PPSC Short questions for interviews, you can also get help from Click here. Questions: Do you know any numerical method for solving ordinary differential equations? What is Newton Raphson’s method? Write the mathematical formula for Newton’s raphson. What are the qualities of a university lecturer? There was an equation given to me and they asked … Read more
Foundations of Mathematics: Some basic mathematics Zero:Zero is neither positive nor negative and is considered an even number. Numbers: Natural Numbers: Number 1: Numbers: Numeral and Place Value: Types of Numbers: Rational Numbers: Irrational Numbers: Real Numbers: Angle Concepts: Types of Angles: Triangles: Types of Triangles (based on Side Length): Types of Triangles (based on … Read more
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
Complex Analysis MSc/BS Notes It 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 analysis … Read more
Linear Algebra New Notes for BS/MSc Scalar: The quantity that have or posses only magnitude, like mass, work, etc. Vector: The quantities that posses both magnitude and direction are called vector quantities. Like displacement, acceleration, velocity, weight etc. Parallel Vector: Two vectors are considered parallel if and only if they can be obtained by multiplying … Read more
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
DIFFERENTIAL GEOMETRY Notes: These are well-written notes by Muhammad Usman Hamid. Easy to understand differential geometry. Differential geometry is a branch of mathematics that combines elements of geometry and calculus. It focuses on the study of geometric properties and structures using the techniques of calculus and differential equations. Differential geometry plays a crucial role in … Read more
Numerical Analysis Notes for BS/MSc written by Muhammad Usman Hamid. He is a brilliant teacher from Sargodha. Numerical analysis is a branch of mathematics that focuses on developing algorithms and methods for solving mathematical problems numerically, typically on a computer. This field is crucial for various applications, including scientific computing, engineering, finance, and many others. … Read more
Calculus and Analytical Geometry Lecture No. 1 The course contents for calculus and analytical geometry are explained below: Limits and Continuity: Definition: In calculus, limits and continuity are fundamental concepts. The limit of a function at a point describes its behavior as the input approaches that point. Continuity refers to the absence of disruptions or … Read more
Complex Analysis Notes: These are well-written notes by Muhammad Usman Hamid. Easy-to-understand Complex Analysis. It is a branch of mathematics that deals with functions of complex numbers, which are numbers of the form (a + bi), where (a) and (b) are real numbers, and (i) is the imaginary unit ((i^2 = -1)). It extends the principles of … Read more
Classical Mechanics Notes: These are well-written notes by Muhammad Usman Hamid. Easy-to-understand classical mechanics. Classical mechanics is a branch of physics that deals with the motion of objects, from everyday objects to celestial bodies, under the influence of forces. It is one of the oldest and most fundamental branches of physics, developed over centuries by scientists such … Read more
Advanced Set Theory Notes: Set theory is the branch of mathematical logics that deals with the sets. The mathematical form of set theory was presented by G. Contor in 1870. A Set is any well-defined collection, list, or class of objects. We are very thankful to student Alshiba Sabar, for providing these notes. We are … Read more
Differential geometry is a branch of mathematics that studies the properties of curves, surfaces, and manifolds in space. It combines techniques from calculus, linear algebra, and topology to investigate the geometry of smooth curves and surfaces. Vector: Scalar: Vector Addition: Scalar Multiplication with a Vector: Position Vector: Unit Vector: Direction Cosine: Scalar Multiplication (with properties): … Read more
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
Calculus and Analytical Geometry Lecture No. 2 In these notes, Calculus 1 at the undergraduate level is well discussed. Relate each concept given in pdf: These concepts bridge the gap between the foundational principles of mathematical reasoning and their application in calculus, where the focus is on understanding and analyzing the behavior of functions and … 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
Calculus and Analytical Geometry Lecture No. 5 In these notes, Calculus 1 at the undergraduate level is well discussed. These notes are handwritten notes; if you find any mistakes, please comment below in the comment section. Federal Urdu University, Islamabad. We invite you to continue exploring our website at www.RanaMaths.com Differentiation Differentiation is a mathematical process that … Read more
Calculus and Analytical Geometry Lecture No. 4 In these notes, Calculus 1 at the undergraduate level is well discussed. These are hand-written written notes. If you come across any errors, kindly provide your feedback in the comments section below. We would like to extend our heartfelt gratitude to Ma’am Nabila Riaz for providing these useful … Read more
Calculus and Analytical Geometry Lecture No. 3 In these notes, Calculus 1 at the undergraduate We would like to extend our heartfelt gratitude to Ma’am Nabila Riaz for providing these useful notes. Ma’am Nabila Riaz is a very talented and energetic lecturer at the Federal Urdu University, Islamabad. Limit: The limit of a function describes the behavior … Read more
Abstract Linear Algebra Notes for BS/MSc Abstract linear algebra, often referred to as advanced or abstract algebra, is a branch of mathematics that extends the concepts of linear algebra to more general algebraic structures. While traditional linear algebra primarily deals with vector spaces over fields (such as real and complex numbers), abstract linear algebra explores … Read more
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
Algebra Notes for BS/MSc Algebra is a fundamental branch of mathematics that deals with symbols, variables, and the rules for manipulating these symbols to solve equations and study mathematical structures. It plays a crucial role in various fields of mathematics, science, engineering, and everyday life. Algebra is a broad area of mathematics that includes various … Read more
Complex Analysis Notes for BS/MSc Complex analysis also known as the theory of functions of a complex variable, is a branch of mathematics that deals with complex numbers and the functions of a complex variable. It explores the properties, functions, and calculus of complex numbers and their extensions. Complex analysis is a branch of mathematics … Read more
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
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
Functional analysis is a branch of mathematics that extends concepts from linear algebra and calculus to infinite-dimensional spaces, particularly vector spaces of functions. It provides a framework for studying spaces of functions, linear operators, and their properties. Functional Analysis is a branch of mathematics that extends and generalizes the concepts of vector spaces and linear … Read more
Topology and functional analysis are two important branches of mathematics that deal with the study of abstract spaces, continuity, and functional relationships. While they are distinct areas of mathematics. They share some connections. They are often used in various mathematical and scientific disciplines. Topology and Functional Analysis courses for BS/MSc: Topology Notes for BS/MSc: Introduction … Read more
Algebra Notes for BS/MSc Algebra is a fundamental branch of mathematics that focuses on the study of mathematical symbols, variables, and the rules governing their manipulation. It plays a crucial role in various fields, including mathematics itself, science, engineering, economics, and more. Algebra Notes for BS/MSc: Algebra, a cornerstone of mathematics, is a diverse field … Read more
Fluid Mechanics II Fluid mechanics is the branch of physics and engineering that deals with the behavior of fluids (liquids, gases, and plasmas) at rest and in motion. It is a fundamental field of study with applications in various industries, including aerospace, civil engineering, chemical engineering, environmental science, and more. Fluid Mechanics II Notes for … Read more
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
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
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
Real Analysis Notes for BS/MSc Real analysis is a branch of mathematical analysis that focuses on the study of real numbers and real-valued functions. It is a fundamental area of mathematics that provides a rigorous foundation for calculus and other branches of mathematics. It deals with the properties and behavior of real numbers, sequences, series, … Read more
Mathematical Physics Notes for BS/MSc “Mathematical physics is a field of science that focuses on using mathematical techniques and methods to describe and understand physical phenomena”. It bridges the gap between theoretical physics and pure mathematics, providing a rigorous framework for modeling, analyzing, and solving complex physical problems. Mathematical physics is a field that combines … Read more
Mathematical Statistics Notes for BS/MSc Mathematical Statistics is a branch of mathematics that deals with the study of statistical concepts, models, and methods using mathematical principles. It provides a rigorous foundation in various fields, including engineering, science, social sciences and economics. Mathematical statistics is a branch of mathematics that deals with the theoretical aspects of … Read more
Prior to delving into the content of Numerical Analysis Notes 2 for BS/MSc, it is essential to thoroughly review Numerical Analysis Notes 1 for BS/MSc. It encompasses a wide range of techniques for solving mathematical problems computationally. Numerical Analysis: Numerical Analysis is a field of study in mathematics that focuses on the development and implementation … Read more
Upon completing Numerical Analysis Notes 1 for BS/MSc, it is imperative to proceed with Numerical Analysis Notes 2 for BS/MSc. Numerical Analysis is a branch of mathematics and computer science that focuses on the development and application of numerical algorithms to solve mathematical problems. It deals with the approximation of mathematical models and the use … Read more
Riemannian geometry notes: It is a branch of differential geometry that focuses on the study of smooth manifolds equipped with Riemannian metrics. It is named after the 19th-century German mathematician Bernhard Riemann. Riemannian geometry has important applications in various areas of mathematics and physics, particularly in the theory of relativity and differential geometry. Some important … Read more
