## Spectral Methods Notes for BS/MS

Spectral methods (SM) are numerical techniques used to approximate solutions to partial differential equations (PDEs) and other mathematical problems. These methods rely on the properties of the spectral decomposition of certain operators, such as the Laplacian operator, to efficiently compute approximate solutions. Spectral Decomposition: Fourier Series: Chebyshev Polynomials: Galerkin Method: Collocation Method: Spectral Accuracy: Applications: … Read more

## Complex Analysis MSc/BS Notes

Complex Analysis MSc/BS Notes Complex analysis is a branch of mathematics that investigates functions of complex numbers. It is a rich and important field with applications in various areas of mathematics and physics. Complex analysis is a vast and rich field with many important topics. These advanced topics build upon the foundational concepts in complex … Read more

## Geometric Function Theory Notes

Geometric Function Theory Notes Geometric Function Theory is a branch of mathematics that deals with the geometric properties of analytic functions, especially those functions defined on the complex plane. Conformal mappings are transformations that preserve angles locally. In Geometric Function Theory, the study of conformal mappings is central. These mappings are often used to map … Read more

## Collision B.Sc Notes Mechanics

Collision B.Sc Notes Mechanics Mechanics: Definition: Mechanics is a branch of physics that deals with the study of motion, the forces that cause motion, and the mathematical description of these motions. It is a fundamental field in classical physics that forms the basis for understanding the behavior of physical objects, from macroscopic bodies to microscopic … Read more

## Abstract Algebra Notes for BS/MSc

Abstract Algebra: Definition: Abstract algebra is a branch of mathematics that studies algebraic structures, which are sets equipped with operations and satisfying specific algebraic properties. Unlike elementary algebra, which primarily deals with arithmetic operations and equations over numbers, abstract algebra focuses on developing general principles that apply to various mathematical structures. Group Theory: Definition: Group … Read more

Advanced Topology-1 covers a variety of concepts and properties related to semi-open sets, mappings, continuity, and various types of topological spaces. Let’s break down and explain each part: Keep visiting our website www.RanaMaths.com Advanced Topology-1

Advanced Partial Differential Equations Notes Advanced Partial Differential Equations (PDEs) refer to a branch of mathematics that deals with the study and solution of partial differential equations that are more complex and sophisticated than those encountered in introductory courses. Partial differential equations involve multiple independent variables and their partial derivatives. Let’s break down and explain … Read more

Advanced Numerical Analysis NotesAdvanced Numerical Analysis involves using sophisticated mathematical techniques and algorithms to solve complex problems in various fields. Explanation to each component given in pdf: In summary This comprehensive overview covers a wide range of numerical analysis topics, providing a solid foundation for understanding and applying advanced numerical methods to solve mathematical problems … Read more

## Advanced Analytical Dynamics Notes for MS/MPhil

Advanced Analytical Dynamics Notes for MS/MPhil Advanced analytical dynamics, often referred to as classical mechanics or theoretical mechanics, is a branch of physics and mathematics that deals with the study of motion and the forces that cause it. It extends and builds upon the principles of Newtonian mechanics, which describe the motion of objects based … Read more

## Numerical Solutions of PDEs I Notes

Numerical Solutions of PDEs are essential in various fields of science and engineering where it is often impossible or impractical to find exact analytical solutions. Some topics in Numerical solution of PDEs: Numerical solution techniques for PDEs are a vast and active area of research, with various methods and algorithms tailored to different types of … Read more

## Linear Algebra BS Notes

Linear algebra is a branch of mathematics that focuses on the study of vector spaces and linear transformations between vector spaces, as well as the properties and structures associated with these concepts. Concepts and topics in linear algebra: Linear algebra provides a foundational framework for understanding and solving a wide range of mathematical and real-world … Read more

## Advanced PDE’s Notes For MS/MPhil

Advanced PDE’s refer to a subset of PDEs that are more complex and challenging than basic or elementary PDEs. These equations often arise in advanced mathematical modeling and have applications in various scientific and engineering disciplines. Advanced Partial Differential Equations (PDEs): Advanced Partial Differential Equations (PDEs) go beyond the elementary equations encountered in introductory courses … Read more

## Viscous Fluid-1 Notes for MS/MPhil

Viscous Fluid-1 Notes Viscous fluid, often referred to as a viscous fluid flow, is a branch of fluid mechanics that deals with the behavior of fluids with internal friction or viscosity. “Viscosity is a property of fluids that describes their resistance to flow. Viscosity is a measure of a fluid’s resistance to deformation or shear … Read more

## Elastodynamics Notes for MS/MPhil

Elastodynamics Notes for MS/MPhil Elastodynamics is a branch of mechanics that deals with the study of the dynamic behavior of elastic materials. It focuses on understanding how solid materials respond to external forces and deformations, particularly when subjected to dynamic loads, such as vibrations, impacts, or waves. Elastodynamics, which falls under the umbrella of continuum … Read more

## Advanced Mathematical Statistics Notes for MS/MPhil

Advanced Mathematical Statistics Notes for MS/MPhil “Advanced Mathematical Statistics” typically refers to a higher-level study in statistical theory that delves into sophisticated methods and theoretical foundations of statistical inference. Explanation of the key components: In summary “Advanced Mathematical Statistics” covers a wide range of sophisticated statistical concepts and methods, emphasizing theoretical foundations and advanced techniques … Read more

## Important Topics to Prepare Mathematical Interviews

Important Topics to Prepare for Mathematical Interviews. Highly recommended notes for preparation for any interview related to mathematics. At the bottom, you can download a pdf. Group Theory Group theory is a branch of abstract algebra that deals with the study of mathematical structures known as groups. A group is a set equipped with a … Read more