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PlatformYouTube529Bilibili44X3

DisciplineMathematical modeling342Calculus83Algebra57Probability & statistics48Discrete mathematics22Applied mathematics17Geometry6General mathematics1

DifficultyIntroductory382Intermediate132Foundational55Advanced7

StyleWhiteboard262Visual explanation163Lecture149Problem solving2

Length5–15 min330Under 5 min21515–45 min31

TopicMatrices29Derivatives23Vectors16Integrals15Probability14Greatest common divisor13Distributions11Linear transformations10Eigenvalues9Means9Graph theory9Chain rule8Expectation8Time series forecasting8Determinants7Basis7Function limit7Normal distribution7Exponential smoothing forecasting7Calculus6Random variables6Independence6Euclidean algorithm6Modular arithmetic6Method of characteristics6Bayes’ theorem5Permutations5Function graph5Definite integral5Conditional probability5Binomial distribution5Gradient5Partial derivative5Dimensional analysis5Game theory modeling5Partial differential equations5Ordinary differential equations5Fourier transform4Fractions4Power series4Taylor series4Multivariable function4Grey prediction model4Regression modeling4ARIMA modeling4Normalization and standardization in modeling4Entropy weight method4Linear programming4Transportation problem4Cluster analysis modeling4Fourier series4Topological spaces4Brownian motion4Pointwise convergence4Singular values4Linear equations4Boundary value problems4Metric spaces4Quadratic forms4Hypothesis testing3Function approximation3Arc length3Mean value theorem3Lagrange multipliers3Series convergence3Partial sums3Infinite series3Total differential3Jacobian determinant3Variance3Fuzzy 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 chains3Sequence convergence3Uniform convergence3Fields3Initial value problems3Discretization3Gradient descent3Cyclic groups3Graphs3Polynomials3Prime ideals3Coordinate geometry3Three-dimensional space2Linear span2Riemann sums2Incidence matrix2Divergence2Error estimate2Outlier 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 distribution2Universal properties2Analysis of variance2Experimental design2Group representations2Counterexamples2Linear regression2Finite element method2Connectedness2Turing patterns2Compound interest2Absolute value2Bisection method2Unit circle2Binary operations2Differential forms2Laurent series2Mathematical induction2Huffman coding2Pythagorean theorem2Extreme value theorem2Inequalities2Logistic regression2Euler's totient2Cosets and Lagrange's theorem2Subgroups2Conditional entropy2Localization2Graph Laplacian2Tensor products2Wave equation2Polyhedra2Ergodicity2Maximum likelihood2Euler characteristic2Hilbert spaces2Inverse functions2Mean–variance optimization2Distance formula2Heat equation2Separation of variables2Tangent spaces2Quantifiers2Finite differences2Equivalence relations2Conic sections2Quadratic equations2Open and closed sets2Invariant subspaces2Categories2Compactness2Prime factorization2Condition numbers2Time value of money2Bolzano–Weierstrass theorem2Groups2Rings2Tangent line1Area under curve1Network conservation1Line integral of a vector field1Sequence limit definition (ε–N)1Function limit definition (ε–δ)1Comparison test1Alternating 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 proof1Angles1Rigid motions1Well-posedness1Complete reducibility1Difference equation model1Sequence limit1Nash equilibrium1Verification and validation1Weak convergence1Quadratic residues1Number theory1Analytic continuation1Almost everywhere1Lebesgue measure1Triangle congruence1Bipartite matching1Chain complexes1Trees1TOPSIS evaluation model1Compact operators1Bounded linear operators1Unique factorization domains1Isolated singularities1Schur's lemma1Area and volume1Matrix norms1Monotone convergence theorem1Transition matrices1Chi-squared distribution1Stochastic processes1Source coding1Gaussian curvature1Intermediate value theorem1Catalan numbers1Radians1Axiomatic systems1Non-Euclidean geometry1Reproduction number1Prime number theorem1Inclusion–exclusion1Stationary distributions1Chinese remainder theorem1Solid geometry1Tangent function1Poisson processes1Principal ideal domains1Finite fields1Singular value decomposition1Discrete dynamical systems1Problem formulation1Propositions1Dominated convergence theorem1Newton's method1Necessary and sufficient conditions1Characteristic equations1Logistic map1Percentages1Orbits1Stopping times1Convex optimization1Galois theory1Field extensions1Noether's theorem1Sigma-algebras1Weights and roots1Lie algebras1Integral domains1Lyapunov exponents1Model risk1Wronskian1Chaotic dynamics1Fixed and periodic points1Polynomial interpolation1Social choice1Law of cosines1Bootstrap1Law of sines1Orthogonal complements1Exact differential equations1Approximation algorithms1Path connectedness1Bifurcations1Geodesics1Convex sets1Data provenance1Likelihood1Modules1Discrete-event simulation1Self-adjoint operators1Simplicial complexes1Burnside's lemma1Existence and uniqueness for ODEs1Cauchy integral formula1Simply connected domain1Expected utility1No-arbitrage1Runge–Kutta methods1Dimensional similarity1Planar graphs1Function composition1Laplace transform1Spectrum of a ring1Holomorphic functions1Inverse trigonometric functions1Pigeonhole principle1Uniform continuity1Mutual information1Irreducible representations1Natural transformations1Functors1Resonance1Martingales1Arithmetic operations1Group actions1Ramsey theory1Graph coloring1Euler and Hamilton paths1Itô calculus1Numerical quadrature1Numerical stability1Conditioning1Symmetric encryption1Lines and planes1Sheaves1Fractions and ratios1Geometric Brownian motion1Relations1Sets1Binomial theorem1Elliptic curve cryptography1Sturm–Liouville problems1Quotient rings1Polynomial rings1Schemes1Digital signatures1Measurable functions1Banach spaces1Fubini and Tonelli theorems1Tensor products of representations1Limits and colimits1Gram–Schmidt process1Regular surfaces1Separable equations1Exponential functions1PDE classification1Linearization1Integrating factors1Maschke's theorem1Function transformations1Mathematical modeling process1Laplace and Poisson equations1Surface integral1Diophantine equations1Cauchy sequences1Mechanism design1Normed spaces1Normal subgroups1Adjunctions1Exact sequences1Modular inverses1Riemannian metrics1Smooth manifolds1Geometric loci1Channel capacity1Double and triple integrals1Generating functions1Hausdorff spaces1Positive-definite matrices1Systems of ODEs1Attractors1Black–Scholes model1Double integral1Change of variables1Polar coordinates1Riemann zeta function1Cauchy–Riemann equations1Singularity1Graph connectivity1Cryptographic hashes1Algorithmic complexity1Diffie–Hellman key agreement1Measures1Continuous flows1Space curve1Factorization1Biological parameter inference1Undetermined coefficients1Calculus of variations1Bernoulli distribution1Ideals1Affine varieties1Bernoulli equations1Cartesian products1Set operations1

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Bilibili17:14.214999999999918

Calculus·English

Ordinary differential equations 2 Singular solutions & envelopes, Picard sequences, Existence and uniqueness for ODEs

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