Multivariable • Differential Equations • Vector Calculus • Turnitin Report Included
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Identifying governing equations, domain boundaries, initial/boundary conditions, and coordinate systems.
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Task: Find stationary fixed points, evaluate Jacobian stability (eigenvalues/eigenvectors), derive closed-form invariant orbits, and simulate phase-plane trajectories using `ode45` in MATLAB.
lotka_volterra_phase.m, LaTeX derivation PDF, phase portrait vector plot.Task: Maximize $f(x,y,z) = x^2 y z$ subject to ellipsoidal constraint $g(x,y,z) = x^2/4 + y^2/9 + z^2/16 = 1$, formulate gradient system $\nabla f = \lambda \nabla g$, and classify critical points with bordered Hessian.
lagrange_multiplier.m, 3D contour surface plot, LaTeX proof.Task: Compute surface flux $\iint_S \mathbf{F} \cdot d\mathbf{S}$ for $\mathbf{F} = \langle 2x y, y z^2, x^2 z \rangle$ over a closed cylinder bounded by $x^2+y^2 \le 4$ and $0 \le z \le 3$, and verify equivalence via volume triple integral $\iiint \nabla \cdot \mathbf{F} \, dV$.
divergence_theorem.m, cylindrical coordinate step proof, 3D vector field.Task: Compute Fourier coefficients ($a_0, a_n, b_n$) for a square wave with period $2\pi$, analyze harmonic convergence, quantify the 8.95% overshoot of the Gibbs phenomenon, and plot N-harmonic partial sums in MATLAB.
fourier_gibbs_sim.m, harmonic convergence table, step-by-step integral proof.Why mathematics professors easily spot AI-generated answers and how verified step-by-step solutions protect your grade.
| Evaluation Criteria | MATLABSolutions | Raw AI (ChatGPT) | Generic Freelancers |
|---|---|---|---|
| Step-by-Step Algebraic & Integral Proofs | Full LaTeX Formatted Proofs | Skipped Steps & Sign Errors | Illegible Handwritten Notes |
MATLAB Numerical Verification (ode45) |
100% Tested MATLAB Scripts | Syntax Errors & Bad Matrix Dims | No Code Verification |
| Turnitin Plagiarism Certificate | 0% Plagiarism Report Attached | Flagged by AI Detectors | Copied from Chegg / Slader |
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.m Files
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Single-variable limits, derivatives, integration methods & simple 1st-order ODEs.
Double/Triple integrals, vector fields (Stokes/Gauss), and non-linear ODE systems.
ode45 / phase-plane scriptFourier-Bessel series, boundary value PDEs & Graduate Applied Mathematics.
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