Skip to content

Commit 4a1b747

Browse files
authored
Remove partial derivatives and related sections
Removed sections on partial derivatives, directional derivative, higher-order formulas, and applications from differentiation documentation.
1 parent c1e1791 commit 4a1b747

1 file changed

Lines changed: 0 additions & 74 deletions

File tree

docs/mathematics/differentiation.md

Lines changed: 0 additions & 74 deletions
Original file line numberDiff line numberDiff line change
@@ -204,54 +204,6 @@ Console.WriteLine($" [{hessian[1,0]:F4}, {hessian[1,1]:F4}]");
204204
```
205205

206206
---
207-
208-
## Partial Derivatives
209-
210-
### Single Partial Derivative
211-
212-
```cs
213-
Func<double[], double> f = x => x[0]*x[0]*x[1] + Math.Sin(x[1]);
214-
double[] point = { 2.0, Math.PI/4 };
215-
216-
// ∂f/∂x₀
217-
double partial0 = NumericalDerivative.PartialDerivative(f, point, variableIndex: 0);
218-
219-
// ∂f/∂x₁
220-
double partial1 = NumericalDerivative.PartialDerivative(f, point, variableIndex: 1);
221-
222-
Console.WriteLine($"∂f/∂x₀ = {partial0:F6}"); // 2x₀x₁
223-
Console.WriteLine($"∂f/∂x₁ = {partial1:F6}"); // x₀² + cos(x₁)
224-
```
225-
226-
### Mixed Partial Derivatives
227-
228-
```cs
229-
// ∂²f/∂x₀∂x₁
230-
double mixed = NumericalDerivative.MixedPartialDerivative(f, point, 0, 1);
231-
Console.WriteLine($"∂²f/∂x₀∂x₁ = {mixed:F6}"); // 2x₀
232-
```
233-
234-
---
235-
236-
## Directional Derivative
237-
238-
The derivative of $f$ in direction $\mathbf{v}$:
239-
240-
```math
241-
D_\mathbf{v}f = \nabla f \cdot \frac{\mathbf{v}}{|\mathbf{v}|}
242-
```
243-
244-
```cs
245-
Func<double[], double> f = x => x[0]*x[0] + x[1]*x[1];
246-
double[] point = { 1.0, 1.0 };
247-
double[] direction = { 1.0, 1.0 };
248-
249-
double directional = NumericalDerivative.DirectionalDerivative(f, point, direction);
250-
Console.WriteLine($"Directional derivative: {directional:F6}");
251-
```
252-
253-
---
254-
255207
## Error Analysis
256208

257209
### Truncation Error
@@ -298,32 +250,6 @@ Typical output shows error decreasing until ~1e-8, then increasing due to roundo
298250

299251
---
300252

301-
## Higher-Order Formulas
302-
303-
### Five-Point Stencil (First Derivative)
304-
305-
Fourth-order accurate:
306-
307-
```math
308-
f'(x) \approx \frac{-f(x+2h) + 8f(x+h) - 8f(x-h) + f(x-2h)}{12h}
309-
```
310-
311-
```cs
312-
double fivePoint = NumericalDerivative.FivePointStencil(f, x, h);
313-
```
314-
315-
### Five-Point Stencil (Second Derivative)
316-
317-
```math
318-
f''(x) \approx \frac{-f(x+2h) + 16f(x+h) - 30f(x) + 16f(x-h) - f(x-2h)}{12h^2}
319-
```
320-
321-
```cs
322-
double secondFivePoint = NumericalDerivative.FivePointSecondDerivative(f, x, h);
323-
```
324-
325-
---
326-
327253
## Applications
328254

329255
### Sensitivity Analysis

0 commit comments

Comments
 (0)