Alphabeta MathWall-defect estimates and capillary-wave energy — Examples
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1 · Prerequisites
- Absolute and Conditional Convergence; Rearrangement; Products
- Arc Length and Rectifiable Curves
- Binary Operations, Monoids, Groups and Subgroups
- Compactness in Metric Spaces
- Completeness, Completion, and Uniform Continuity
- Complex Coordinate and Path Transport
- Complex Differentiability and the Cauchy–Riemann Equations
- Complex Power Series and Analytic Functions
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- Filters and Ultrafilters
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- Formal parameterized fluid systems and observables
- Foundations of the Real Numbers for Analysis
- Fubini and Change of Variables
- Gaussian Elimination, Elementary Matrices and Reduced Row Echelon Form
- Group Actions, Orbits, Stabilisers and Cayley's Theorem
- Ideals, Quotient Rings and the Isomorphism Theorems for Rings
- Improper and Parameter-Dependent Multiple Integrals
- Inner Product Spaces, Gram-Schmidt, Projections and Adjoints
- Limits of Real Functions
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- Rⁿ as a Normed Space; Vector-Valued Functions
- Roots, Rational Powers, and Classical Inequalities
- Sequences and Limits
- Sequences and Series of Functions; Uniform Convergence
- Series: Convergence and the Nonnegative Tests
- Simple Field Extensions and the Construction of the Complex Numbers
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- The Complex Exponential and Euler's Formula
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- The Divergence Theorem and Classical Stokes
- The Exponential Function
- The Fundamental Theorems of Calculus
- The Inverse and Implicit Function Theorems
- The Inverse Function Theorem Completed
- The Logarithm and General Powers
- The Riemann Integral in Rᵐ and Jordan Content
- The Riemann Integral: Definition and Integrability
- The Total Derivative in ℝᵐ → ℝⁿ
- The ZFC Axioms and the Basic Set Constructions
- Topological Spaces and Continuity
- Topology of ℝ
- Vector Spaces, Linear Subspaces, Span and Direct Sums
- Volumes of Elementary Solids and Solids of Revolution
- Wall-defect estimates and capillary-wave energy
2 · Logical flowchart
3 · Items
Example