## Mathematics for Chemical Engineering IBack JP / EN

Numbering Code Year/Term U-ENG27 27302 LJ55U-ENG27 27302 LJ76 2021 ・ Second semester 2 Lecture Japanese Thu.1 NAGAMINE SHINSUKE (Graduate School of Engineering Associate Professor)TANIGUCHI TAKASHI (Graduate School of Engineering Associate Professor) The aim of this class is to learn the fundamental mathematics commonly used in Chemical Process Engineering, Chemical System Engineering, such as ordinary differential equations, Laplace transformation, methods to solve differential equations by using Laplace transformation, and vector analysis. The style of the class is mainly lecture style. To attain the mathematical knowledge and skill how to calculate a line, surface and volume integrals, and to calculate differentiations of scalar and vector fields, and to solve ordinal differential equations by using Laplace transformations. Vector Analysis, (7-times) We learn the following items: 1. Vector Analysis (including differentiation of vectors) 2. Integration of vectors Integral Theorem (Gauss divergence Theorem, Stokes Theorem) Ordinary differential Equation, (4-times) We learn that various physical phenomena seen in our daily life can be described by ordinary differential equations. As a method to solve 1st and 2nd order ordinary differential equation, the following methods will be learned : 1. Method of separation of variables 2. Method of variation of parameters Laplace Transformation, (3-times) After learning the historical background and the discovery of Laplace transformation, we learn how to solve ordinal differential equations and integral equations by using Laplace transformation, and also learn applications of Laplace transformation to definite integration. Confirmation of the level of attainment, (1-time) Confirmation of the level of attainment Comments on the term-end Exam Grade will be evaluated by (i) the examination at the end of semester and (ii) homework during semester. Basic knowledge on differentiation, integral, matrix operations After each class of vector analysis, homework is given to students, and their solution will be shown at the class in two weeks. It is highly recommended that students solve them before the class. ベクトル解析 (理工系の数学入門コース 3), 戸田 盛和, (岩波書店), ISBN:4000077732ラプラス変換と常微分方程式, 布川 昊, (昭晃堂), ISBN:4785670215 自然の数理と社会の数理, 佐藤 總夫, (日本評論社), ISBN:4535603014化学者のための数学十講, 大岩 正芳, (化学同人), ISBN:4759800085