Math can be terrifying for many people. This list will hopefully improve your general knowledge of mathematical tricks and your speed when you need to do math in your head. 1. Multiplying by 9, or 99, or 999 Multiplying by 9 is really multiplying by 10-1. So, 9×9 is just 9x(10-1) which is 9×10-9 which is 90-9 or 81. Let’s try a harder example: 46×9 = 46×10-46 = 460-46 = 414. One more example: 68×9 = 680-68 = 612. To multiply by 99, you multiply by 100-1. So, 46×99 = 46x(100-1) = 4600-46 = 4554. Multiplying by 999 is similar to multiplying by 9 and by 99. 38×999 = 38x(1000-1) = 38000-38 = 37962. 2. To multiply a number by 11 you add pairs of numbers next to each other, except for the numbers on the edges. Let me illustrate: To multiply 436 by 11 go from right to left. First write down the 6 then add 6 to its neighbor on the left, 3, to get 9. Write down 9 to the left of 6. Then add 4 to 3 to get 7. Then, write down the leftmost digit, 4. So, 436×11 = is 4796. Let’s do another example: 3254×11. 3. 4. 5.
Van der Pol oscillatorEvolution of the limit cycle in the phase plane. Notice the limit cycle begins as circle and, with varying μ, become increasingly sharp. An example of a Relaxation oscillator. In dynamics, the Van der Pol oscillator is a non-conservative oscillator with non-linear damping. It evolves in time according to the second order differential equation: History Two dimensional form Liénard's Theorem can be used to prove that the system has a limit cycle. , where the dot indicates the time derivative, the Van der Pol oscillator can be written in its two-dimensional form: Another commonly used form based on the transformation is leading to Results for the unforced oscillator Relaxation oscillation in the Van der Pol oscillator without external forcing. Two interesting regimes for the characteristics of the unforced oscillator are: When μ = 0, i.e. there is no damping function, the equation becomes: When μ > 0, the system will enter a limit cycle. Popular culture See also
Pauls Online Math NotesPictures of MathLots of Jokes - Funny Jokes, Pictures and VideosNBC Learn and Carnegie Learning, Inc. announced today that they are teaming up to produce "Decision 2012: Election Math" – a collection of free online math education resources related to the 2012 election season.Posted on 04/30/2012 12:09 PM NBC Learn, the educational arm of NBC News, and Carnegie Learning, Inc., a leader in research-based math programs for middle school, high school, and post-secondary students, today announced they are teaming up to produce "Decision 2012: Election Math" – a collection of free online math education resources related to the 2012 election season and developed especially for middle and high school teachers and students. "Decision 2012: Election Math" will appear as a Free Resources Special Collection with streaming videos on www.nbclearn.com and linked to interactive math problems on www.carnegielearning.com, beginning in Summer 2012. For full coverage, visit PR Newswire.
OctaveGNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable. Octave is distributed under the terms of the GNU General Public License. Version 4.0.0 has been released and is now available for download. An official Windows binary installer is also available from Thanks to the many people who contributed to this release!
Calculus Online BookLearning the Habits of Mind that Enable Mathematical and Scientific BehaviorMath/Science Matters: Resource Booklets on Research in Math and Science Learning Booklet 2 Issues of Instructional Technique in Math and Science Learning Learning the Habits of Mind that Enable Mathematical and Scientific Behavior By Tina A. Harvard Graduate School of Education This work was supported by a grant from the Exxon Education Foundation to the Harvard Project on Schooling and Children, 14 Story Street, Cambridge, MA 02138. The ideas presented within do not necessarily reflect the policy or position of the supporting agency. Summary Points Knowing the thinking skills relevant to math and science is not enough for children to enact the skills. Øsensitive to opportunities to apply the skills. Øable to perform the skills in the real world. Øinclined to apply the skills. What habits of mind are important to math and science? Øopenness and appreciation for new ideas. Øskepticism and appreciation for evidence, logic. Øconsideration of alternatives. Øcreative use of imagination. Table 1.