[...]... A. 1 A. 2 A. 3 A. 4 A. 5 A. 6 A. 7 A. 8 A. 9 A. 10 A. 11 A. 12 A. 13 A. 14 A. 15 A. 16 A. 17 A. 18 A. 19 A. 20 A. 21 A. 22 A. 23 A. 24 A. 25 A. 26 Make super- and subclass for a point Modify a function class by subclassing Explore the accuracy of difference formulas Implement a subclass Make classes for numerical differentiation Implement a new subclass for differentiation... Computing with Formulas 1 Our first examples on computer programming involve programs that evaluate mathematical formulas You will learn how to write and run a Python program, how to work with variables, how to compute with mathematical functions such as ex and sin x, and how to use Python for interactive calculations We assume that you are somewhat familiar with computers so that you know what files and folders1... have been removed and many new ones added, and numerous exercises are reformulated after feedback from teachers The associated SciTools package is also extensively upgraded The reorganized and extended material covers Chapter 4.2.4 on command-line parsing, Chapter 5.5 on vectorization, and Appendix E.2.8 on building simulation software for ODEs The new material consists of Chapter 6.2.4 on dictionaries... Vistnes The excellent assistance from the Springer system, in particular Martin Peters, Thanh-Ha Le Thi, Ruth Allewelt, Peggy Glauch-Ruge, Nadja Kroke, Thomas Schmidt, Patrick Waltemate, Donatas Akmanaviˇius, and Edita Baronait˙ , is highly appreciated, and ensured a c e smooth and rapid production of all editions of this book Oslo Hans Petter Langtangen Contents 1 Computing with Formulas ... function for numerical differentiation Make an adaptive Trapezoidal integration rule Compute a polynomial via a product Implement the factorial function Compute velocity and acceleration from position data; one dimension Compute velocity and acceleration from position data; two dimensions Find the max and min values of a. .. Explain why array computations fail Read a two-column data file Read a data file Simplify the implementation of Exer 6.1 Fit a polynomial to data Read acceleration data and find velocities Read acceleration data and plot velocities Find velocity from GPS coordinates Make a dictionary from a. .. dictionaries with default values and ordering, Chapter 9.4 on making a drawing program, Appendix A. 1.7 on integrals as difference equations, Appendix G on using Cython and combining Python with fast C code, and the bioinformatics examples in Chapters 3.3, 6.6, 8.3.4, and 9.5 Four new projects are added: numerical integration (Exercises 3.5– 3.8, 5.38–5.39, A. 16), piecewise constant functions (Exercises...Preface Chapter 5 in the first edition, Sequences and Difference Equations, has now become Appendix A Chapter 6 in the first edition, Files, Strings, and Dictionaries, has been substantially revised Chapter 6.4 on downloading and interpreting data from web pages have now completely new examples Exercises are also reworked to fit with the new examples The material on differential equations in chapters on classes... differentiation Understand if a class can be used recursively Represent people by a class hierarchy Add a new class in a class hierarchy Change the user interface of a class hierarchy Compute convergence rates of numerical integration methods Add common functionality in a class hierarchy Make a class hierarchy for root finding Make a calculus... Now random always refers to Python s random module, while the random module in numpy is normally invoked as np.random (or occasionally as numpy.random) The associated software has been revised similarly Changes to the Second Edition Many typos have been fixed in the third edition, a lot of examples have been improved, some material has been reorganized and extended, some material is new, several exercises . Roose Tamar Schlick Hans Petter Langtangen A Primer on Scientific Programming with Python Third Edition Hans Petter Langtangen Simula Research Laboratory Lysaker,. Patrick Waltemate, Donatas Akma- naviˇcius, and Edita Baronait˙e, is highly appreciated, and ensured a smooth and rapid production of all editions of this