Year 3 · 17 years old
Year 3 — Integral, ODEs, Inference, Linear Algebra
The synthesis: integral calculus, ODEs (with the bridge to the Black-Scholes PDE), statistical inference, and introductory linear algebra. Whoever finishes Year 3 is ready for Calculus I in any federal-university engineering program.
JP Math III + Math C · DE Klasse 12 LK · SG JC 2 (H2 Math final)
Schedule by term
Click a term to see Classes and Lessons (each Lesson opens the content). Lessons grouped into Classes didactic groups (3-5 lessons per Class). Or use the tabs below to browse by subject.
Term 9 — Integral Calculus
open →Antiderivative, definite integral, FTC, techniques, applications.
10 lessons · ~32h of study
- ~9hClass A — Antiderivative, definite integral and FTC(3 lessons)
- ~9hClass B — Substitution, integration by parts, partial fractions(3 lessons)
- ~3hClass C — Trigonometric integrals(1 lessons)
- ~9hClass D — Area, volume + synthesis(3 lessons)
Term 10 — Differential Equations
open →1st and 2nd order ODEs, physical models, basic numerical methods.
10 lessons · ~32h of study
- ~9hClass A — Introduction and 1st-order separable/linear ODEs(3 lessons)
- ~6hClass B — Growth, decay, Newton(2 lessons)
- ~9hClass C — 2nd-order ODEs: vibrations and RLC(3 lessons)
- ~6hClass D — Euler's method + synthesis(2 lessons)
Term 11 — Inferential Statistics and Regression
open →Confidence intervals, hypothesis tests, linear regression.
10 lessons · ~32h of study
- ~6hClass A — Sampling and confidence interval(2 lessons)
- ~6hClass B — Hypothesis testing (z, t)(2 lessons)
- ~9hClass C — Simple and multiple linear regression, ANOVA(3 lessons)
- ~9hClass D — Chi-squared, intro to Bayes + synthesis(3 lessons)
Term 12 — Advanced Linear Algebra and Synthesis
open →Vector spaces, eigenvalues, PCA, final integration of the program.
10 lessons · ~32h of study
- ~9hClass A — Vector spaces and transformations(3 lessons)
- ~9hClass B — Eigenvalues, diagonalization, symmetric/orthogonal matrices(3 lessons)
- ~6hClass C — SVD and PCA(2 lessons)
- ~6hClass D — Synthesis (Black-Scholes) + Final workshop(2 lessons)
Lessons organized by subject
Integral Calculus
Antiderivative, definite integral, FTC, integration techniques, applications.
- Lesson 81publishedF'(x) = f(x), indefinite integral notation
- Lesson 82published∫ₐᵇ f(x) dx as Riemann sum limit
- Lesson 83publishedFTC parts 1 and 2, applications
- Lesson 84publishedu-substitution, change of variables
- Lesson 85published∫ u dv = uv - ∫ v du, LIATE
- Lesson 86publishedPartial fraction decomposition, rational functions
- Lesson 87published∫ sin^n cos^m, ∫ sec^n tan^m, identities
- Lesson 88publishedArea between two curves, integration along y
- Lesson 89publishedDisk method, shell method, revolution solids
- Lesson 90publishedSynthesis: 60 mixed integral problems
Differential Equations
1st and 2nd order ODEs, physical models, basic numerical methods.
- Lesson 91publishedy' = f(x,y), order, separability
- Lesson 92publishedy' = g(x)h(y), solution by integration
- Lesson 93publishedy' + p(x)y = q(x), integrating factor
- Lesson 94publishedExponential growth, logistic, predator-prey
- Lesson 95publisheday'' + by' + cy = 0, characteristic equation
- Lesson 96publishedSpring-mass, free, damped, forced oscillations
- Lesson 97publishedResistor + inductor + capacitor circuits, analogy with springs
- Lesson 98publishedyₙ₊₁ = yₙ + h·f(xₙ,yₙ), error analysis
- Lesson 99publisheddT/dt = -k(T-Tₐ), real-world application
- Lesson 100publishedSynthesis: 50 mixed ODE problems
Statistical Inference
Confidence intervals, hypothesis tests, simple linear regression.
- Lesson 101publishedRandom sampling, bias, sample size
- Lesson 102publishedx̄ ± z·σ/√n, interpretation
- Lesson 103publishedH₀, H₁, p-value, type I and II errors
- Lesson 104publishedWhen to use z vs t, degrees of freedom
- Lesson 105publishedy = β₀ + β₁x, least squares, R²
- Lesson 106publishedy = β₀ + β₁x₁ + ... + βₖxₖ, applications
- Lesson 107publishedCompare more than two means, F-statistic
- Lesson 108publishedIndependence test, goodness of fit
- Lesson 109publishedPrior, likelihood, posterior, Bayesian inference
- Lesson 110publishedSynthesis: 60 mixed inference problems
Linear Algebra
Vector spaces, eigenvalues, PCA — final synthesis of the program.
- Lesson 111publishedVectors as elements of a vector space, axioms
- Lesson 112publishedT: V → W, matrix representation
- Lesson 113publishedker(T), im(T), rank-nullity theorem
- Lesson 114publisheddet(A - λI) = 0, geometric interpretation
- Lesson 115publishedA = PDP⁻¹, when diagonalizable, applications
- Lesson 116publishedSymmetric, orthogonal, projection matrices
- Lesson 117publishedA = UΣVᵀ, applications, intuition
- Lesson 118publishedEigendecomposition of covariance, dimensionality reduction
- Lesson 119publishedHeat equation, change of variables, normal distribution
- Lesson 120published40 problems from Years 1–3