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Scientific Computing and the MATLAB Language

Central South University via XuetangX

Overview

In many fields, such as non-ferrous metals, transportation, chemistry and chemical engineering, aviation and aerospace, financial engineering and bio-medicine, computational challenged are often encountered. For example, we may come across linear and non-linear equations with dozens of variables and complex differential equations, which are known for their complexity and require large amounts of computing to solve. Give the overwhelming computational task, theoretical solutions tended to be unobtainable. However, thanks to the rapid development of computer technology, such challenge now can be effectively met, giving rise to a new interdisciplinary subject known as scientific computing, which has become the third scientific research method after theoretical research and scientific experiment.
Scientific computing aims to provide approximation method to solve engineering and technical problems and other application-based problems through computer programming. It features not only abstractness and rigorousness that characterize mathematics, but also the practicability characterizing computer programming. Thanks to scientific computing software such as MATLAB, it has been convenient and efficient for people to deal with scientific computing problems since the 1980s.
As one of the best scientific computing software, MATLAB integrates the functions of numerical computing, computer algebra, graphic processing, system simulation and program flow control into a unified system environment. It has developed into a programming language widely used in interdisciplinary engineering and scientific research. With the help of MATLAB, people do not need to pay attention to the specific details and calculation formulas which are required by numerical computing methods, nor do they need complicated bottom-level programming. In this way, more efforts can be put into analyzing practical problems and designing solutions, thus greatly improving the efficiency and quality of work and providing an important new approach for scientific research and application-based engineering. In colleges and universities, MATLAB has become a basic computing tool which is enthusiastically embraced in courses by college students and graduate students.
This course is divided into 10 chapters focusing on scientific computing with MATLAB. The 10 chapters are as follows: Basic Knowledge of MATLAB, Manipulating MATLAB Matrices, MATLAB Program Flow Control, MATLAB Plotting, Data Analysis and Polynomial Evaluation, Numerical Calculus and Equations, MATLAB Symbolic Computations, MATLAB Graphical User Interface Design, Simulink System Simulation and External Program Interface.

Syllabus

  • Chapter 0 Getting into MATLAB
    • Course Introduction
  • Chapter 1 Basic Knowledge of MATLAB
    • 1.1 MATLAB System Environment
    • 1.2 MATLAB Numerical Data
    • 1.3 Variables
    • 1.4 MATLAB Matrix Representation
    • 1.5 Matrix Elements Reference
    • 1.6 Basic Operations of MATLAB
    • 1.7 String Processing
  • Chapter 2 MATLAB Matrix Manipulation
    • 2.1 Special Matrices
    • 2.2 Matrix Transformations
    • 2.3 Matrix Evaluations
    • 2.4 Matrix Eigenvalues and Eigenvectors
    • 2.5 Sparse Matrices
  • Chapter 3 MATLAB Program Flow Control
    • 3.1 Programming with Sequence Structure
    • 3.2 Selection Structure with the if Statement
    • 3.3 Selection Structure with the switch Statement
    • 3.4 Loop Structure with the for Statement
    • 3.5 Loop Structure with the while Statement
    • 3.6 Definition and Call of Function File
    • 3.7 Recursive Call of function
    • 3.8 Function Arguments and Variable Scope
  • Chapter 4 MATLAB Plotting
    • 4.1 2-D Line Plots
    • 4.2 Formatting and Annotation
    • 4.3 Other 2-D plots
    • 4.4 3-D Line Plots
    • 4.5 3-D Surface Plots
    • 4.6 Graphics Decoration
    • 4.7 Interactive Plotting Tools
  • Chapter 5 Data Analysis and Polynomial Evaluation
    • 5.1 Statistical Analysis of Data
    • 5.2 Polynomial Evaluation
    • 5.3 Data Interpolation
    • 5.4 Examples of Data Interpolation Application
    • 5.5 Curve Fitting
    • 5.6 Examples of Curve Fitting Application
  • Chapter 6 Numerical Calculus and Solutions of Equations
    • 6.1 Numerical Differentiation and Integration
    • 6.2 Solve System of Linear Equations
    • 6.3 Application Examples of System of Linear Equations
    • 6.4 Solve Nonlinear Equation and Find Extreme Value of Function
    • 6.5 Numerical Solution for Ordinary Differential Equations
    • 6.6 Application Examples of Ordinary Differential Equations
  • Chapter 7 MATLAB Symbolic Computations
    • 7.1 Symbolic Objects
    • 7.2 Symbolic Calculus
    • 7.3 Series
    • 7.4 Solving Symbolic Equations
  • Chapter 8 MATLAB Graphical User Interface Design
    • 8.1 Figure and Axes
    • 8.2 Line and Surface
    • 8.3 Ways to Develop Apps
    • 8.4 App Development Using GUIDE
    • 8.5 App Development Using App Designer
    • 8.6 Examples of App Development
  • Chapter 9 Simulink System Simulation
    • 9.1 Basic Operations of Simulink Simulation
    • 9.2 Creation and Mask of Subsystem
    • 9.3 Design and Application of the S-Function
    • 9.4 Example of Simulink Simulation Application
  • Chapter 10 External Program Interfaces
    • 10.1 Using MATLAB within Excel
    • 10.2 File Operations in MATLAB
    • 10.3 Read and Write MATLAB Data Files From Other Language Applications
    • 10.4 Calling Functions in Other Languages from MATLAB
    • 10.5 Calling MATLAB Functions from Other Language Applications
  • Course Examination

    Taught by

    Weiguo Liu, Xuhui Cai, Geli Lv, and Xiaoxian He

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