Create Aura.xlsx

Author: Web4application

math/Aura.xlsx

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+Simulation Problems
+
+with pd.ExcelWriter("/mnt/data/Aura.xlsx", engine="openpyxl", mode="a", if_sheet_exists="replace") as writer:
+    # Sheet 14: Pure Mathematics
+    pure_math = pd.DataFrame({
+        "Topic": ["Algebra", "Calculus", "Number Theory"],
+        "Formula/Theorem": [
+            "Quadratic Formula: x = (-b ± √(b²-4ac)) / 2a",
+            "d/dx (sin x) = cos x",
+            "Prime Number Theorem: π(n) ~ n / ln(n)"
+        ],
+        "Notes": [
+            "Solves quadratic equations",
+            "Basic derivative rule",
+            "Distribution of primes"
+        ]
+    })
+    pure_math.to_excel(writer, sheet_name="Pure_Mathematics", index=False)
+
+    # Sheet 15: Further Mathematics
+    further_math = pd.DataFrame({
+        "Concept": ["Matrix Multiplication", "Eigenvalues", "Diff Eq"],
+        "Expression": [
+            "[[a,b],[c,d]] * [[e,f],[g,h]]",
+            "det(A - λI) = 0",
+            "dy/dx + Py = Q"
+        ],
+        "Application": [
+            "Transforms and linear systems",
+            "Stability and quantum states",
+            "Model growth/decay"
+        ]
+    })
+    further_math.to_excel(writer, sheet_name="Further_Mathematics", index=False)
+
+    # Sheet 16: Applied Physics
+    applied_physics = pd.DataFrame({
+        "Field": ["Mechanics", "Thermodynamics", "Electromagnetism", "Quantum Physics"],
+        "Equation": [
+            "F = ma",
+            "ΔU = Q - W",
+            "∇·E = ρ/ε₀",
+            "Ψ(x,t) Schrödinger Eq"
+        ],
+        "Notes": [
+            "Newton's 2nd Law",
+            "First Law of Thermodynamics",
+            "Gauss's Law",
+            "Wavefunction evolution"
+        ]
+    })
+    applied_physics.to_excel(writer, sheet_name="Applied_Physics", index=False)
+
+    # Sheet 17: Reasoning Logic
+    reasoning_logic = pd.DataFrame({
+        "Premise": ["All humans are mortal", "Socrates is a human", "If it rains, ground gets wet"],
+        "Conclusion": ["Socrates is mortal", "Valid logical step", "Ground is wet"],
+        "Truth_Value": ["True", "True", "True"]
+    })
+    reasoning_logic.to_excel(writer, sheet_name="Reasoning_Logic", index=False)
+
+    # Sheet 18: Simulation Problems
+    simulation_problems = pd.DataFrame({
+        "Problem": ["Projectile Motion", "Heat Transfer", "Quantum Tunneling"],
+        "Setup": [
+            "v0=20 m/s, θ=45°, g=9.8",
+            "Rod: length=1m, k=200 W/mK",
+            "Particle energy<E barrier"
+        ],
+        "Expected_Result": [
+            "Range ≈ 40.8 m",
+            "Temperature profile along rod",
+            "Nonzero probability of tunneling"
+        ]
+    })
+    simulation_problems.to_excel(writer, sheet_name="Simulation_Problems", index=False)
+
+"/mnt/data/Aura.xlsx"