Foundations of Computational Mathematics with Python

Ever wondered how computers solve complex mathematical problems, from simulating physical systems to analyzing data? This course demystifies the core algorithms that power modern scientific computing. You will gain a solid understanding of fundamental numerical methods and learn how to implement them effectively in Python. You'll move beyond theoretical formulas to write practical code that approximates solutions, analyzes data, and models dynamic systems, building a strong foundation for further study in data science, engineering, and quantitative fields. What you'll learn: - Understand the principles of numerical analysis, including error, stability, and convergence. - Apply numerical methods to solve systems of linear equations and find eigenvalues. - Learn to approximate functions using interpolation and perform numerical integration. - Implement algorithms to find the roots of equations and optimize functions. - Solve ordinary differential equations numerically to model real-world phenomena. - Utilize Python libraries like NumPy and SciPy to perform efficient numerical computations. - Practice building computational models from mathematical descriptions. The course begins with the essential concepts of computational mathematics and an introduction to scientific programming in Python. You will then progress through key topics such as linear algebra, interpolation, and optimization, applying each concept through written exercises. This course is designed for absolute beginners. No prior experience in advanced mathematics or computational programming is required, making it ideal for students, aspiring engineers, and data scientists. Start your journey into the world of numerical computing today.