数学表現

1. 動詞

定義する: define
AをBで置き換える: replace A with/by B
AをBという記号で表す: designate A as/by B
表す, 与える: express, give, provide
組み合わせる: combine
消去する: eliminate
適用する: apply
計算する: calculate, compute
〜に等しい: is equal to 〜
〜と同様である: is similar to 〜
考える: consider
一般化する: generalize
整合する, 対応する, 一致する: coincide with
無視する: neglect
A を 式(1) に代入する: insert A into (1), substitute A into (1)
A の代わりに B で置き換える(代用する): substitute B for A
展開する: expand, develop
導入する: introduce
得る: obtain
適用できる, 成り立つ: hold
〜と関係する: is related to 〜
〜のことを言う: refer to 〜
最適化する: optimize
Δx → 0 のとき f(x) に収束する: converge to f(x) as Δx → 0
A + B = C: A plus B equals C. A and B make/are C. The sum of A and B is C. Add B to A.
A – B = C: A minus B equals C. B from A leaves C. The difference of A and B is C. Subtract B from A.
A × B = C: A times B equals C. Multiply A by B. A multiplied by B is/makes C.
A^2 = B: A squared is B.
AとBの積: the product of A and B
A ÷ B = C: A divided by B equals C.
AとBの商: A divided by B, the quotient of A and B
yをxで微分する: differentiate y with respect to x
yのxによる偏微分: partial derivative of y with respect to x
積分する: integrate
xのaからbまでの積分: the integral from a to b of x
xをn乗する: raise x to the nth power
xとyの関数である: is a function of x and y
方程式を解く: solve an equation
式を再整理する: rearrange the equation
〜に比例する: is in proportion to 〜, is proportional to 〜
〜に反比例する: is in inverse proportion to 〜, is inversely proportional to 〜
10^−4のオーダーである: is of the order of 10^−4
高次の項を無視する: ignore/disregard the higher order terms
Aの上限(下限): an upper (lower) bound on A
その方程式の数値積分: numerical integration of the equation
その方程式の解: the solution of/to the equation
式 (1) の形の〜: of the form (1)
方程式系を構築する: develop a system of equations
仮定に反する: contradict the assumption

2. 名詞

関数: function
有効数字: significant figure
変数: variable
( ) 括弧: parentheses
括弧: brakets
{ } 括弧: braces
分数: fraction
分母: denominator
分子: numerator
被積分関数: integrand
約分: reduction
比例定数: constant of proportionality
多項式: polynomial
境界条件: boundary condition
初期条件: initial condition
差分法: finite difference method
有限要素法: finite element method
行列: matrix
行列式: determinant
固有値: eigenvalue
連立方程式: simultaneous equations
変分原理: variational principle
最小二乗法: least-squares method
数値計算: numerical calculation
シミュレーション: simulation
数値積分: numerical integration
不等号の向き: sense of the inequality

3. 例文集

• Let us consider a given A-B alloy. (あるA-B合金を考えてみよう。)
• Consider an A-B binary system. (A-B二元系について検討しよう。)
• Let us consider the transfer of one mole of a solute from the bulk of a phase to its interface with another face.
• Let a solution contain components A, B, C, ... with the mole fractions x_A, x_B, x_C, ...
• The ordinary partition function of an ensemble is defined by the expression below.
• An ideal solution has been defined as one in which the activities of its components are proportional to their mole fractions.
• The equation is expressed in terms of some basic physical quantities.
• The last equation gives 〜
• (By) combining equations (1), (2), and (3), we get equation (4).
• (By) inserting (1) into (2), we obtain the entropy of mixing.
• Substitution of Eqs. (1) and (2) in Eq. (3) leads to Eq. (4).
• we may assume that f(x,y,z) can be developed into a Taylor series with respect to the mole fractions x, y, and z, of the solutes.
• Equation (1) is similar to the virtual equation of stat for a gas.
• It is possible to generalize Eq. (2) by writing it in from 〜.
• Coefficients in a volume series are related to those in a pressure series by eq. (3).
• the equations chosen to fit the data were optimized to give the following expression.
• By using Guggenheim’s maximum term method, the summation in the above expression can be replaced by the maximum term in the series.
• Neglecting the concentrations in the gas phase, we obtain the reduced adsorption as the next equation:
• Let us designate/express/represent by ζ the fraction of surface sites occupied by the solute.
• The mixture is designated/expressed/represented by the formula A.
• Elimination of A between these two equations gives the next expression.
• Applying the mass action law to the above equation, we have found the following relationship.
• For simplicity, we introduce a drastic assumption about the structure of a liquid.
• Let us now consider equilibrium between a liquid and a gaseous phase.
• Finally, combining eq. (1) and eq. (2), we obtain/have 〜.
• The equation holds for solid metals.
• The subscripts 1 and 2 refer to the components
• Taking the limit x → 0, it follows that the function satisfies the condition.
• THe possibility of 〜 can be avoided by using 〜

3. Tips

f(x) = g(x) = sinx      (1)

この場合、式 (1) は複数とする。すなわち eqations (1) とする。