Programming Tools 2

Section outline

• Select section Programming tools 2

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  Programming tools 2

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  This module, Programming Tools 2, introduces essential computational skills with Scilab that are increasingly vital for mathematics students.

  This course reflects six years of teaching experience in the Department of Mathematics at Djilali Bounaâma University, Khemis-Miliana, and is designed for second-year undergraduate students majoring in Mathematics.

  The goal is not to make students specialists in programming, but to show how Scilab can be used effectively to perform numerical calculations, manipulate vectors and matrices, solve equations, analyze functions, and visualize mathematical concepts efficiently. By integrating programming with mathematical reasoning, students can deepen their understanding, explore complex problems, and develop practical skills that are indispensable in both academic research and real-world applications.

  Each chapter includes exercises with detailed solutions to support classroom learning and laboratory works.

  The material follows the official syllabus outlined in the most recent Canevas for the 2018–2019 academic year. Programming techniques are introduced step by step, with emphasis on two main aspects: mastering commands and practicing them to solve exercises. The presentation is limited to what is necessary, ensuring clarity without oversimplification.

  The primary bibliographic source used in preparing this course is the help documentation of the latest version of Scilab (Scilab-2025.1.0), available at [https://help.scilab.org/docs/2025.1.0/en_US/]. Other works cited in the bibliography have also been used as supporting material to enrich and complement the content presented here.

  Students are expected to have a basic background in algorithms, data structures, and programming languages to fully benefit from this course.

  The recommended weekly schedule includes 1 hour and 30 minutes of lectures and 1 hour and 30 minutes of laboratory work. Assessment consists of continuous evaluation and a final exam. The module carries a coefficient of 1 and is worth 3 academic credits.

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      Module Content

      Chapter 1: Getting Started

      1. Startup and variable help

      2. Variables

      3. Working directory

      4. Saving the work environment

      5. Functions and commands

      Laboratory Work 1

      Solution of Laboratory Work 1

      Chapter 2: Numbers in Matlab with license or Scilab

      1. Natural integers

      2. Representation of real numbers

      3. Complex numbers

      Laboratory Work 2

      Solution of Laboratory Work 2

      Chapter 3: Vectors and Matrices

      1. Operations on vectors and matrices

      2. Basic mathematical functions

      Laboratory Work 3

      Solution of Laboratory Work 3

      Chapter 4: Programming Basics

      1. Scripts

      2. Functions

      3. Control loops

      4. Conditional statements

      5. Reading and displaying variables (Input and Output)

      Laboratory Work 4

      Solution of Laboratory Work 4

      Chapter 5: Polynomials

      1. Polynomials in Matlab with license or Scilab

      2. Zeros of a polynomial

      3. Operations on polynomials

      Laboratory Work 5

      Solution of Laboratory Work 5

      Chapter 6: Graphics in Scilab

      1. Displaying 2D and 3D plots

      2. Graphs of functions

      3. Analytical surfaces

      Laboratory Work 6

      Solution of Laboratory Work 6

      Chapter 7: Symbolic Computation

      1. Using the symbolic toolbox

      2. Expanding and functionalizing an expression

      3. Derivatives and integrals of a function

      4. Calculating the Taylor expansion of a function

      Laboratory Work 7

      Solution of Laboratory Work 7

      Bibliography
• Select section Chapter 1. Getting Started

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  Chapter 1. Getting Started

  In this chapter, we introduce the basic tools needed to start working with Scilab. First, we explain how to start Scilab and how to use the help system to understand variables and commands. Next, we study variables and how to define and manipulate them. We also explain how to manage the working directory and organize files. Then, we show how to save the work environment to keep your results. Finally, we present the main functions and commands used in Scilab.

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      Laboratory Work 1

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      Solution of Laboratory Work 1

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• Select section Chapter 2. Numbers in Scilab

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  Chapter 2. Numbers in Scilab

  In this chapter, we study how numbers are represented and manipulated in Scilab. First, we introduce natural integers and how they are handled in the software. Then, we explain the representation of real numbers and discuss precision and approximation. Finally, we present complex numbers and show how to perform basic operations with them in Scilab.

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      Laboratory Work 2

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      Solution of Laboratory Work 2

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• Select section Chapter 3. Vectors and Matrices

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  Chapter 3. Vectors and Matrices

  In this chapter, we introduce vectors and matrices, which are fundamental objects in Scilab. We study the main operations on vectors and matrices, such as addition, multiplication, and transposition. We also present basic mathematical functions and show how to apply them to vectors and matrices.

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      Laboratory Work 3

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      Solution of Laboratory Work 3

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• Select section Chapter 4. Programming Basics

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  Chapter 4. Programming Basics

  In this chapter, we introduce the basic concepts of programming in Scilab. First, we explain scripts and functions, and how to write and organize programs. Then, we study control loops and conditional statements, which allow us to control the execution of a program. Finally, we present how to read input data and display results (input and output).

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      Laboratory Work 4

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      Solution of Laboratory Work 4

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• Select section Chapter 5. Polynomials

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  Chapter 5. Polynomials

  In this chapter, we study polynomials in Scilab. First, we explain how to define and represent polynomials in the software. Then, we show how to compute the zeros of a polynomial. Finally, we present the main operations on polynomials, such as addition, multiplication, and factorization.

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      Laboratory Work 5

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      Solution of Laboratory Work 5

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• Select section Chapter 6. Graphics in Scilab

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  Chapter 6. Graphics in Scilab

  In this chapter, we introduce graphical tools in Scilab. First, we explain how to display 2D and 3D plots. Then, we show how to draw graphs of functions. Finally, we present analytical surfaces and how to visualize them in three dimensions.

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      Laboratory Work 6

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      Solution of Laboratory Work 6

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• Select section Chapter 7. Symbolic computation

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  Chapter 7. Symbolic computation

  In this chapter, we introduce symbolic computation in Scilab using the symbolic toolbox. First, we explain how to use the toolbox to define and manipulate symbolic expressions. Then, we show how to expand and transform an expression into a function. We also study how to compute derivatives and integrals symbolically. Finally, we explain how to calculate the Taylor expansion of a function.

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      Laboratory Work 7

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      Solution of Laboratory Work 7

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  Bibliography

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