Multivariable calculus is a branch of calculus that extends the concepts of differential and integral calculus to functions of more than one variable. Functions of Several Variables: Partial Derivatives: Gradient: Directional Derivative: Tangent Plane and Normal Line: Double and Triple Integrals: Change of Variables in Multiple Integrals: Line Integrals: Surface Integrals: Vector Fields: A vector … Read more
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
Advanced Analysis (Set Theory and Measure Theory) MSc Notes Set theory is a branch of mathematical logic that studies sets, which are collections of objects. It is a fundamental part of modern mathematics and serves as the foundation for many other mathematical disciplines. Set: Element: Subset: Union: Intersection: Complement: Cardinality: Power Set: Set theory provides … Read more
Mechanics B.Sc Notes Classical Mechanics: Definition: Classical mechanics is a branch of physics that deals with the motion of objects and the forces acting upon them. It is based on the principles formulated by Sir Isaac Newton in the 17th century. Key Principles: Newton’s Laws of Motion (First, Second, and Third Laws). Conservation of Energy. … Read more
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
