1、Theory Analysis,Mathematics Analysis Model Introduction Equation Description,Mathematics Analysis,1. Introduce theme and objective. 2. Describe relative hypothesis, condition or definition. 3. Present primary problems or basic equations. 4. Analyze and get some results. 5. Discuss or infer according

2、 to above results. 3-5 may repeat.,1. Describe background or theory basis of the model. use references 2. List and analyze some basic equations. 3. Describe the model in detail. 4. Explain or discuss the important characteristics of the model. 5. Depict how to apply the model in certain situation wi

3、th an example. 2-5 repeat for each part, sub theme, or stage of the model.,Model Introduction,Layout Punctuation,Equation Description,Notice,Describe the definition of hypothesis or concepts before using them. Present the problem before depicting the equations used. State each sub theme of the theor

4、y with summary at the end of each statement. Express the relationship among sub themes if necessary.,Tense: Present tense for facts. (most) E.g. The solution can be obtained by solving Eq. (2). Future tense for new theme description in new paragraph. E.g. We will solve this problem in the context of

5、 the following model. If X = 0, then the process will ,Past tense for Past work or experiment results of the author of this paper. Hypothesis of original authors.,Voice: Passive voice. Avoid using: It is There is/are “We” as subject.,Sentences: It is supposed that . We suppose that (good) Let us sup

6、pose that Suppose that (good),After substituting this term for y in Equation (4), the equation can be rewritten as follows. After substituting this term for y in Equation (4), We can rewrite the equation as follows. (good) If this term is substituted for y in Equation (4), the equation can be rewrit

7、ten as follows. (good) Substituting this term for y in Equation (4) yields the following equation. (good),The relationship between x and y is now considered. Now let us consider the relationship between x and y. (good) Consider the relationship between x and y. (good) x and y are related in the foll

8、owing way. (good),Sample sentences: Consider the case in which Let us now consider the case Suppose that Let d and V be scalings for the length and width. We assume that under consideration here. If x = 1, then we have the following equations: (equation) Given that m = 1.2, we obtain (equation) The

9、equation for Ag/At becomes (equation) The equation for Ag/At can be written/expressed as Substituting m into Equation 3, we obtain The relationship between m and n is as follows. (equation) A is inversely proportional to B, as shown below.,Eq. 5 takes the form . From this equation, the relation betw

10、een x and y can be expressed as If the same material is used, the above equation reduce to We will now reduce Eq. 3 to a simpler form. On substituting this equation into Eq. 16 and solving for x2, The is defined as. The is given by Upon performing the integration using Eq.19, substituting a+b for x, let z = c/d,