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PlatformBilibili53YouTube10X3

Language中文53English13

DisciplineCalculus52Algebra10Applied mathematics2Probability & statistics1Discrete mathematics1

DifficultyFoundational37Intermediate29

StyleVisual explanation52Proof11Whiteboard3

LengthUnder 5 min5715–45 min55–15 min4

TopicSequence convergence9Sequence limit6Sequence limit definition (ε–N)6Function graph6Infinitesimal method5Riemann sums4Supremum principle4Monotone bounded theorem4Definite integral4Double integral4Vector field4Derivatives3Tangent vector3Function limit3Multivariable function3Nested interval theorem3Surface integral3Series convergence3Partial derivative3Tangent plane3Linear transformations2Green’s theorem2Curl density2Singularity2Boundary orientation2Limit process2Closed loop integral2Cauchy convergence criterion2Limit nonexistence2Arc length2Volume by integration2Solid region2Iterated integral2Multivariable extrema2Parametric curve2Hessian matrix2Taylor series2Local linearization2Circulation2Flux2Directional derivative2Function approximation2Wave superposition2Solid beneath a surface2Infinite series2Fourier transform1Vectors1Eigenvalues1Chain rule1Matrices1Determinants1Three-dimensional space1Bayes’ theorem1Integrals1Calculus1Linear span1Basis1Means1Permutations1Fractions1Curve integral1Arc length differential1Direction cosine1Vector field projection1Rectangle partition1Internal boundary cancellation1Hole method1Multiply connected domain1Method of inscribed polygons1Polygon approximation1Path independence1Conservative field1Simply connected domain1Heine theorem1Babylonian square-root method1Iterative method1Choosing parameters in proofs1Area under curve1Curved trapezoid1Region bounded by surfaces1Moment of inertia1Physical quantity1Triple integral1Constrained extrema1Lagrange multipliers1Level curve1Space curve1Normal plane1Second derivative test1Point set topology1Neighborhood1Interior point1Boundary point1Cauchy–Schwarz inequality1Vector geometry1Algebraic proof1Multivariable limit1Path limit1Tangent line1Secant line1Cluster point1Mean value theorem1Cauchy mean value theorem1Finite covering theorem1Compactness1Proof by contradiction1Infimum principle1Bounded set1Real number completeness1Stokes’ theorem1Line integral of a vector field1Normal vector1Gauss’ divergence theorem1Divergence1Alternating series1Error estimate1Gradient1Level surface1Fourier series1Volume under surface1Change of variables1Polar coordinates1Jacobian determinant1Partial sums1Comparison test1Positive term series1Power series1Total differential1Uniform continuity1Function limit definition (ε–δ)1Coordinate grid1Zeno’s paradox1Animation timing1

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Algebra·English

Three-dimensional linear transformations | Chapter 5, Essence of linear algebra

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