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PlatformYouTube517Bilibili23X3

DisciplineMathematical modeling335Calculus77Algebra53Probability & statistics45Discrete mathematics17Applied mathematics12Geometry3General mathematics1

DifficultyIntroductory357Intermediate126Foundational53Advanced7

StyleWhiteboard251Visual explanation149Lecture141Problem solving2

Length5–15 min312Under 5 min20315–45 min28

TopicMatrices25Derivatives20Vectors14Integrals14Probability13Greatest common divisor12Linear transformations9Distributions9Eigenvalues8Expectation8Graph theory8Time series forecasting8Chain rule7Function limit7Normal distribution7Exponential smoothing forecasting7Basis6Random variables6Independence6Euclidean algorithm6Modular arithmetic6Determinants5Bayes’ theorem5Means5Permutations5Function graph5Definite integral5Conditional probability5Binomial distribution5Game theory modeling5Partial differential equations5Fourier transform4Calculus4Fractions4Power series4Taylor series4Grey prediction model4Regression modeling4ARIMA modeling4Normalization and standardization in modeling4Entropy weight method4Dimensional analysis4Linear programming4Transportation problem4Cluster analysis modeling4Fourier series4Linear equations4Ordinary differential equations4Hypothesis testing3Function approximation3Arc length3Mean value theorem3Partial derivative3Lagrange multipliers3Infinite series3Multivariable function3Variance3Fuzzy comprehensive evaluation3Interpolation methods for modeling3Agent-based modeling3System dynamics modeling3Error propagation in models3Principal component analysis3Network flow modeling3Monte Carlo simulation3Markov chain modeling3Cellular automaton model3Minimum spanning tree model3Model validation techniques3Least squares fitting3Inventory model3Assignment problem3Exponential growth3Markov chains3Brownian motion3Singular values3Discretization3Boundary value problems3Method of characteristics3Linear span2Riemann sums2Gradient2Divergence2Series convergence2Partial sums2Total differential2Jacobian determinant2Outlier handling in modeling2SIR epidemic model2Logistic growth model2Similarity and scaling in modeling2Model assumptions and simplification2Traveling salesman modeling2Shortest path models2Branch and bound2Structure of a modeling report2Population growth model2Uniform distribution2Topological spaces2Universal properties2Experimental design2Group representations2Sequence convergence2Counterexamples2Linear regression2Finite element method2Connectedness2Uniform convergence2Pointwise convergence2Compound interest2Bisection method2Fields2Unit circle2Differential forms2Laurent series2Huffman coding2Pythagorean theorem2Initial value problems2Gradient descent2Cosets and Lagrange's theorem2Subgroups2Cyclic groups2Conditional entropy2Tensor products2Metric spaces2Polyhedra2Ergodicity2Maximum likelihood2Graphs2Euler characteristic2Inverse functions2Mean–variance optimization2Prime ideals2Coordinate geometry2Separation of variables2Tangent spaces2Invariant subspaces2Categories2Time value of money2Three-dimensional space1Tangent line1Area under curve1Incidence matrix1Network conservation1Line integral of a vector field1Sequence limit definition (ε–N)1Function limit definition (ε–δ)1Comparison test1Error estimate1Alternating series1Zeno’s paradox1Limit nonexistence1Secant line1Local linearization1Tangent plane1Normal vector1Directional derivative1Multivariable limit1Iterated integral1Volume under surface1Moment of inertia1Rectangle partition1Curve fitting in modeling1Discriminant analysis1Factor analysis1Optimization modeling1Duality in linear programming1Differential equation modeling1Common mistakes in mathematical modeling1Integer programming1Multi-objective optimization1Dynamic programming for modeling1Queueing model1Analytic hierarchy process1Poisson distribution1Zero-knowledge proofs1Simplex method1Yoneda lemma1Autocorrelation1Trigonometric identities1Logistic growth1Value at Risk1Proof by contradiction1Direct proof1Analysis of variance1Angles1Rigid motions1Well-posedness1Complete reducibility1Difference equation model1Sequence limit1Nash equilibrium1Verification and validation1Turing patterns1Weak convergence1Quadratic residues1Number theory1Analytic continuation1Absolute value1Almost everywhere1Lebesgue measure1Triangle congruence1Bipartite matching1Chain complexes1Trees1TOPSIS evaluation model1Compact operators1Bounded linear operators1Unique factorization domains1Binary operations1Isolated singularities1Schur's lemma1Area and volume1Matrix norms1Monotone convergence theorem1Mathematical induction1Transition matrices1Chi-squared distribution1Stochastic processes1Source coding1Gaussian curvature1Intermediate value theorem1Catalan numbers1Radians1Axiomatic systems1Non-Euclidean geometry1Reproduction number1Prime number theorem1Inclusion–exclusion1Stationary distributions1Chinese remainder theorem1Extreme value theorem1Solid geometry1Tangent function1Poisson processes1Principal ideal domains1Finite fields1Singular value decomposition1Discrete dynamical systems1Problem formulation1Propositions1Dominated convergence theorem1Newton's method1Inequalities1Necessary and sufficient conditions1Characteristic equations1Logistic map1Percentages1Logistic regression1Orbits1Euler's totient1Stopping times1Convex optimization1Galois theory1Field extensions1Noether's theorem1Sigma-algebras1Weights and roots1Lie algebras1Localization1Integral domains1Lyapunov exponents1Model risk1Wronskian1Chaotic dynamics1Fixed and periodic points1Graph Laplacian1Polynomial interpolation1Social choice1Law of cosines1Bootstrap1Law of sines1Orthogonal complements1Exact differential equations1Approximation algorithms1Path connectedness1Wave equation1Bifurcations1Geodesics1Convex sets1Data provenance1Likelihood1Modules1Discrete-event simulation1Graph connectivity1Self-adjoint operators1Simplicial complexes1Hilbert spaces1Black–Scholes model1Burnside's lemma1Existence and uniqueness for ODEs1Cauchy integral formula1Simply connected domain1Expected utility1No-arbitrage1Runge–Kutta methods1Dimensional similarity1Planar graphs1Polynomials1Function composition1Laplace transform1Spectrum of a ring1Distance formula1Heat equation1Holomorphic functions1Inverse trigonometric functions1Pigeonhole principle1Uniform continuity1Mutual information1Irreducible representations1Natural transformations1Functors1Resonance1Quantifiers1Finite differences1Martingales1Arithmetic operations1Group actions1Ramsey theory1Graph coloring1Euler and Hamilton paths1Itô calculus1Numerical quadrature1Numerical stability1Conditioning1Symmetric encryption1Equivalence relations1Lines and planes1Conic sections1Sheaves1Fractions and ratios1Geometric Brownian motion1Relations1Sets1Binomial theorem1Elliptic curve cryptography1Sturm–Liouville problems1Quotient rings1Polynomial rings1Schemes1Digital signatures1Measurable functions1Banach spaces1Fubini and Tonelli theorems1Tensor products of representations1Quadratic equations1Limits and colimits1Gram–Schmidt process1Open and closed sets1Regular surfaces1Separable equations1Exponential functions1PDE classification1Linearization1Compactness1Integrating factors1Maschke's theorem1Function transformations1Prime factorization1Mathematical modeling process1Condition numbers1Laplace and Poisson equations1Surface integral1Diophantine equations1Cauchy sequences1Mechanism design1Normed spaces1Normal subgroups1Adjunctions1Bolzano–Weierstrass theorem1Exact sequences1Modular inverses1Riemannian metrics1Smooth manifolds1Geometric loci1Quadratic forms1

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Bilibili9:8.606999999999971

Calculus·English

Mathematical Methods in Physics 1-3.2 Cauchy integral formula

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