Julia practice in Scientific Computing

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• Peak Reading

  A sensor array overheated for an instant. Report the single highest reading it captured.

  vectors. Free with an account.

• Signal Average

  The detector logged a burst of readings. The control room needs their average before the next sweep.

  vectors. Free with an account.

• Signal RMS

  An audio meter can report signal level using the root-mean-square of its samples. Compute the RMS; perceived loudness also depends on frequency and hearing.

  vectors. Free with an account.

• Total Flux

  Sum signed, already integrated contributions in compatible units. Raw flux densities would need area or time weights before this total.

  vectors. Free with an account.

• Squared vector magnitude

  Compute a real vector's sum of squares. Interpreting this as physical energy would also require the model's units and coefficients.

  vectors, dot-product. Free with an account.

• Peak Magnitude

  A stability check needs the largest deviation in either direction. Return the infinity norm, the maximum absolute value across the vector.

  linear-algebra. Free with an account.

• Running Total

  The fuel log needs a running total after each burn, not just the final figure.

  vectors. Free with an account.

• Vector Length

  Mission control needs the magnitude of the thruster vector before the burn.

  vectors, norm. Free with an account.

• Area Under the Signal

  Integrate a sampled signal with the trapezoidal rule to get the area it swept.

  integration, trapezoid. Free with an account.

• Root Locator

  Calibration needs the square root of a reference value, found by bracketing, not the built-in.

  root-finding, bisection. Free with an account.

• Trapezoid Slice

  Numerical integration adds up trapezoids under the curve. Compute the area of one slice from its two edge heights and width, the building block of the trapezoid rule.

  integration. Free with an account.

• Trend Slope

  Fit a least-squares line to evenly spaced readings and report the slope of the trend.

  least-squares, interpolation. Free with an account.

• Descent Trim

  Drive a control parameter to the setpoint a by gradient descent on a quadratic cost.

  optimization, gradient-descent. Free with an account.

• Euler Step

  An ODE solver marches forward one step at a time. Implement the explicit Euler update: the new state is the old plus step-size times the derivative.

  odes. Free with an account.

• Scalar growth propagation

  Propagate the benchmark y'=y from y(0)=1 with RK4 and compare it with exponential growth. This exercise models one scalar state.

  odes, runge-kutta. Free with an account.

• Precise Area

  Apply Simpson's rule to evenly spaced samples with an odd sample count. Its fourth-order error rate requires sufficient smoothness and a suitable refinement regime.

  integration, simpson. Free with an account.

• Conservation Check

  Evolve the insulated rod and measure the trapezoidally weighted total. Endpoint half weights match this mirror-node discretization.

  heat-equation, validation. Free with an account.

• Dart Estimate

  Estimate pi from seeded random darts. Use the specified generator and draw order so the same runtime can replay the sample.

  monte-carlo. Free with an account.

• Heat Pulse

  Advance a rod temperature field by one simultaneous fixed-end step at r=0.25, preserving the original samples.

  heat-equation, finite-difference. Free with an account.

• Residual Norm

  Compare a computed vector with its target using the L2 norm of their difference. A small residual is a useful diagnostic; conditioning and the model determine what it says about solution error.

  linear-algebra. Free with an account.