Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.
Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.
This calculus 3 video tutorial provides a basic introduction into vectors. It contains plenty of examples and practice problems.
Here is a list of topics:
1. Scalar quantities vs vector quantities
2. Speed vs velocity
3. Vectors as directed line segments
4. How to find the vector given the initial point and terminal point
5. How to find the find the component form of a vector
6. How to calculate the magnitude of a vector using its components
7. How to determine if two vectors are equivalent
8. Adding and subtracting vectors graphically
9. Performing vector operations
10. Position vectors and unit vectors
11. How to find the unit vector given the components of a vector
12. Standard unit vectors - i j k
13. Linear combination of standard unit vectors
14. How to find the com...
This calculus 3 video tutorial provides a basic introduction into vectors. It contains plenty of examples and practice problems.
Here is a list of topics:
1...
This calculus 3 video tutorial provides a basic introduction into vectors. It contains plenty of examples and practice problems.
Here is a list of topics:
1. Scalar quantities vs vector quantities
2. Speed vs velocity
3. Vectors as directed line segments
4. How to find the vector given the initial point and terminal point
5. How to find the find the component form of a vector
6. How to calculate the magnitude of a vector using its components
7. How to determine if two vectors are equivalent
8. Adding and subtracting vectors graphically
9. Performing vector operations
10. Position vectors and unit vectors
11. How to find the unit vector given the components of a vector
12. Standard unit vectors - i j k
13. Linear combination of standard unit vectors
14. How to find the components of a vector given its magnitude and angle
15. How to find the magnitude and angle of a vector in component form
16. How to calculate the resultant force of two vectors
Physics and Calculus Tutors: https://bit.ly/Find-A-Tutor
Useful Textbooks: https://www.amazon.com/shop/theorganicchemistrytutor
Access Premium Videos: https://www.patreon.com/MathScienceTutor
Vectors - Basic Introduction - Physics: https://www.youtube.com/watch?v=EwSHKuSxX_8
Scalars and Vectors: https://www.youtube.com/watch?v=rcDXQ-5H8mk
Resultant - Two Force Vectors: https://www.youtube.com/watch?v=RxV06Oj5sMc
Parallelogram Method - Resultant Vector: https://www.youtube.com/watch?v=LrwYAC_4ThY
Addition of Vectors - Using Components: https://www.youtube.com/watch?v=xS-gdFgZel0
Position Vectors and Displacement Vectors: https://www.youtube.com/watch?v=NxAvWfs92U4
Adding and Subtracting Vectors: https://www.youtube.com/watch?v=DxwT7fn6GtE
Scalar Multiplication of Vectors: https://www.youtube.com/watch?v=g14-ACo5vnc
Vectors - Precalculus: https://www.youtube.com/watch?v=iXdMpXMuEGI
The Dot Product of Two Vectors: https://www.youtube.com/watch?v=VzX8KJKFhlM
The Cross Product of Two Vectors: https://www.youtube.com/watch?v=pWbOisq1MJU
Calculus 3 - Intro to Vectors: https://www.youtube.com/watch?v=2_21erD-nBg
Calculus 3 - The Dot Product: https://www.youtube.com/watch?v=Te8eL5r7aJs
Angle Between Two Vectors - Calculus 3: https://www.youtube.com/watch?v=dYPRYO8QhxU
Parallel and Orthogonal Vectors: https://www.youtube.com/watch?v=8fIZ2v-33xw
Area of a Parallelogram - Cross Product: https://www.youtube.com/watch?v=YbZmAqGUkqc
Parallelpiped - The Triple Scalar Product: https://www.youtube.com/watch?v=6NeAK0rJwlk
Direction Cosines Angles of a Vector: https://www.youtube.com/watch?v=ZoCxUV893fo
Vector Projections - Calculus 3: https://www.youtube.com/watch?v=Rw70zkvqEiE
Vector Equations - Calculus 3: https://www.youtube.com/watch?v=MkjazYnvNP8
Organic Chemistry Tutor - Playlists: https://www.video-tutor.net/
Subscribe To My YouTube Channel: https://bit.ly/37WGgXl
E-Book & E-mail Newsletter: https://www.video-tutor.net/math-and-science-ebook.html
Affiliate Marketing Disclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
This calculus 3 video tutorial provides a basic introduction into vectors. It contains plenty of examples and practice problems.
Here is a list of topics:
1. Scalar quantities vs vector quantities
2. Speed vs velocity
3. Vectors as directed line segments
4. How to find the vector given the initial point and terminal point
5. How to find the find the component form of a vector
6. How to calculate the magnitude of a vector using its components
7. How to determine if two vectors are equivalent
8. Adding and subtracting vectors graphically
9. Performing vector operations
10. Position vectors and unit vectors
11. How to find the unit vector given the components of a vector
12. Standard unit vectors - i j k
13. Linear combination of standard unit vectors
14. How to find the components of a vector given its magnitude and angle
15. How to find the magnitude and angle of a vector in component form
16. How to calculate the resultant force of two vectors
Physics and Calculus Tutors: https://bit.ly/Find-A-Tutor
Useful Textbooks: https://www.amazon.com/shop/theorganicchemistrytutor
Access Premium Videos: https://www.patreon.com/MathScienceTutor
Vectors - Basic Introduction - Physics: https://www.youtube.com/watch?v=EwSHKuSxX_8
Scalars and Vectors: https://www.youtube.com/watch?v=rcDXQ-5H8mk
Resultant - Two Force Vectors: https://www.youtube.com/watch?v=RxV06Oj5sMc
Parallelogram Method - Resultant Vector: https://www.youtube.com/watch?v=LrwYAC_4ThY
Addition of Vectors - Using Components: https://www.youtube.com/watch?v=xS-gdFgZel0
Position Vectors and Displacement Vectors: https://www.youtube.com/watch?v=NxAvWfs92U4
Adding and Subtracting Vectors: https://www.youtube.com/watch?v=DxwT7fn6GtE
Scalar Multiplication of Vectors: https://www.youtube.com/watch?v=g14-ACo5vnc
Vectors - Precalculus: https://www.youtube.com/watch?v=iXdMpXMuEGI
The Dot Product of Two Vectors: https://www.youtube.com/watch?v=VzX8KJKFhlM
The Cross Product of Two Vectors: https://www.youtube.com/watch?v=pWbOisq1MJU
Calculus 3 - Intro to Vectors: https://www.youtube.com/watch?v=2_21erD-nBg
Calculus 3 - The Dot Product: https://www.youtube.com/watch?v=Te8eL5r7aJs
Angle Between Two Vectors - Calculus 3: https://www.youtube.com/watch?v=dYPRYO8QhxU
Parallel and Orthogonal Vectors: https://www.youtube.com/watch?v=8fIZ2v-33xw
Area of a Parallelogram - Cross Product: https://www.youtube.com/watch?v=YbZmAqGUkqc
Parallelpiped - The Triple Scalar Product: https://www.youtube.com/watch?v=6NeAK0rJwlk
Direction Cosines Angles of a Vector: https://www.youtube.com/watch?v=ZoCxUV893fo
Vector Projections - Calculus 3: https://www.youtube.com/watch?v=Rw70zkvqEiE
Vector Equations - Calculus 3: https://www.youtube.com/watch?v=MkjazYnvNP8
Organic Chemistry Tutor - Playlists: https://www.video-tutor.net/
Subscribe To My YouTube Channel: https://bit.ly/37WGgXl
E-Book & E-mail Newsletter: https://www.video-tutor.net/math-and-science-ebook.html
Affiliate Marketing Disclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
This calculus 3 video tutorial provides a basic introduction into vectors. It contains plenty of examples and practice problems.
Here is a list of topics:
1. Scalar quantities vs vector quantities
2. Speed vs velocity
3. Vectors as directed line segments
4. How to find the vector given the initial point and terminal point
5. How to find the find the component form of a vector
6. How to calculate the magnitude of a vector using its components
7. How to determine if two vectors are equivalent
8. Adding and subtracting vectors graphically
9. Performing vector operations
10. Position vectors and unit vectors
11. How to find the unit vector given the components of a vector
12. Standard unit vectors - i j k
13. Linear combination of standard unit vectors
14. How to find the components of a vector given its magnitude and angle
15. How to find the magnitude and angle of a vector in component form
16. How to calculate the resultant force of two vectors
Physics and Calculus Tutors: https://bit.ly/Find-A-Tutor
Useful Textbooks: https://www.amazon.com/shop/theorganicchemistrytutor
Access Premium Videos: https://www.patreon.com/MathScienceTutor
Vectors - Basic Introduction - Physics: https://www.youtube.com/watch?v=EwSHKuSxX_8
Scalars and Vectors: https://www.youtube.com/watch?v=rcDXQ-5H8mk
Resultant - Two Force Vectors: https://www.youtube.com/watch?v=RxV06Oj5sMc
Parallelogram Method - Resultant Vector: https://www.youtube.com/watch?v=LrwYAC_4ThY
Addition of Vectors - Using Components: https://www.youtube.com/watch?v=xS-gdFgZel0
Position Vectors and Displacement Vectors: https://www.youtube.com/watch?v=NxAvWfs92U4
Adding and Subtracting Vectors: https://www.youtube.com/watch?v=DxwT7fn6GtE
Scalar Multiplication of Vectors: https://www.youtube.com/watch?v=g14-ACo5vnc
Vectors - Precalculus: https://www.youtube.com/watch?v=iXdMpXMuEGI
The Dot Product of Two Vectors: https://www.youtube.com/watch?v=VzX8KJKFhlM
The Cross Product of Two Vectors: https://www.youtube.com/watch?v=pWbOisq1MJU
Calculus 3 - Intro to Vectors: https://www.youtube.com/watch?v=2_21erD-nBg
Calculus 3 - The Dot Product: https://www.youtube.com/watch?v=Te8eL5r7aJs
Angle Between Two Vectors - Calculus 3: https://www.youtube.com/watch?v=dYPRYO8QhxU
Parallel and Orthogonal Vectors: https://www.youtube.com/watch?v=8fIZ2v-33xw
Area of a Parallelogram - Cross Product: https://www.youtube.com/watch?v=YbZmAqGUkqc
Parallelpiped - The Triple Scalar Product: https://www.youtube.com/watch?v=6NeAK0rJwlk
Direction Cosines Angles of a Vector: https://www.youtube.com/watch?v=ZoCxUV893fo
Vector Projections - Calculus 3: https://www.youtube.com/watch?v=Rw70zkvqEiE
Vector Equations - Calculus 3: https://www.youtube.com/watch?v=MkjazYnvNP8
Organic Chemistry Tutor - Playlists: https://www.video-tutor.net/
Subscribe To My YouTube Channel: https://bit.ly/37WGgXl
E-Book & E-mail Newsletter: https://www.video-tutor.net/math-and-science-ebook.html
Affiliate Marketing Disclaimer: Some of the links associated with this video may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.
Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.
The Boy Vs. The Cynic, Chapter one, page one. I'll start from the top... I'll embrace dreams again when I can breath again And at that point I won't be needing them It became clear to me that I was fighting a war I couldn't win You don't make it on your own merit Only royalty inherits the kingdom And that's a system good intentions can't help Your courage is not good here so don't try to excel What a sad day when you realize nothing can change The revolution didn't leave you it never came There will be no parades, no royal balls Just long days topped off with last calls for alcohol Go to sleep wake up and repeat the same routine Smooth skin dressed with wrinkles and brown eyes With dark rings and entertainers sing of extremes that don't exist for you or me When real life is reality TV no wonder our youth don't believe in anything It's all a joke there are no heroes just those of us with high hopes It's just not that simple I'm not trying to save it all I just want to create a ripple And even if one individual is affected it's monumental with an unusual perspective That's beautiful in essence traditional thinking won't suggest this Is life really that precious well yes it is But there will be no celebrations or congratulations No pat on the back just your mind intact And the freedom to feel your heart beat at the speed of life Go to sleep tonight knowing you did it right And rest easy outside of a system that resents you for not doing what they expect you to do Psychologically wear you down and then they make the suggestion that you get on a prescription to deal with your depression Anxious lazy temperamental obese That's what money makers like to call a disease And they'll be looking for or creating new problems with profitable solutions To solve them but you won't get any better you'll just come back for more Until your medicine drawer is filled with unreliable cures And that's the way of the beast And I can't do nothing about it I could shout it in a room that's crowded but I doubt it'd make a difference So ignorance will be my disguise cause 21st century America likes its witchcraft civilized