College10 topics · 40h

Calculus I

Limits, derivatives, and integrals — the complete first-semester calculus sequence, organized as a prerequisite DAG.

0/10

01LimitsCurrent

30 min Difficulty 2/5

02Continuity

25 min Difficulty 2/5

03The Derivative

35 min Difficulty 3/5

04Differentiation Rules

40 min Difficulty 3/5

05Chain Rule

35 min Difficulty 4/5

06Applications of Derivatives

45 min Difficulty 4/5

07Integration Basics

40 min Difficulty 3/5

08Substitution Rule

35 min Difficulty 4/5

09Integration by Parts

30 min Difficulty 4/5

10Final Review

60 min Difficulty 5/5

College10 topics · 45h

Calculus II

Integration techniques, applications, and infinite series — the second-semester calculus sequence.

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01Improper Integrals

40 min Difficulty 4/5

02Trigonometric Integrals

35 min Difficulty 4/5

03Trigonometric Substitution

40 min Difficulty 4/5

04Partial Fractions

45 min Difficulty 4/5

05Applications of Integration

45 min Difficulty 3/5

06Separable ODEs

30 min Difficulty 3/5

07Sequences

35 min Difficulty 3/5

08Series & Convergence Tests

55 min Difficulty 5/5

09Power Series

45 min Difficulty 4/5

10Taylor Series

50 min Difficulty 5/5

College10 topics · 45h

Calculus III

Multivariable and vector calculus — from vectors in space to the fundamental theorems of Green, Stokes, and Gauss.

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01Vectors & 3D GeometryCurrent

45 min Difficulty 3/5

02Vector Functions

40 min Difficulty 3/5

03Functions of Several Variables

40 min Difficulty 3/5

04Partial Derivatives

40 min Difficulty 4/5

05Chain Rule (Multivariable)

40 min Difficulty 4/5

06Directional Derivatives & Gradient

45 min Difficulty 4/5

07Double Integrals

45 min Difficulty 4/5

08Double Integrals in Polar

35 min Difficulty 4/5

09Triple Integrals

40 min Difficulty 4/5

10Vector Calculus

60 min Difficulty 5/5

College10 topics · 45h

Ordinary Differential Equations

From first-order equations to Laplace transforms and series solutions — the complete ODE toolkit.

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01What Is a Differential Equation?Current

25 min Difficulty 2/5

02Separable Equations

30 min Difficulty 3/5

03Linear First-Order Equations

35 min Difficulty 3/5

04Exact Equations

35 min Difficulty 4/5

05Second-Order Linear Equations

40 min Difficulty 4/5

06Undetermined Coefficients

35 min Difficulty 4/5

07Variation of Parameters

35 min Difficulty 4/5

08Systems of ODEs

45 min Difficulty 5/5

09Laplace Transforms

45 min Difficulty 5/5

10Series Solutions

45 min Difficulty 5/5

Graduate10 topics · 50h

Partial Differential Equations

The classical equations of mathematical physics — heat, wave, and Laplace — solved by separation, series, and transforms.

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01What Is a PDE?Current

30 min Difficulty 3/5

02First-Order PDEs

35 min Difficulty 4/5

03The Heat Equation

40 min Difficulty 4/5

04The Wave Equation

40 min Difficulty 4/5

05Laplace's Equation

35 min Difficulty 4/5

06Separation of Variables

45 min Difficulty 5/5

07Fourier Series

45 min Difficulty 4/5

08Sturm–Liouville Theory

40 min Difficulty 5/5

09The Fourier Transform

45 min Difficulty 5/5

10Green's Functions

45 min Difficulty 5/5

Graduate10 topics · 50h

Numerical PDEs

Finite differences, volumes, and elements — turning PDEs into computations that actually converge.

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01Finite Difference Approximations

35 min Difficulty 3/5

02Explicit Schemes for the Heat Equation

40 min Difficulty 4/5

03Implicit Schemes

40 min Difficulty 4/5

04Numerical Wave Equation

40 min Difficulty 4/5

05Solving Elliptic Equations

45 min Difficulty 4/5

06Consistency, Stability, Convergence

40 min Difficulty 5/5

07Finite Volume Methods

40 min Difficulty 4/5

08Introduction to Finite Elements

45 min Difficulty 5/5

09Advection Schemes

35 min Difficulty 4/5

10Iterative Solvers for Large Systems

45 min Difficulty 5/5