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1、MATHEMATICAL ENGLISHMathematical English，School of Appl.Math.Aim of the Course:Expected progress in the following aspects:.Reading skills of the original mathematical articles and books.Writing skills of mathematical and other scientific articles.Translating skills of mathematical articles:both tran
2、slation from Chinese to English and English to Chinese*Reading,writing and translation of mathematical materials should be brife,simple,exact and easy to be understood 2Some English expressions of numbers:The set of numbers consists of real numbers and pure imaginary numbers shown as followsComplex
3、numbers(C)Pure imaginary numbers(I)Real numbers(R)Rational numbers(Q)Irrational numbers(Q)Integers(Z)Fractions(F)Natural numbers(N),Zero,Negatives of Natural Numbers Notice:Reading of Integers one,ten,hundred,thousand,ten thousand,hundred thousand,million.Ten million,hundred million,billion3Expressi
4、ons of some basic mathematical signs:1.General signs of operation+Plus,positive-Minus,negativeExample:2+3 read as two plus three Example:6-2 read as six minus two Plus or minus,Positive or negative Example:read as equals plus or minus 3Multiplied by,timesExample:read as 5 times 6 or 5 multiplied by
5、6Over or is to or divided byExample:read as 3 over 4,three quarters,3 divided by 44Proportion Example:read as the ratio of 1 to 2Percent,Per centExample:read as 2 PercentPermille,per milleExample:read as 5 per mille2.Basic signs of relationshipsBe equal to,equals Be identical with/to,be equivalent t
6、oExample:read as c is identical with(to)5,c is equivalent to 55Be not equal to Example:c plus d times a is not equals to 0Be approximately equal to3 divided by 7 is approximately Equal to zero point four two nine Example:Be less than,be greater thanExample:a is less than b,c is greater than dBe less
7、 than or equal to,be greater than or equal to Example:x is greater than or equal to minus 3and less than or equal to 8Be far less than,be far greater thanExample:c is far greater than minus 66x belongs to Ax is an element(or a member)of Ax does not belong to Ax is not an element(or a member)of AA is
8、 contained in B or A is a subset of BA contains B or B is a subset of AA cap B or A meet B or A intersection BA cup B or A join B or A union B A minus B or the difference between A and B6Signs of elementary algebraAbsolute value Example:The absolute value of 2 times x plus 1 equals 7Factorial nExamp
9、le:Factorial 5 equals 5 times 4 times 3 times 2 times1The sum of the terms indicated,summation ofExample:The sum of sn from n equals 1 to 5The product of the terms indicatedExample:Product of all an from n equals 1 to infinity7max,min maximum value,minimum valueEample:Maximum value of f(x)Maximum va
10、lue of the series a1 to anPowers and rootsExample:x squaredx cubedx to the fourth,or x to the power fourx to the nth,or x to the power nx to the power minus nx inverseExample:(square)root x,the square root of xcube root(of)x8Imaginary number and two common irrational numbers ratio of the circumferen
11、ce of a circle to its diameter,approximate value 3.14159269Example:Two to the fourth power is sixteenfourth root(of)xnth root(of)xx plus y all squared x over y all squared Some signs in elemetary analysisIntervalsOpen intervalThe open interval refersto the set of all real numbers x between left endp
12、oint a to the right endpoint b(excluding a and b)with axb.Closed intervalThe closed interval refersto the set of all real numbers x between left endpoint a to the right endpoint b(including a and b)with Half open(closed)intervalThe half open interval refersreal numbers x between left endpoint a to t
13、he rightendpoint b(including a but not b)with to the set of all10Function Example:The function of x equals a times the square of x plus b times x plus c,where a is not equal to zero.Approach,tend toExample:approaches(tends to)infinitylimitExample:The limit of f(x)as x tends tox0 is A11infinityExampl
14、e:The limit of xn as n approachesinfinity is a.Example:The limit as x approaches zeroThe limit as x approaches zero from aboveThe limit as x approaches zero from belowthe integral from zero to infinityExample:integral from a to b of f(x)dxdouble integral over the domain Dtriple integral over the domain D12f prime x,f dashed xExample:f double-prime x,f double-dashed xf triple-prime x,f triple-dashed xf four xd by dxExample:df by dxthe partial(derivative)of f with respect to the second partial(derivative)of f with respect to 13