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    INTUITION MATTERS! Applied Calculus in Engineering: Complete

    BY
    Udemy

    Learn more about the fundamental and advanced strategies associated with applied calculus in control engineering.

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    Mode

    Online

    Fees

    ₹ 2699

    Quick Facts

    particular details
    Medium of instructions English
    Mode of learning Self study
    Mode of Delivery Video and Text Based

    Course overview

    INTUITION MATTERS! Applied Calculus in Engineering: Complete online certification is created by Mark Misin Engineering Ltd, an educational platform that provides courses in math, control systems, python, and mechanics which is presented by Udemy, which is designed for scientists who want to learn more about the benefits of using calculus in control engineering. INTUITION MATTERS! Applied Calculus in Engineering: Complete online course focuses on offering learners a strong understanding and knowledge of Calculus, as well as training them to apply it in real-world situations.

    INTUITION MATTERS! Applied Calculus in Engineering: Complete online training contains more than 33.5 hours of prerecorded video based accompanied by 3 downloadable resources, 6 articles, and assignments that discuss various topics of calculus which include functions, single variable function, multidimensional functions, single variable integrals, multivariate integrals, integral control, parametric equation, differential equation, proportional integral derivatives and more.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 33.5 hours of pre-recorded video content
    • 6 articles 
    • 3 downloadable resources
    • Assignments

    Program offerings

    • Online course
    • Learning resources. 30-day money-back guarantee
    • Unlimited access
    • Accessible on mobile devices and tv

    Course and certificate fees

    Fees information
    ₹ 2,699
    certificate availability

    Yes

    certificate providing authority

    Udemy

    Who it is for

    Scientist It engineer

    What you will learn

    After completing the INTUITION MATTERS! Applied Calculus in Engineering: Complete certification course, learners will gain a solid understanding of the core concepts of calculus and multivariable calculus for orientation involving control engineering. Learners will study the functions of various aspects of calculus, such as vectors, limits, integrals, and derivatives, as well as trigonometric functions, single variable functions, and multidimensional functions. Learners will also study single integrals,  multivariable integrals, differential equations, parametric equations, proportional integral derivatives, and integral control.

    The syllabus

    Single variable functions

    • Functions - what are they - high school review 1
    • Functions - what are they - high school review 2
    • SIM: Straight line functions in motion
    • Intro to (Linux & macOS Terminal) & (Windows Command Prompt)
    • Installing the Python environment and its libraries (Linux Ubuntu)
    • Installing the Python environment and its libraries (Windows 10)
    • Installing the Python environment and its libraries (macOS)
    • The Simulation Python codes
    • Practice functions - airplane homework
    • Abstract World VS Real World - 1
    • Abstract World VS Real World - 2
    • Straight line functions - How to manipulate them
    • Inverse functions - what are they and how to find them
    • Find inverse functions - example
    • Parabolic functions - How to manipulate them
    • Cubic functions - How to manipulate them
    • SIM: Car race exercise - who will win the race?
    • SIM: Car race exercise - who will win the race - SOLUTION
    • What is a function, what is not - 1
    • What is a function, what is not - 2
    • Inverse function of a parabola - how to find it
    • Inverse function of a cubic function- how to find it
    • Functions in general form - how to manipulate them
    • SIM: General functions in motion
    • Piecewise defined functions - how to form them
    • How to shift functions
    • How to do function operations
    • Practice function operations
    • Quadratic function roots - How to get them 1
    • Quadratic function roots - How to get them 2
    • Which terms dominate in functions
    • SIM: 3 airplane race - who wins, and when?
    • Follow-up

    Trigonometric functions

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

    Multidimensional functions

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

    Limits

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

    Derivatives - single variable

    • Derivatives - what are they - falling sphere example 1
    • Where does the the equation Hi-5*t^2 come from?
    • Derivatives - what are they - falling sphere example 2
    • Derivatives - what are they - falling sphere example 3
    • SIM: Earth, Mars, Moon - exercise
    • SIM: Earth, Mars, Moon - solution
    • Derivatives - What are they - multidimensional point of view
    • Practice your derivative intuition - exercises
    • Prove that d(sin(theta))/d(theta)=cos(theta)
    • chain rule - how to apply it to a multi link problem - water pipe example 1
    • chain rule - how to apply it to a multi link problem - water pipe example 2
    • Differential operators - What are they and how to apply them
    • Multilevel derivatives - double, triple, quadruple
    • Derivative rules - shortcuts 1
    • Derivative rules - shortcuts 2
    • Implicit VS Explicit functions - chain rule - water pipe example
    • Derivative rules - BIG exercise
    • Trigonometric function derivatives - how to take them 1
    • Trigonometric function derivatives - how to take them 2
    • Minimize the material used to produce a can - how to apply derivatives 1
    • Minimize the material used to produce a can - how to apply derivatives 2
    • Minimize the material used to produce a can - how to apply derivatives 3
    • Exponential functions - what are they - how to manipulate them
    • Logarithmic functions & log scale - what are they & derivatives
    • Maximize your profit - how to apply derivatives for that
    • Motion of a Projectile (The Crazy Motorcyclist)

    Vectors

    • Vectors in 2 dimensions - what are they
    • Vectors in multiple dimensions - what are they
    • Vector terminology and disclaimers
    • Vector magnitude - what is it
    • Vector components - exercise
    • Vector operations - how do they work
    • Apply the dot product - Forces on a box example
    • Cross product intuition- what is it
    • Cross product - how to calculate it
    • Apply the cross product - electron and magnetic field example
    • MEGA Application - Water tank example 1
    • MEGA Application - Water tank example 2
    • MEGA Application - Water tank example 3
    • CORRECTION: MEGA Application - Water tank example 3
    • MEGA Application - Water tank example 4
    • CORRECTION: MEGA Application - Water tank example 4
    • MEGA Application - Water tank example 5
    • SIM: MEGA Application - Water tank example - Complete
    • MEGA Application - Water tank example - exercise 1
    • MEGA Application - Water tank example - exercise 2
    • SIM: MEGA Application - Water tank example - exercise
    • MEGA Application - Water tank mass flow- use derivatives to get it
    • Distance VS Position vectors - what's the difference
    • Displacement VS Velocity VS Acceleration vectors - what's the difference
    • Average displacement, velocity, and acceleration vectors - clarification
    • Graph Displacement, Velocity, & Acceleration vectors
    • Acceleration vector - intuition
    • Vector derivatives - how do they work

    Transformations

    • 2D Cartesian VS Polar coordinate systems - what are they
    • 3D Cartesian VS Cylindrical VS Spherical coordinate systems - what are they
    • Apply 3 dimensional coordinate systems - when to use what
    • Going from Polar to Cartesian
    • Going from Cartesian to Polar
    • Going between 3 dimensional coordinate systems - how to switch between them

    Parametric Equations

    • Intro into Parametric Equations - Intuition
    • MEGA Application - Landing Airplane in 2D
    • SIM: MEGA Application: Landing simulation
    • MEGA Application - Airplane flying in an oscillatory way (in 2D)
    • MEGA Application - Airplane's velocity and acceleration in 2D
    • SIM: MEGA Application - Sin trajectory simulation
    • MEGA Application - Airplane doing circles in 2D - Cartesian & Polar coordinates
    • MEGA Application - Airplane doing circles in 2D - Velocity & Acceleration
    • SIM: MEGA Application - Circle simulation
    • MEGA Application - Airplane flying in a spiral in 3D
    • SIM: MEGA Application - 3D trajectories - simulation 1
    • SIM: MEGA Application - 3D trajectories - simulation 2
    • SIM: MEGA Application - 3D trajectories - simulation 3
    • SIM: MEGA Application - 3D trajectories - simulation 4
    • SIM: MEGA Application - 3D trajectories - simulation 5
    • MEGA Application - 2 joint robot - Angular position, velocity, and acceleration
    • MEGA Application - 2 joint robot - 2 joints rotating simultaneously
    • MEGA Application - 2 joint robot - assigning multiple reference frames
    • MEGA Application - 2 joint robot - describing a point in two different frames
    • MEGA Application - 2 joint robot - deriving a 2D rotational matrix
    • MEGA Application - 2 joint robot - describing rotating and translating joints
    • MEGA Application - 2 joint robot - joints rotating at different frequencies
    • SIM: MEGA Application - 2 joint robot - simulation 1
    • SIM: MEGA Application - 2 joint robot - simulation 2
    • 3D Rotational matrix - how to derive it 1
    • 3D Rotational matrix - how to derive it 2
    • 3D Rotational matrix - how to derive it 3
    • Spiral - Final shape

    Multivariable Calculus

    • Implicit functions - what are they and how to graph them
    • Implicit function derivatives - how to take them
    • Expanding function dimensions 1
    • Expanding function dimensions 2
    • Machine Learning example - how to apply multidimensionality
    • Partial derivatives - intro 1
    • Partial derivatives - intro 2
    • Partial derivatives - intro 3
    • Higher dimensional partial derivatives & its graph
    • Airplane example - Chain rule in parametric equations - partial derivatives 1
    • Airplane example - Chain rule in parametric equations - partial derivatives 2
    • Multilevel partial derivatives - how to take them
    • Gradient - what is it and how to find it
    • Neural Networks + Calculus (Article recommendation)
    • Taylor Series - what is it and how to formulate it 1
    • Taylor Series - what is it and how to formulate it 2
    • Linearization and Quadratic Approximation - what is it and how to do it
    • Multidimensional linearization - practical exercise
    • Multidimensional quadratic approximation - Hessian Matrix
    • Representing a system mathematically, in vector-matrix form, and block diagrams

    Single variable integrals

    • Discrete VS Continuous functions - what's the difference
    • Intro to Integrals - The area of the wall calculation 1
    • Intro to Integrals - The area of the wall calculation 2
    • Integrals - what's the meaning of it 1
    • Integrals - what's the meaning of it 2
    • Integrals - what's the meaning of it 3
    • Integrals - what's the meaning of it 4
    • Indefinite Integrals VS Definite Integrals - what's the difference
    • Definite Integrals - Area of the wall calculation 1
    • Definite Integrals - Area of the wall calculation 2
    • Improper Integrals - made intuitive
    • Definite Integrals - formal definition
    • Area of a circle & initial conditions - integrals applied
    • Area of a circle - 2nd approach - integrals applied
    • Volume of a solid - integrals applied
    • Integration by parts - where it comes from and how to apply it
    • Curve length calculation - integrals applied 1
    • Curve length calculation - integrals applied 2
    • Spiral length calculation in 3D - integrals applied
    • Spiral trajectory length

    Multivariable integrals

    • Multivariable integrals - intuition 1
    • Multivariable integrals - intuition 2
    • Multivariable integrals - intuition 3
    • Triple Integrals -intuition
    • Quadruple Integrals - intuition
    • Mass calculation with varying density - applied triple integrals

    Introduction to Differential Equations

    • Differential Equations - intuition & different representations 1
    • Differential Equations - intuition & different representations 2
    • Wave representation in time & frequency domain

    Calculus in Control Engineering - PID controller

    • Intro to Control - how to control systems with a controller 1
    • Intro to Control - how to control systems with a controller 2
    • Open VS Closed Loop System
    • Controlling the water tank in a Python simulation
    • Intro to a proportional controller
    • Modelling the water tank 1
    • Modelling the water tank 2
    • Numerical integration applied to the water tank model
    • Combining math with the control structure
    • Water tank simulation - proportional controller
    • Intro to a PID simulation
    • PID: Modelling the train with forces 1
    • PID: Modelling the train with forces 2
    • PID: Going from system input to system output using numerical integration
    • PID: Magnetic train simulation - proportional controller
    • PID: Proportional controller overshoot explanation 1
    • PID: Proportional controller overshoot explanation 2
    • PID: Proportional controller overshoot explanation 3
    • PID: Intro to Derivative Control
    • PID: Tuning the controller
    • PID: Proportional & Derivative controller & magnetic train simulation in Python
    • PID: Intro to Integral Control
    • PID: Python magnetic train simulation at an inclination angle
    • PID: Mathematical modelling of the train with the inclination angle 1
    • PID: Mathematical modelling of the train with the inclination angle 2
    • PID: Proportional, Derivative, Integral Control combined
    • PID: Magnetic train simulation (inclination angle & PID)
    • Test your PID fundamental understanding
    • PID train code explanation 1
    • PID train code explanation 2
    • PID train code explanation 3
    • Short intro to Python animation tools
    • PID: Quick code & animation explanation (water tanks)
    • Codes for the P & PID controllers (Python 3, Numpy & Matplotlib needed)

    Last Words

    • Well done! You did it! But don't stop here! Keep going forward!

    Instructors

    Mr Mark Misin

    Mr Mark Misin
    Instructor
    Freelancer

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