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Beginner

What Will You Learn?

  • 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

Curriculum

32h 8m
Section 1: Promotional Video
02:31
Section 2: Single variable functions
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
Section 3: Trigonometric functions
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
Section 4: Introduction to multidimensional functions
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
Section 5: Limits
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
Section 6: Derivatives - single variable
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
Section 7: Vectors
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
Section 8: Transformations
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
Section 9: Parametric equations
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
Section 10: Multivariable Calculus
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
Section 11: Single variable integrals
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
Section 12: Multivariable integrals
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
Section 14: Intro into Differential Equations
28:51
Differential Equations - intuition & different representations part 1
16:09
Differential Equations - intuition & different representations part 2
12:42
Section 15: Extra wisdom
05:45
Wave representation in time & frequency domain
05:45

Description

Requirements

  • Basic understanding in algebra
  • Willingness to learn and experiment

About the Instructor

100% of students rated this instructor as excellent!
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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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