Numerical Analysis - II - Mutual Academy

Advanced Set Theory

In Advanced Set Theory, we study many important ideas related to the size and structure of sets. We begin by discussing equivalent sets and understanding the difference between countable and uncountable sets, along with their examples. We explore cardinal numbers as a way to compare set sizes and learn about Cantor’s theorem which shows that some infinities are bigger than others. We also look at partially ordered sets, chains, and lattices, which help us understand the order and arrangement of elements. The Cantor-Bernstein theorem helps in proving when two sets have the same size. We learn how to add, multiply, and take powers of cardinal numbers. Important logical tools like the Axiom of Choice and Zorn’s Lemma are also studied, along with their equivalence. Finally, we discuss well-ordered sets, ordinal numbers, and how we can perform addition and multiplication with them. All these concepts help us deeply understand infinite sets and the foundations of modern mathematics. Notes ●...

Numerical Analysis - II

Numerical Analysis – II is a continuation of the study of numerical methods used to solve mathematical problems that cannot be solved analytically. This course typically focuses on advanced techniques for solving systems of linear and nonlinear equations, interpolation and approximation, numerical differentiation and integration, and solving ordinary and partial differential equations. In Numerical Analysis – II, students often explore iterative methods like Newton-Raphson, Gauss-Seidel, and Runge-Kutta methods for solving more complex problems. These techniques are essential in scientific computing, engineering simulations, and real-world problem-solving where exact solutions are difficult or impossible to obtain. The course emphasizes algorithm development, error analysis, and implementation using computational tools such as MATLAB or Mathematica.

Notes

📘 Difference Equation and its types (305)
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🎥 Numerical Analysis - II Video Playlist
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Numerical Analysis - II

Numerical Analysis - II

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