This detailed treatment pioneers the adaption of the method of finite elements from engineering to econometric models useful in analyzing risk factors in financial problems, e.g., pricing options. With examples and case studies, Topper (a manager with a German company specializing in financial and commodity risk consulting) introduces both linear differential equation-based and nonlinear methods "without being too rigorous in a mathematical sense." Technical appendices present analyses based on calculus, stochastics, and linear algebra; and introduce PDE2D, a general purpose partial differential equation solver.