Outline of lecture

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We must solve many kinds of differential equations to understand and predict natural phenomena in the environment. Under the condition of practical problems in the environment, however, it is often difficult to obtain a strict solution of differential equations in an explicit form. On the other hand, purely numerical approach, which always gives individual solution under a specified condition, is not convenient to survey the total picture of the system窶冱 response. In this lecture, the weighted residual method (WRM) and its derivatives are introduced to give an idea 窶徂ow to obtain an approximate analytical solution窶� of given differential equation under practical conditions. It is also described that WRM is a general form of mathematics to understand connectedly a variety of mathematical techniques through the idea of orthogonality.