Math for Thought
Math for Thought
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Linear Algebra Final exam review: Part 2
The second part of the linear algebra review! We continue from question 21 onwards.
00:00 - Question 21 (Subspaces with linear combinations)
03:33 - Question 22 (Finding what is and isn't a subspace)
15:59 - Question 23 (Checking if a set of vectors forms a basis)
19:45 - Question 24 (Transformation of polynomials)
25:00 - Question 25 (Basis for the span of vectors)
27:02 - Question 26 (Row space, column space, null space, Rank and nullity)
33:39 - Question 27 (Row space with transposes)
35:58 - Question 28 (Dimension and subspaces with the Rank nullity theorem)
39:48 - Question 29 (Gram schmidt and orthogonal decomposition)
57:00 - Question 30 (Orthogonal complement with row space)
1:00:57 - Question 31 (Transition matrix + Coordinates)
1:04:21 - Question 32 (Orthonormal vectors with linear transformations)
1:25:55 - Question 33 (Linear transformation of orthogonal projection)
1:32:40 - Question 34 (Vector closest to row space)
1:37:24 - Question 35 (Rotations and isometries)
1:39:25 - Question 36 (Complex eigen values + Diagonalization to find large matrices)
1:59:53 - Question 37 (Definition of eigenvectors and eigenvalues)
2:02:10 - Question 38 (Diagonalizing a matrix)
2:11:33 - Question 39 (Orthogonal Diagonalization of a matrix + Eigenvalue properties)
2:25:32 - Question 40 (Determinants using eigenvalues)
Переглядів: 6 382

Відео

Linear Algebra Final exam review: Part 1
Переглядів 12 тис.3 роки тому
Welcome to to calculus II final exam review! In this video, we go over a standard final exam review for Linear algebra. Feel free to use the timestamps to go the question you wish! Please not that because the exam review is so large, it has been split into two parts. 00:00 - Introduction 01:02 - Question 1 (Elementary row operations) 11:47 - Question 2 (The inverse of a matrix) 17:48 - Question...
Calculus II: Final exam review!
Переглядів 8 тис.3 роки тому
Welcome to to calculus II final exam review! In this video, we go over a standard final exam review for Calculus II. Feel free to use the timestamps to go the question you wish! 00:00 - Introduction 01:26 - Question 1 (Radius and interval of convergence) 13:24 - Question 2 (Radius and interval of convergence) 18:24 - Question 3 (Integration as a power series) 23:25 - Question 4 (Power series re...
Calculus II: Unit Tangent, Unit normal and Binormal vectors
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In this video, we close off the last topic in Calculus II by discussing the last topic, which is the idea of Unit tangent, Normal and the Bi-normal vectors. We also discuss Osculating and normal planes. 00:00 - Introduction 00:45 - Definition 03:40 - Example 1 14:14 - Normal and osculating planes
Calculus II: Curvature
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In this video, we discuss the notion of curvature and how it relates to other topics we learned about in Calculus 1 regarding rate of change. 00:00 - Introduction 00:19 - Definition of Curvature 01:40 - Calculating Curvature 03:14 - Example 1 09:49 - Alternative method for calculating Curvature 11:01 - Example 2
Calculus II: Surface of revolution
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In this video, we discuss how to compute the surface area of a curve rotated about a line. 00:00 - Introduction 00:18 - Definition 00:56 - Surface area about x and y axis 03:35 - Example 1 06:29 - Surface area involving parametric equations 08:05 - Example 2
Calculus II: Arc length of a curve
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In this video, we discuss how to find the arc length of a cartesian curve, a parametric curve, and a polar curve. 00:00 - Introduction 00:18 - Arc length of a Cartesian curve 01:50 - Example 1 04:53 - Arc length of a Parametric curve 06:05 - Example 2 08:40 - Arc length of a Polar curve 09:30 - Example 3 23:35 - Arc length of a Space curve 24:55 - Example 4 30:38 - Example 5
Calculus II: Limits, derivatives and Integrals of Vector functions
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In this video, we discuss how to find limits, derivatives and integrals of vector valued functions in space. 00:00 - Introduction 00:30 - Limits of vector valued functions 01:47 - Example 1 02:59 - Derivatives of vector valued functions 06:58 - Integration of vector valued functions 08:03 - Example 2 10:43 - Example 3 12:45 - Example 4 14:31 - Example 5
Calculus II: Parametrization of surfaces
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In this video, we extend our understanding of space curves and discuss hot do describe equations of various quadric functions with vectors. 00:00 - Introduction 00:50 - Example 1 03:28 - Example 2 14:29 - Example 3 16:47 - Example 4 18:57 - Example 5
Calculus II: Vector functions and space curves
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In this very brief video, we introduce the idea of a vector valued function and space curves and discuss finding domains of space curves. 00:00 - Introduction 00:38 - Definition of vector functions and space curves 02:55 - Example 1 04:56 - Example 2
Calculus II: Cylindrical and Spherical coordinates
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In this video, we discuss cylindrical and Spherical coordinates which can be useful on occasion when working with different coordinate systems to approach different kinds of problems. 00:00 - Introduction 00:12 - Definition of Cylindrical and Spherical coordinates 13:53 - Example 1 15:32 - Example 2 18:19 - Example 3 19:21 - Example 4 23:48 - Example 5 27:37 - Example 6 30:22 - Example 7 37:19 ...
Linear algebra: Basis and dimension
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In this video we talk about what a basis is, what it means for something to be a basis and how to find a basis for some vector space. 00:00 - Introduction 00:20 - Definition of a basis (With a example to explain) 03:19 - How to check if something is a basis 04:14 - Example 1 12:38 - Example 2 16:38 - Common basis vectors for a vector space 19:35 - Definition of dimension 20:47 - Dimension of si...
Calculus II: Cylinders and quadric surfaces
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In this video, we discuss cylinders in 3D space and the idea of quadric surfaces. imgur.com/a/Y8BzdAj (Link to Quadric surfaces) 00:00 - Introduction 00:17 - Definition of quadric surfaces 02:39 - List of quadric surfaces and equations of quadric surfaces 05:35 - Definition of a trace 10:23 - Example 1 16:57 - Example 2 29:28 - Example 3 32:28 - Example 4
Calculus II: Equations of lines and planes
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In this video, we discuss the first part of vector calculus by prefacing the idea of how to get equations of lines and planes in 3 dimensions using vectors. We also do many examples on how to use lines and planes. 00:00 - Introduction 00:59 - Equation of a lines and various forms of a line 09:00 - Example 1 13:11 - Equation of a plane 21:08 - Distance between a point and a plane 22:54 - Example...
Calculus II: Integration over polar curves
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In this video, we discuss how to find the region bounded by polar curves. We also cover several examples on how to find the area bounded by a polar curve. 00:00 - Introduction 00:18 - Area bounded by a polar curve 02:54 - Example 1 06:29 - Example 2 12:07 - Example 3 19:37 - Example 4 26:04 - Example 5
Calculus II: Tangents to Polar curves
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Calculus II: Tangents to Polar curves
Calculus II: Polar coordinates
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Calculus II: Polar coordinates
Calculus II: Integration over parametric curves
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Calculus II: Integration over parametric curves
Calculus II: Binomial series
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Calculus II: Binomial series
Calculus II: Tangents to parametric curves
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Calculus II: Tangents to parametric curves
Calculus II: Parametric curves
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Calculus II: Parametric curves
Linear Algebra: Linear Independence
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Linear Algebra: Linear Independence
Linear Algebra: Subspaces
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Linear Algebra: Subspaces
Linear Algebra: Vector spaces
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Linear Algebra: Vector spaces
Linear Algebra: Cramer's rule
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Linear Algebra: Cramer's rule
Linear Algebra: Geometry with determinants
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Linear Algebra: Geometry with determinants
Calculus II: Taylor and Maclaurin series
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Calculus II: Taylor and Maclaurin series
Calculus II: Taylor's inequality
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Calculus II: Taylor's inequality
Linear Algebra: Important matrices
Переглядів 6133 роки тому
Linear Algebra: Important matrices
Linear Algebra: Determinants and orientated volume
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Linear Algebra: Determinants and orientated volume

КОМЕНТАРІ

  • @FinnFinn-h8x
    @FinnFinn-h8x 14 днів тому

    He never finished linear algebra 😢

  • @Dazzletoad
    @Dazzletoad 17 днів тому

    I don't know if I commented before, but this video is terrible. Too much yapping on, and not very clear in parts. For example, why bring up the mystery of the formulae for simple shapes just to go straight on to say the FTOC shows how differentiation and manipulation are related? I would recommend scripting this. You obviously enjoy this, and it seems you have a good understanding, that's just wasted ig your video is messy - especially given all the other material on UA-cam. I appreciate the upload, however 👍🏻

  • @SanjiVinsmoke-u8y
    @SanjiVinsmoke-u8y 18 днів тому

    i really want to thank you because you greatly helped my studies and if your seeing this THE VIDEOS YOU PROVIDE ARE SIMPLE AND A LOT HELPFUL than any modules and teachers I've ever met. Please continue uploading and you have got yourself a loyal subscriber. Thanks a lot

  • @raysontan1021
    @raysontan1021 20 днів тому

    In example 1, isn't (-2x^3 / 3) + (6x / 3) = (-2x^3 + 6x) / 3 ?

  • @AdiahLangilao
    @AdiahLangilao Місяць тому

    calculus for grade 7 plsss🙏

  • @AdiahLangilao
    @AdiahLangilao Місяць тому

    whaf if his written mine.😢

  • @YohanesZakariasRadjaHedo-mr9rj
    @YohanesZakariasRadjaHedo-mr9rj Місяць тому

    Sudah....

  • @abramsirois7777
    @abramsirois7777 Місяць тому

    Correct me if I'm wrong but wouldn't (-1) (-7) = 7 and NOT -7?

  • @abelgongora5856
    @abelgongora5856 Місяць тому

    Trolling hats!! Lol😂

  • @AltAcc-cp6eu
    @AltAcc-cp6eu Місяць тому

    Dont tell anyone im learning this in g7 >:D

  • @republicofvegans712
    @republicofvegans712 Місяць тому

    Which lecture is about linear Transformations? Having a hard time finding it but other than that great vid!

  • @user-tw8tj3lw3i
    @user-tw8tj3lw3i Місяць тому

    in the first example, you got n >-9 but then you summed the first 10 terms, why is that? why not sum up the first 9 terms since n is greater than and equal to 9? Thanks.

  • @user-kg9ls1vw3d
    @user-kg9ls1vw3d Місяць тому

    Thank you so much for the videos, do you have plans to make a Math 209 playlist?

  • @mash2068
    @mash2068 2 місяці тому

    I just fell in love with math. Am gonna go through all your videos, man.

  • @b.994
    @b.994 2 місяці тому

    This serie is awesome. Thank you!

  • @KIIZAAloysiusAkiiki
    @KIIZAAloysiusAkiiki 2 місяці тому

    You are nice lecturer

  • @mixerbd791
    @mixerbd791 2 місяці тому

    Nice explanation and presentation. Thanks Sir. Love feom Bangladesh.

  • @williamcripfoe6754
    @williamcripfoe6754 2 місяці тому

    How did you get -11 pi/4 for example 7 wouldnt it be -14pi/4?

  • @jonathanE-do6ss
    @jonathanE-do6ss 2 місяці тому

    What is the difference between the span of d and U in example 8?Is the span of d not equal to U? Don't they both share the same line through the origin? If this is the case, why did you have to say the span of d belongs to U if we already know U has the same span as the span of d. I am confused because @41:28 , you state that the span of vector d belongs to U.

  • @shaikhtariq-8495
    @shaikhtariq-8495 3 місяці тому

    Excellent.

  • @user-yz5ei1ss1e
    @user-yz5ei1ss1e 3 місяці тому

    wigshaneza turakwemera

  • @user-yz5ei1ss1e
    @user-yz5ei1ss1e 3 місяці тому

    kabisa umuntu agerageza kubyumva basi

  • @djdanzo206
    @djdanzo206 3 місяці тому

    this needs more views,thank you so much💯🙏

  • @dimitrivahlas8505
    @dimitrivahlas8505 3 місяці тому

    For question 6, I notice you go back and forth between which side you put your inverses when cancelling. Does it matter or can i just put it on any side?

  • @gysl3790
    @gysl3790 3 місяці тому

    link da goat

  • @JamieVisser-xt7lc
    @JamieVisser-xt7lc 3 місяці тому

    Thank you for the videos!

  • @xxslayerxxa5884
    @xxslayerxxa5884 3 місяці тому

    Appreciate the videos man

  • @user-iq3dj3dy7u
    @user-iq3dj3dy7u 3 місяці тому

    how do we identify if we are going in the positive or negative direction ? eg in example 1

  • @user-iq3dj3dy7u
    @user-iq3dj3dy7u 3 місяці тому

    at 24:00 could u explain why f^n(2)= (-1)^(n+1) *and everything else* because when we previously discussed a general formula before putting a value of x(=2) we had (-1)^n term to account for alternating signs in terms

    • @user-iq3dj3dy7u
      @user-iq3dj3dy7u 3 місяці тому

      and can we use (-1)^(n-1) unstead inside the sigma notation part

  • @aminalnemr2861
    @aminalnemr2861 3 місяці тому

    For example 3 wouldn’t you have to pick a constant that is in between the function 2^x and the function x^3? How do you know that 0 is in between them?

    • @MathforThought
      @MathforThought 3 місяці тому

      No. It can be any constant actually.

  • @aikarpao2016
    @aikarpao2016 3 місяці тому

    I am about to go into Economics field which needs solid Maths skills especially calculus and linear algebra. I start learning from now on. Thank you so much for your time and effort.

  • @fatass6203
    @fatass6203 4 місяці тому

    i have a re-exam in calculus, can anyone tell me if its worth the time to go through the playlist?

    • @MathforThought
      @MathforThought 3 місяці тому

      You could just watch the Final exam and midterm exam review.

  • @michaeldevito5035
    @michaeldevito5035 4 місяці тому

    ROBUX

  • @michaeldevito5035
    @michaeldevito5035 4 місяці тому

    cool video though

  • @michaeldevito5035
    @michaeldevito5035 4 місяці тому

    shh bye bye/LOL I am just being stupid don't take this offensive please

  • @michaeldevito5035
    @michaeldevito5035 4 місяці тому

    wow🤫🤔mewing streak 1000

  • @michaeldevito5035
    @michaeldevito5035 4 місяці тому

    this was 3 years ago

  • @republicofvegans712
    @republicofvegans712 4 місяці тому

    Is there a vid on linear transformations?

  • @user-iq3dj3dy7u
    @user-iq3dj3dy7u 4 місяці тому

    could u tell me how the conclusion of b(n+1) < bn was reached in example 3

    • @MathforThought
      @MathforThought 4 місяці тому

      You can just look at it and see if it's decreasing.

  • @Math_Academy2482
    @Math_Academy2482 4 місяці тому

    can you by any chance upload this text/pdf you written please ?

  • @user-iq3dj3dy7u
    @user-iq3dj3dy7u 4 місяці тому

    for example 4 could u tell me how u got the formula 3/2 (1-1/3^n)

  • @1KosovoJeSrbija1
    @1KosovoJeSrbija1 4 місяці тому

    Could you perhaps write your Ks and Xs differently?

  • @PeterParker-wy5zd
    @PeterParker-wy5zd 5 місяців тому

    Just to confirm and make sure I'm getting this right: in general, when we set out to prove that something given with some properties is or is not a vector space, we should start with the property given, then try to get the same result using the properties of a vector space, and whether we are successful or not determines whether what is given is a vector space? Another thing to confirm because I'm still having trouble wrapping my head around the concept of a vector space: a vector space is to vectors what R is to numbers. It is the "space" within which all vectors can occur? Just like R^2 is the space within which all tuples (x,y) can occur. Thanks again and all the best!

  • @PeterParker-wy5zd
    @PeterParker-wy5zd 5 місяців тому

    In example, just before 40:00, you write |x+1| < 1, but the radius of convergence is in the form |x-a| < 1. Is it okay to still take the radius of convergence to be one when the sign is not negative? (Btw, thank you so much for these! They're saving my life :)

  • @garnikmikayelian4271
    @garnikmikayelian4271 5 місяців тому

    Thank you so much, everything was very clear. You really helped me ✍️✍️

  • @syandaofficial
    @syandaofficial 5 місяців тому

    Why don’t you explain of where you got the cases from😢

    • @MathforThought
      @MathforThought 5 місяців тому

      I did examples in my other videos.

  • @syandaofficial
    @syandaofficial 5 місяців тому

    Made it easier

  • @syandaofficial
    @syandaofficial 5 місяців тому

    You good at this 👍🏽

  • @-G-GaziAbrerZakir
    @-G-GaziAbrerZakir 5 місяців тому

    Thank you so much for this video, you made it so easy to understand