Exponential functions - what are they - how to manipulate them
  • Lecture 22 :
  • Logarithmic functions & log scale - what are they & derivatives
  • Lecture 23 :
  • Maximize your profit - how to apply derivatives for that
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Mark Misin,

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.
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