Jacobian Matrix Definition Determinant Definition $C^1$ Function Definition Weak Euler-Lagrange Equation Implies the Classical Euler-Lagrange Equation Under Regularity Analysis Sequential Characterization of Compact Operators Analysis Closed Ideals of $C_0(X)$ Analysis Dual of a Subspace Analysis Integration By Parts Integration Sequential Characterisation of Schwartz Convergence Functional Analysis Limit Equals Limit Superior for Convergent Real Sequences Analysis Holomorphicity of the Resolvent Analysis Analysis Area