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Format: 1 Online-Ressource (XXIII, 323 Seiten) : , Diagramme, Illustrationen.

Edition: Second edition

ISBN: 978-3-030-16877-3

Series Statement: Texts in Computational Science and Engineering 15

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16876-6

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16878-0

Language: English

Subjects: Computer Science , Mathematics

Keywords: Python 3.x ; Programmierung ; Informatik ; Python

DOI: 10.1007/978-3-030-16877-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Langtangen, Hans Petter 1962-

UID:

Format: 1 Online-Ressource (XXIII, 323 Seiten) : , Diagramme, Illustrationen.

Edition: Second edition

ISBN: 978-3-030-16877-3

Series Statement: Texts in Computational Science and Engineering 15

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16876-6

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16878-0

Language: English

Subjects: Computer Science , Mathematics

Keywords: Python 3.x ; Programmierung ; Informatik ; Python

DOI: 10.1007/978-3-030-16877-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Langtangen, Hans Petter 1962-

UID:

Format: 1 Online-Ressource (XXIII, 323 Seiten) , Diagramme, Illustrationen

Edition: Second edition

ISBN: 9783030168773

Series Statement: Texts in Computational Science and Engineering 15

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16876-6

Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-16878-0

Language: English

Subjects: Computer Science , Mathematics

Keywords: Python 3.x ; Programmierung ; Informatik ; Python

DOI: 10.1007/978-3-030-16877-3

URL: Volltext  (kostenfrei)

URL: Volltext  (kostenfrei)

Author information: Langtangen, Hans Petter 1962-

UID:

Format: 1 online resource (350 pages)

Edition: 2nd ed.

ISBN: 9783030168773

Series Statement: Texts in Computational Science and Engineering Ser. ; v.15

Note: Intro -- Preface -- Abstract -- Contents -- List of Exercises -- 1 The First Few Steps -- 1.1 What Is a Program? And What Is Programming? -- 1.1.1 Installing Python -- 1.2 A Python Program with Variables -- 1.2.1 The Program -- 1.2.2 Dissecting the Program -- 1.2.3 Why Use Variables? -- 1.2.4 Mathematical Notation Versus Coding -- 1.2.5 Write and Run Your First Program -- 1.3 A Python Program with a Library Function -- 1.4 Importing from Modules and Packages -- 1.4.1 Importing for Use Without Prefix -- 1.4.2 Importing for Use with Prefix -- 1.4.3 Imports with Name Change -- 1.4.4 Importing from Packages -- 1.4.5 The Modules/Packages Used in This Book -- 1.5 A Python Program with Vectorization and Plotting -- 1.6 Plotting, Printing and Input Data -- 1.6.1 Plotting with Matplotlib -- 1.6.2 Printing: The String Format Method -- 1.6.3 Printing: The f-String -- 1.6.4 User Input -- 1.7 Error Messages and Warnings -- 1.8 Concluding Remarks -- 1.8.1 Programming Demands You to Be Accurate! -- 1.8.2 Write Readable Code -- 1.8.3 Fast Code or Slower and Readable Code? -- 1.8.4 Deleting Data No Longer in Use -- 1.8.5 Code Lines That Are Too Long -- 1.8.6 Where to Find More Information? -- 1.9 Exercises -- Exercise 1.1: Error Messages -- Exercise 1.2: Volume of a Cube -- Exercise 1.3: Area and Circumference of a Circle -- Exercise 1.4: Volumes of Three Cubes -- Exercise 1.5: Average of Integers -- Exercise 1.6: Formatted Print to Screen -- 2 A Few More Steps -- 2.1 Using Python Interactively -- 2.1.1 The IPython Shell -- 2.1.2 Command History -- 2.1.3 TAB Completion -- 2.2 Variables, Objects and Expressions -- 2.2.1 Choose Descriptive Variable Names -- 2.2.2 Reserved Words -- 2.2.3 Assignment -- 2.2.4 Object Type and Type Conversion -- 2.2.5 Automatic Type Conversion -- 2.2.6 Operator Precedence -- 2.2.7 Division-Quotient and Remainder. , 2.2.8 Using Parentheses -- 2.2.9 Round-Off Errors -- 2.2.10 Boolean Expressions -- 2.3 Numerical Python Arrays -- 2.3.1 Array Creation and Array Elements -- 2.3.2 Indexing an Array from the End -- 2.3.3 Index Out of Bounds -- 2.3.4 Copying an Array -- 2.3.5 Slicing an Array -- 2.3.6 Two-Dimensional Arrays and Matrix Computations -- 2.4 Random Numbers -- 2.5 Exercises -- Exercise 2.1: Interactive Computing of Volume -- Exercise 2.2: Interactive Computing of Circumference and Area -- Exercise 2.3: Update Variable at Command Prompt -- Exercise 2.4: Multiple Statements on One Line -- Exercise 2.5: Boolean Expression-Even or Odd Number? -- Exercise 2.6: Plotting Array Data -- Exercise 2.7: Switching Values -- Exercise 2.8: Drawing Random Numbers -- 3 Loops and Branching -- 3.1 The for Loop -- 3.1.1 Example: Printing the 5 Times Table -- 3.1.2 Characteristics of a Typical for Loop -- 3.1.3 Combining for Loop and Array -- 3.1.4 Using the range Function -- 3.1.5 Using break and continue -- 3.2 The while Loop -- 3.2.1 Example: Finding the Time of Flight -- 3.2.2 Characteristics of a Typical while Loop -- 3.3 Branching (if, elif and else) -- 3.3.1 Example: Judging the Water Temperature -- 3.3.2 The Characteristics of Branching -- 3.3.3 Example: Finding the Maximum Height -- 3.3.4 Example: Random Walk in Two Dimensions -- 3.4 Exercises -- Exercise 3.1: A for Loop with Errors -- Exercise 3.2: The range Function -- Exercise 3.3: A while Loop with Errors -- Exercise 3.4: while Loop Instead of for Loop -- Exercise 3.5: Compare Integers a and b -- Exercise 3.6: Area of Rectangle Versus Circle -- Exercise 3.7: Frequency of Random Numbers -- Exercise 3.8: Game 21 -- Exercise 3.9: Simple Search: Verification -- Exercise 3.10: Sort Array with Numbers -- Exercise 3.11: Compute -- 4 Functions and the Writing of Code -- 4.1 Functions: How to Write Them?. , 4.1.1 Example: Writing Our First Function -- 4.1.2 Characteristics of a Function Definition -- 4.1.3 Functions and the Main Program -- 4.1.4 Local Versus Global Variables -- 4.1.5 Calling a Function Defined with Positional Parameters -- 4.1.6 A Function with Two Return Values -- 4.1.7 Calling a Function Defined with Keyword Parameters -- 4.1.8 A Function with Another Function as Input Argument -- 4.1.9 Lambda Functions -- 4.1.10 A Function with Several Return Statements -- 4.2 Programming as a Step-Wise Strategy -- 4.2.1 Making a Times Tables Test -- 4.2.2 The 1st Version of Our Code -- 4.2.3 The 2nd Version of Our Code -- 4.2.4 The 3rd Version of Our Code -- 4.3 Exercises -- Exercise 4.1: Errors with Colon, Indent, etc. -- Exercise 4.2: Reading Code 1 -- Exercise 4.3: Reading Code 2 -- Exercise 4.4: Functions for Circumference and Area of a Circle -- Exercise 4.5: Function for Adding Vectors -- Exercise 4.6: Function for Area of a Rectangle -- Exercise 4.7: Average of Integers -- Exercise 4.8: When Does Python Check Function Syntax? -- Exercise 4.9: Find Crossing Points of Two Graphs -- Exercise 4.10: Linear Interpolation -- Exercise 4.11: Test Straight Line Requirement -- Exercise 4.12: Fit Straight Line to Data -- Exercise 4.13: Fit Sines to Straight Line -- 5 Some More Python Essentials -- 5.1 Lists and Tuples: Alternatives to Arrays -- 5.2 Exception Handling -- 5.2.1 The Fourth Version of Our Times Tables Program -- 5.3 Symbolic Computations -- 5.3.1 Numerical Versus Symbolic Computations -- 5.3.2 SymPy: Some Basic Functionality -- 5.3.3 Symbolic Calculations with Some Other Tools -- 5.4 Making Our Own Module -- 5.4.1 A Naive Import -- 5.4.2 A Module for Vertical Motion -- 5.4.3 Module or Program? -- 5.5 Files: Read and Write -- 5.6 Measuring Execution Time -- 5.6.1 The timeit Module -- 5.7 Exercises -- Exercise 5.1: Nested for Loops and Lists. , Exercise 5.2: Exception Handling: Divisions in a Loop -- Exercise 5.3: Taylor Series, sympy and Documentation -- Exercise 5.4: Fibonacci Numbers -- Exercise 5.5: Read File: Total Volume of Boxes -- Exercise 5.6: Area of a Polygon -- Exercise 5.7: Count Occurrences of a String in a String -- Exercise 5.8: Compute Combinations of Sets -- 6 Computing Integrals and Testing Code -- 6.1 Basic Ideas of Numerical Integration -- 6.2 The Composite Trapezoidal Rule -- 6.2.1 The General Formula -- 6.2.2 A General Implementation -- 6.2.3 A Specific Implementation: What's the Problem? -- 6.3 The Composite Midpoint Method -- 6.3.1 The General Formula -- 6.3.2 A General Implementation -- 6.3.3 Comparing the Trapezoidal and the Midpoint Methods -- 6.4 Vectorizing the Functions -- 6.4.1 Vectorizing the Midpoint Rule -- 6.4.2 Vectorizing the Trapezoidal Rule -- 6.4.3 Speed up Gained with Vectorization -- 6.5 Rate of Convergence -- 6.6 Testing Code -- 6.6.1 Problems with Brief Testing Procedures -- 6.6.2 Proper Test Procedures -- 6.6.3 Finite Precision of Floating-Point Numbers -- 6.6.4 Constructing Unit Tests and Writing Test Functions -- 6.7 Double and Triple Integrals -- 6.7.1 The Midpoint Rule for a Double Integral -- 6.7.2 The Midpoint Rule for a Triple Integral -- 6.7.3 Monte Carlo Integration for Complex-Shaped Domains -- 6.8 Exercises -- Exercise 6.1: Hand Calculations for the Trapezoidal Method -- Exercise 6.2: Hand Calculations for the Midpoint Method -- Exercise 6.3: Compute a Simple Integral -- Exercise 6.4: Hand-Calculations with Sine Integrals -- Exercise 6.5: Make Test Functions for the Midpoint Method -- Exercise 6.6: Explore Rounding Errors with Large Numbers -- Exercise 6.7: Write Test Functions for 04xdx -- Exercise 6.8: Rectangle Methods -- Exercise 6.9: Adaptive Integration -- Exercise 6.10: Integrating x Raised to x. , Exercise 6.11: Integrate Products of Sine Functions -- Exercise 6.12: Revisit Fit of Sines to a Function -- Exercise 6.13: Derive the Trapezoidal Rule for a Double Integral -- Exercise 6.14: Compute the Area of a Triangle by Monte Carlo Integration -- 7 Solving Nonlinear Algebraic Equations -- 7.1 Brute Force Methods -- 7.1.1 Brute Force Root Finding -- 7.1.2 Brute Force Optimization -- 7.1.3 Model Problem for Algebraic Equations -- 7.2 Newton's Method -- 7.2.1 Deriving and Implementing Newton's Method -- 7.2.2 Making a More Efficient and Robust Implementation -- 7.3 The Secant Method -- 7.4 The Bisection Method -- 7.5 Rate of Convergence -- 7.6 Solving Multiple Nonlinear Algebraic Equations -- 7.6.1 Abstract Notation -- 7.6.2 Taylor Expansions for Multi-Variable Functions -- 7.6.3 Newton's Method -- 7.6.4 Implementation -- 7.7 Exercises -- Exercise 7.1: Understand Why Newton's Method Can Fail -- Exercise 7.2: See If the Secant Method Fails -- Exercise 7.3: Understand Why the Bisection Method Cannot Fail -- Exercise 7.4: Combine the Bisection Method with Newton's Method -- Exercise 7.5: Write a Test Function for Newton's Method -- Exercise 7.6: Halley's Method and the Decimal Module -- Exercise 7.7: Fixed Point Iteration -- Exercise 7.8: Solve Nonlinear Equation for a Vibrating Beam -- 8 Solving Ordinary Differential Equations -- 8.1 Filling a Water Tank: Two Cases -- 8.1.1 Case 1: Piecewise Constant Rate -- 8.1.2 Case 2: Continuously Increasing Rate -- 8.1.3 Reformulating the Problems as ODEs -- 8.2 Population Growth: A First Order ODE -- 8.2.1 Derivation of the Model -- 8.2.2 Numerical Solution: The Forward Euler (FE) Method -- 8.2.3 Programming the FE Scheme -- the Special Case -- 8.2.4 Understanding the Forward Euler Method -- 8.2.5 Programming the FE Scheme -- the General Case -- 8.2.6 A More Realistic Population Growth Model. , 8.2.7 Verification: Exact Linear Solution of the Discrete Equations.

Additional Edition: Print version: Linge, Svein Programming for Computations - Python Cham : Springer International Publishing AG,c2019 ISBN 9783030168766

Language: English

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Format: 1 Online-Ressource (332 p.)

ISBN: 9783030168773

Series Statement: Texts in Computational Science and Engineering

Content: Mathematics; Computer mathematics; Numerical analysis; Computer software; Numerical analysis

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Format: 1 online resource (332)

ISBN: 3030168778 , 9783030168773

Series Statement: Texts in Computational Science and Engineering Ser. ; v. 15

Content: Mathematics; Computer mathematics; Numerical analysis; Computer software; Numerical analysis.

Note: English.

Additional Edition: 303016876X

Language: English

Keywords: Electronic books.

DOI: 10.1007/978-3-030-16877-3.

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Format: XXIII, 332 p. 65 illus., 58 illus. in color. , online resource.

Edition: 2nd ed. 2020.

ISBN: 9783030168773

Series Statement: Texts in Computational Science and Engineering, 15

Content: This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

Note: Preface -- 1 The first few steps -- 2 A few steps more -- 3 Loops and branching -- 4 Functions and the writing of code -- 5 Some more Python essentials -- 6 Computing integrals and testing code -- 7 Solving nonlinear algebraic equations -- 8 Solving ordinary differential equations -- 9 Solving partial differential equations -- A Installation and use of Python -- References -- Index.

In: Springer eBooks

Additional Edition: Printed edition: ISBN 9783030168766

Additional Edition: Printed edition: ISBN 9783030168780

Language: English

DOI: 10.1007/978-3-030-16877-3

URL: https://doi.org/10.1007/978-3-030-16877-3

UID:

Format: xxiii, 323 Seiten : , Diagramme, Illustrationen (teilweise farbig).

Edition: Second edition

ISBN: 978-3-030-16876-6

Series Statement: Texts in computational science and engineering 15

Additional Edition: Erscheint auch als Online-Ausgabe ISBN 978-3-030-16877-3

Language: English

Subjects: Computer Science , Mathematics

Keywords: Python 3.x ; Programmierung ; Informatik ; Python

Author information: Langtangen, Hans Petter 1962-

UID:

Format: 1 online resource (332)

Edition: 2nd ed. 2020.

ISBN: 3-030-16877-8

Series Statement: Texts in Computational Science and Engineering, 15

Content: This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

Note: Preface -- 1 The first few steps -- 2 A few steps more -- 3 Loops and branching -- 4 Functions and the writing of code -- 5 Some more Python essentials -- 6 Computing integrals and testing code -- 7 Solving nonlinear algebraic equations -- 8 Solving ordinary differential equations -- 9 Solving partial differential equations -- A Installation and use of Python -- References -- Index. , English.

Additional Edition: ISBN 3-030-16876-X

Language: English

DOI: 10.1007/978-3-030-16877-3

UID:

Format: 1 online resource (332)

Edition: 2nd ed. 2020.

ISBN: 3-030-16877-8

Series Statement: Texts in Computational Science and Engineering, 15

Content: This book is published open access under a CC BY 4.0 license. This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

Note: Preface -- 1 The first few steps -- 2 A few steps more -- 3 Loops and branching -- 4 Functions and the writing of code -- 5 Some more Python essentials -- 6 Computing integrals and testing code -- 7 Solving nonlinear algebraic equations -- 8 Solving ordinary differential equations -- 9 Solving partial differential equations -- A Installation and use of Python -- References -- Index. , English.

Additional Edition: ISBN 3-030-16876-X

Language: English

DOI: 10.1007/978-3-030-16877-3