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# Tag Archives: Calculus

## 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 – changing graph color of plot()

plot() handles color names for RGB color codes. SymPy document doesn’t explain it clearly or sample codes don’t exit. Here is another example.

## 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 – proof of the derivative of sin(x) is cos(x)

In IPython-notebook on the web browser interface, checking value of expression is simply typing the name of expression in the following line.

Posted in GNU/Linux, Python, Science and technologies
Tagged Calculus, cos(x), derivative, mathmatics, python, sin(x), SymPy
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## 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 – plot(): draw many graphs on one window.

Graph in a window that has 0 <= x <= 2. Then, on the same screen, graph for h = -1, -0.5, -0.1, 0.1, 0.5, 1.

Posted in Science and technologies
Tagged Calculus, derivative, graph, plot function, python, SymPy
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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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