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IN1900 Scientific Programming with Python

创建日期：2024-08-02 17:24:24

所属分类：计算机computer science

标签： IN1900

Scientific Programming with Python

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Exercises for IN1900

Preface

This document contains a number of programming exercises made for the course

IN1900. The chapter numbers and titles correspond to the chapters of the book

“A primer on Scientific Programming with Python” by Hans Petter Langtangen.

The exercises are meant to be a supplement to the exercise collection in the book,

and most are motivated by applications in science and applied mathematics.

The exercise collection is used for the first time in 2018, and there may be typos

and small errors. If you find any errors, or have other comments or questions

about the exercises, please send them to Joakim Sundnes: [email protected].

Chapter 1

Computing with Formulas

Problem 1.1. Throw a ball

When throwing a ball in the air, the position of the ball can be calculated using

the acceleration of the ball. When neglecting air resistance, the acceleration will

be the negative of the gravitational constant, ?g. The height of the ball relative

to its starting point is

y(t) = v0t ?12gt2,

where v0 is the initial velocity of the ball and t is the time after the throw. The

ball reaches its maximum height at time

tmax =v0g.

Write a program computing the maximum height of the ball, that is y(tmax),

when v0 = 8.2m/s and g = 9.81m/s2. Print the result.

Filename: ball.py

Problem 1.2. Population growth

The growth of a population can often be described by a logistic function

N(t) = B1 + Ce?kt ,

where B is the carrying capacity of the species in the environment, i.e., the

maximum size of the population that the environment can sustain indefinitely.

The constant k tells us something about how fast the population grows, while C

is given by the initial conditions. Let us consider a bacterial colony where we

take the carrying capacity to be B = 50000 and k = 0.2h?1. If the population is

5000 at t = 0, find C and write a code that finds the number of bacteria in the

colony after 24 hours.

Filename: population.py

Problem 1.3. Solve the quadratic equation

Given a quadratic equation

ax2 + bx + c = 0,

the two roots are.

Make a program evaluating the roots of.

Print out both roots with two decimals.

Filename: find_roots.py

Problem 1.4. Forces in the hydrogen atom

There are two kinds of forces acting between the proton and the electron in the

hydrogen atom; Coulomb force and gravitational force. The Coulomb force can

be expressed as,

where ke is Coulomb’s constant, e is the elementary charge, and r is the distance

between the proton and the electron.

The gravitational force can be expressed as

FG = Gmpmer2,

where G is the gravitational constant, mp is the mass of the proton, me is the

mass of the electron, and r is the distance between the particles.

We can use these expressions for FC and FG to illustrate the difference in

strength of these two forces, i.e., the electromagnetic force and gravitational force.

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