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Computational Mathematics

Partial Differential Equations

Advanced mastery of computational approaches to partial differential equations. Focus on judgment, restraint, and calibration under ambiguity.
Goal:
Learn how PDEs are solved computationally.
3Lessons
6Micro-lessons
AdvancedDifficulty
Lesson 1

Boundary Conditions and Unexpected Instability

Judging when boundary choices create instability in computational PDEs.
Start2 Micro-lessons

Micro lesson 1
Ambiguous Boundary Placement
Micro lesson 2
Overfitting to Boundary Data
Lesson 2

Discretization Trade-offs and Hidden Errors

Calibrating discretization decisions to avoid compounding errors.
Start2 Micro-lessons

Micro lesson 1
Grid Refinement Without Calibration
Micro lesson 2
Ignoring Nonlinear Effects in Discretization
Lesson 3

Long-Term Effects of Numerical Schemes

Recognizing delayed consequences and feedback loops in numerical PDE solutions.
Start2 Micro-lessons

Micro lesson 1
Scheme Selection Under Uncertainty
Micro lesson 2
Delayed Feedback and Error Amplification