These Mental Math techniques can be applied to everyday situations such as mentally estimating a grocery bill, calculating the tip at a restaurant, and more.
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Emphasizes acquisition of solution techniques; illustrates ideas with specific example problems arising in science and engineering. Includes applications of vector differential calculus, complex variables; line-surface integrals; integral theorems; and Taylor and Laurent series, and contour integration. This is a Graduate level course.
Quick: What's 25 × 45? How about 742 × 300? Or 4821 ÷ 9? Most of us, when faced with math problems like these, immediately reach for a calculator or a pen. But imagine if you could perform these and other seemingly difficult—but surprisingly easy—calculations right in your head. Seems like an impossible feat? It's not.