This course, led by P.B. Sunil Kumar from the Department of Physics at IIT Madras, provides a comprehensive introduction to numerical methods and programming.
The curriculum includes:
Students will gain practical skills through lectures and examples, empowering them to apply these methods effectively across various scientific applications.
This module introduces programming basics, essential for anyone starting in computational science. You'll learn:
Mastering these concepts will lay the groundwork for more advanced computational techniques.
This module delves into pointers, a critical concept in programming that allows for more efficient data manipulation. Key topics include:
By mastering pointers, you will enhance your ability to write complex and efficient programs.
In this module, you will learn about the relationship between pointers and arrays. Topics include:
Understanding this relationship will improve your programming skills and efficiency.
This module covers external functions and argument passing, crucial for modular programming. Key aspects include:
Learning these concepts will promote better code organization and reusability.
This module introduces the representation of numbers in programming, which is essential for accurate computations. Key topics include:
Understanding numeric representation is vital for preventing errors in calculations.
This module focuses on numerical error, a crucial aspect of computational methods. You will learn about:
Comprehending numerical error will enhance the reliability of your computational results.
This module covers error propagation and stability, essential for understanding how errors affect computations. Key topics include:
Mastering these concepts will improve your ability to develop robust computational methods.
This module introduces polynomial interpolation and its fundamental concepts. You will explore:
Understanding these concepts will equip you with techniques to estimate values between known data points.
This module continues the study of polynomial interpolation with advanced techniques. You will learn about:
These advanced techniques will enhance your ability to handle complex interpolation problems.
This module addresses errors in interpolation polynomials, helping you understand their impact. Key topics include:
By understanding these errors, you will improve the accuracy of your interpolation results.
This module further explores polynomial interpolation, focusing on practical applications. You will learn:
Practical experience will reinforce your understanding of polynomial interpolation techniques.
This module introduces cubic spline interpolation, a powerful method for smooth curve fitting. Key topics include:
Mastering cubic spline techniques will enhance your data fitting capabilities.
This module focuses on data fitting techniques, starting with linear fitting. You will discover:
Understanding linear fitting will form the basis for more complex data analysis techniques.
This module continues the exploration of linear fitting, emphasizing advanced techniques and applications. Key topics include:
Mastering these advanced techniques will allow for robust data analysis.
This module covers non-linear data fitting techniques, enhancing your analytical skills. You will learn about:
Understanding these techniques will improve your ability to model complex datasets accurately.
This module introduces matrix elimination methods, essential for solving linear systems. Key topics include:
Mastering these methods will enhance your capabilities in solving complex linear equations.
This module focuses on solutions to linear equations, a key aspect of numerical methods. You will learn about:
Understanding these methods will improve your problem-solving skills in numerical analysis.
This module addresses matrix elimination techniques, enhancing your understanding of solving linear systems. Key topics include:
Mastering these techniques will enable efficient solutions to complex linear systems.
This module introduces eigenvalues and their significance within linear algebra. You will explore:
This foundational knowledge is crucial for analyzing complex systems in various disciplines.
This module continues the study of eigenvalues, focusing on their applications and implications. Key topics include:
Understanding these concepts is essential for advanced studies in systems analysis and modeling.
This module introduces methods for solving non-linear equations, a core concept in numerical methods. Key topics include:
Mastering these methods will enhance your analytical skills in complex problem-solving.
This module focuses on Newton's method for solving non-linear equations, providing depth in numerical techniques. Key topics include:
Mastering this method enhances your ability to tackle complex non-linear problems.
This module explores various methods for solving non-linear equations, enhancing your analytical toolkit. Key topics include:
By mastering these methods, you will improve your ability to address complex numerical challenges.
This module focuses on systems of non-linear equations, a critical area in numerical methods. You will learn about:
Mastering these systems will enhance your ability to solve complex problems in computational science.
This module introduces numerical differentiation, a vital skill in computational methods. Key topics include:
Understanding these concepts will improve your analytical capabilities in various scientific fields.
This module covers high-order derivatives from difference formulas, enhancing your understanding of numerical methods. Key topics include:
Mastering these concepts will expand your analytical tools for solving complex problems.
This module introduces numerical integration, an essential area in computational methods. Key topics include:
Mastering these principles will enhance your computational skills in scientific research.
This module compares various numerical integration rules, helping you understand their effectiveness. Key topics include:
By mastering these comparisons, you will improve your decision-making skills in numerical integration.
This module introduces Gaussian rules for numerical integration, a vital topic in computational methods. Key topics include:
Mastering Gaussian integration will enhance your computational capabilities in analysis.
This module compares different Gaussian rules for numerical integration, enhancing your understanding of their effectiveness. Key topics include:
By mastering these comparisons, you will improve your proficiency in numerical integration.
This module covers solving ordinary differential equations (ODEs), a fundamental topic in numerical methods. Key topics include:
Mastering ODEs will enhance your analytical skills in scientific research.
This module continues with solving ordinary differential equations, emphasizing advanced techniques. Key topics include:
Mastering these advanced techniques will strengthen your problem-solving skills in dynamic systems analysis.
This module covers adaptive step size Runge-Kutta schemes for solving ODEs, enhancing your numerical methods toolkit. Key topics include:
Mastering adaptive methods will enhance your ability to solve complex ODEs effectively.
This module introduces partial differential equations (PDEs), a key area in advanced numerical methods. You will learn:
Understanding PDEs will enhance your capacity to model complex systems.
This module focuses on explicit and implicit methods for solving PDEs, a crucial area in numerical analysis. Key topics include:
Mastering these methods will improve your PDE solving capabilities in research.
This module introduces the Crank-Nicholson scheme for solving PDEs with two spatial dimensions, enhancing your numerical methods toolkit. Key topics include:
Mastering this technique will improve your efficiency in solving complex PDEs.
This module introduces Fourier transforms, a critical tool in numerical analysis. Key topics include:
Mastering Fourier transforms will enhance your analytical skills in various scientific applications.
This module focuses on fast Fourier transforms (FFT), an essential algorithm in numerical methods. Key topics include:
Mastering FFT will significantly improve your computational efficiency in handling complex datasets.