Initial training in pure and applied sciences tends to present problem-solving as the process of elaborating explicit closed-form solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closed-form solutions to exist. Unfortunately, most real-life problems are too complex to be amenable to this type of treatment. Numerical Methods and Optimization - A Consumer Guide presents methods for dealing with them.
From Calculus to Computation.- Notation and Norms.- Solving Systems of Linear Equations.- Solving Other Problems in Linear Algebra.- Interpolation and Extrapolation.- Integrating and Differentiating Functions.- Solving Systems of Nonlinear Equations.- Introduction to Optimization.- Optimizing Without Constraint.- Optimizing Under Constraints.- Combinatorial Optimization.- Solving Ordinary Differential Equations.- Solving Partial Differential Equations.- Assessing Numerical Errors.- WEB Resources to go Further.- Problems.