台灣黑皮歐巴桑的學習祕笈

暑期高中課程自學(中英文版)

1
數學
EP.7 空間向量的內積｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=3HbGLygGQZI
Dot Product and Angle Between 3D Vectors
https://www.youtube.com/watch?v=ECNH_1TTOjs
Dot product and angle between two vectors proof
https://www.youtube.com/watch?v=bbBGgHDhmVg
The Vector Cross Product
https://www.youtube.com/watch?v=gPnWm-IXoAY
Inner & outer products | Lecture 5 | Matrix Algebra for Engineers
https://www.youtube.com/watch?v=FCmH4MqbFGs
Linear Algebra: Inner Product Spaces (Sec. 5.2 Part 1)
https://www.youtube.com/watch?v=WYjcukICUnA
Linear Algebra: Projection (Sec. 5.2 Part 2)
https://www.youtube.com/watch?v=40q13JqNdrk

物理
Elastic and Inelastic Collisions
https://www.youtube.com/watch?v=M2xnGcaaAi4
Bowling Ball Elastic Collisions
https://www.youtube.com/watch?v=51IFubnEAsU
Collisions - Momentum - IB Physics
https://www.youtube.com/watch?v=fzxq7hmy6nA
26.2 Kinetic Energy in Collisions
https://www.youtube.com/watch?v=4ZnijNan49U
26.3 Totally Inelastic Collisions
https://www.youtube.com/watch?v=CcJoqITNvh0
27.1 Worked Example: Elastic 1D Collision
https://www.youtube.com/watch?v=6-7BOpZ2k04
Physics - Example Problem, Inelastic Collisions
https://www.youtube.com/watch?v=KRsBZ55UK5M

歷史
高中_歷史_中國斷代史_宋朝(上)
https://www.youtube.com/watch?v=qQBa19kC-kc
高中_歷史_中國斷代史_宋朝(下)
https://www.youtube.com/watch?v=VaPd5EDmopE

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2
數學
高中_數學_正射影
https://www.youtube.com/watch?v=9pC1SwhAfhQ
EP.8 柯西不等式｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=dC-bHWh-gms
Linear Algebra 6.2.2 Orthogonal Projections
https://www.youtube.com/watch?v=fqbwErsP8Xw
Projection Vector Proof
https://www.youtube.com/watch?v=aTBtgW7U-Y8
Calculus 3 - Vector Projections & Orthogonal Components
https://www.youtube.com/watch?v=Rw70zkvqEiE
Find an Orthogonal Projection of a Vector Onto a Plane Given an Orthogonal Basis (R3
https://www.youtube.com/watch?v=NA0lC3wucG0
Proof of the Cauchy-Schwarz inequality | Vectors and spaces | Linear Algebra | Khan Academy
https://www.youtube.com/watch?v=r2PogGDl8_U
12.5 Inner product spaces. Angles and Cauchy Schwarz theorem
https://www.youtube.com/watch?v=qxOzLOav85U

物理
【美英物理】201 - 高二物理B(下) | 10-1彈性碰撞_課程I
https://www.youtube.com/watch?v=BaYrAOzmzkg

歷史
高中_歷史_中國斷代史_元朝
https://www.youtube.com/watch?v=rBW_iWlIJW4
高中_歷史_中國斷代史_明朝政治
https://www.youtube.com/watch?v=M3Mjg2rnrBo

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3
數學
EP.9 外積｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=fjsfgOahUOE
Basics of Inner Product Spaces
https://www.youtube.com/watch?v=1ySJCG6hVPg
Outer Products
https://www.youtube.com/watch?v=fc1xyxVA-5Y
Applied Linear Algebra, Lesson 9, Video 1: Definition of Outer Product
https://www.youtube.com/watch?v=REaybRkV_4Q
Outer Product of nx1 and 1xn Vectors
https://www.youtube.com/watch?v=shEofmCb1lc
3 1 Cross Product of Two Vectors in Space
https://www.youtube.com/watch?v=hM5F-cmZbaw

物理
【美英物理】202 - 高二物理B(下) | 10-1彈性碰撞_課程II
https://www.youtube.com/watch?v=-gz76cFzZj0

歷史
高中_歷史_中國斷代史_明朝社會與文化
https://www.youtube.com/watch?v=JbhgdWc8JxA
高中_歷史_中國斷代史_盛清社會
https://www.youtube.com/watch?v=Y75dmrKicuA

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4
數學
EP.10 體積｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=nRff9klhb80
Volume of a parallelepiped | MIT 18.02SC Multivariable Calculus, Fall 2010
https://www.youtube.com/watch?v=QCGJVKaCDuI
Calculus 3: Vector Calculus in 3-D (33 of 35) Volume of a Tetrahedron
https://www.youtube.com/watch?v=xDGsafxeujE
Calculus 3: Vector Calculus in 3-D (34 of 35) Volume of a Tetrahedron: Example
https://www.youtube.com/watch?v=9plY4HhxO1Q
Volume of a Parallelpiped Using Vectors (Multivariable Calculus)
https://www.youtube.com/watch?v=X-4BmdjQROE

物理
【美英物理】203 - 高二物理B(下) | 10-1彈性碰撞_課程III
https://www.youtube.com/watch?v=VmEex66mmLI
Momentum (15 of 16) Elastic Collisions, Example 5
https://www.youtube.com/watch?v=Qb1IGcQPihc
Momentum (16 of 16) Elastic Collisions, Example 6
https://www.youtube.com/watch?v=eRwovMBcsJ4
Solving elastic collision problems the hard way | Physics | Khan Academy
https://www.youtube.com/watch?v=9yXrEZy5WME

歷史
高中_歷史_中國斷代史_清中葉以降的內憂
https://www.youtube.com/watch?v=I1_m3GLQJxs
高中_歷史_中國斷代史_晚清導論
https://www.youtube.com/watch?v=AydOUv4sLa4
高中_歷史_中國斷代史_晚清外患
https://www.youtube.com/watch?v=f_4WVg9E2t0

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5
數學
EP.11 三階行列式｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=Dg_XJwWrv40
EP.12 三階行列式的應用｜第四冊 空間向量 | 高中數學 ｜108新課綱
https://www.youtube.com/watch?v=luPcVAdoj5w
MATH 3191: Checking if Matrices with Determinant 1 is a Vector Space
https://www.youtube.com/watch?v=JyTd9j3B9hU
Linear Independence
https://www.youtube.com/watch?v=9kDpbZCK62Y
Matrix Determinants (1 of 3: Matrices as Vectors)
https://www.youtube.com/watch?v=jh1m0IgiAJI
Matrix Determinants (2 of 3: The Determinant's Geometric Meaning)
https://www.youtube.com/watch?v=_L8roj-8HfM
Matrix Determinants (3 of 3: How to Calculate It)
https://www.youtube.com/watch?v=dlAe4dcihv8&t=4s
What is a determinant?
https://www.youtube.com/watch?v=vvR3JSXO2fo
3.5: Determinants in 3D - Valuable Vector Calculus
https://www.youtube.com/watch?v=JmVtcSqgCdM
Linear Algebra: Ch 2 - Determinants (31 of 48) Multiplying by a Constant: 2x2 Determinants
https://www.youtube.com/watch?v=FzioP4b466E
Linear Algebra: Ch 2 - Determinants (20 of 48) The Minor of a Matrix (3x3)
https://www.youtube.com/watch?v=Ej-PdTHzrPo

物理
【美英物理】204 - 高二物理B(下) | 10-1彈性碰撞_課程IV
https://www.youtube.com/watch?v=tZBd5NoEshU

歷史
高中_歷史_中國斷代史_晚清自強與立憲
https://www.youtube.com/watch?v=7R7SkN4gHO8
高中_歷史_中國斷代史_晚清革命運動
https://www.youtube.com/watch?v=yGts5jkoozM