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# Tag Archives: mathematics

## Converting rotation matrices of left-handed coordinate system

In left-handed coordinate system, positive angle is clockwise direction. In right-handed coordinate system, positive angle is anti-clockwise direction. I spent many hours to find out how to convert rotation matrices of left-handed coordinate system. The solution is to replace the … Continue reading

## A differential equation on Kahn academy

I began to study Differential equations lately. It has been relentless days. Tools I use: Paper and digital text books Pencil and printing papers Scientific calculator CAS (Computer Algebra System) – Sympy and ipython notebook Knowing Kahn academy site was … Continue reading

Posted in Science and technologies
Tagged Calculus, differential equations, Kahn academy, mathematics
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## sympy – find equations for the lines that are tagent and normal to the curve at (1, 2).

Chapter 2 Practice Exercises, p183

Posted in Python
Tagged Calculus, mathematics, normal line, python, SymPy, tangent line
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## sympy – sawtooth function

Calculus and Analytic Geometry, George B. Thomas and Ross L. Finney Exercises 2.5 81, p163 s = 0.78540 – 0.63662*cos(2*t) – 0.07074*cos(6*t) – 0.02546*cos(10*t) – \ 0.01299*cos(14*t) plot(s, (t, -pi, pi)) dsdt = 1.27324*sin(2*t) + 0.42444*sin(6*t) + 0.2546*sin(10*t) + 0.18186*sin(14*t) … Continue reading

Posted in Python, Science and technologies
Tagged Calculus, cos(x), derivative, mathematics, python, sawtooth function, sin(x), step function, SymPy
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## sympy – appling the chain rule manually to find derivative of a function.

I spent few hours to figure out how to apply the chain rule manually to find derivative of a function due to poor documentation of SymPy. I’m not that smart guy.

## sympy example – finding tangent lines to a function

Chapter 2: Derivatives Exercises 2.2, p130 43. Find the tangents to Newton’s Serpentine (graphed here) at the origin and the point (1, 2). 47. a) Find an equation for the line that is tangent to the curve at point (-1, … Continue reading

Posted in Python, Science and technologies
Tagged Calculus, mathematics, python, SymPy, tangent slope
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## sympy – continuity test of functions

All functions I used here from Chapter 1 Exercises on Calculus and Analytic Geometry (9th Edition) by George B. Thomas, Ross L. Finney. It has discontinuity at 2 of x. Smooth graph of a function means it has continuity in … Continue reading

Posted in Python, Science and technologies
Tagged Calculus, limit, mathematics, python, symbolic, symbolic computation, SymPy
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## IPython notebook installation in Debian Wheezy

$ sudo apt-get install ipython-notebook python-matplotlib Reading package lists… Done Building dependency tree Reading state information… Done python-matplotlib is already the newest version. python-matplotlib set to manually installed. The following extra packages will be installed: ipython-notebook-common libjs-mathjax libpgm-5.1-0 libzmq1 python-mysqldb … Continue reading

## Volume of pyramid

Fig 35, p12, Precalculus Mathmatics In a Nutshell, George F. Simmons Volume of pyramid = (1/3)Bh B is Base area h is height

Posted in Science and technologies
Tagged Blender 2.69, Geometry, George F. Simmons, mathematics, volume of cone
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## An impossible triangle

I study mathematics from time to time. Mathematics is a great tool for science and technologies. I guess nowadays Korean kids at grade three or four study trigonometry I want to have deeper understanding for practical applications. Two sides and … Continue reading

Posted in Science and technologies
Tagged mathematics, the laws of sines, triangle, trigonometry
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