数学猜题（Mathematical guess）.doc

数学猜题（Mathematical guess） **2011 math must be an exam question: First, Green, Gauss, or, Stokes three formulas 1. How can Greens formula be proved? (see several books) 2. What are the conditions for the use of Green and Gauss? What about singularities? (dig holes ~!) 3, Stokes formula how to remember? When should I use it? (surface area easy to find or can produce symmetry, rotation, bringing into) Two. Calculus mean value theorem 1, how can Rolles theorem be used again and again? (constantly creating equal value ends) 2. How does Rolles theorem function? (addition subtraction multiplication, division, function and derivative index) 3. How do you combine all the mean theorems? (break the interval with the middle value, and then use the mean value theorem) Three, constant series, convergence, divergence, discrimination 1, what are the common Counterexamples in the abstract technology discrimination method? (harmonic series, + 1 alternating series, harmonic alternating series) 2. Do I remember clearly the convergence and divergence of mixed series? 3, in the identification of convergence and dispersion, I pay attention to the positive series? 4, judge convergence and dispersion, how to choose the appropriate method according to the form of an? 5. How many series are used as a basis for comparison? Do they remember what they mean? (P series, geometric series, logarithmic P Series) 6, including trigonometric series appeared, how to do? (the Equivalent Infinitesimal Substitution (n^2+a^2) of the sin square root of PI is conditional convergence) Four, the symmetry theorem, rotation theorem and bringing theorem in integral 1. How should symmetry be used? How do you realize the use of symmetry? (before you do any integral, you must observe the interval or region!!)! 2, what are the conditions for the use of the rotation theorem? What is the function of it in different integrals? (of regions relating to ISO surfaces, lines, symmetries, and functions that can be disassembled i