Mathematics with Ali Raza Razzaq

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Law of Sines and Law of Cosines Explained
This post explains the Law of Cosines and the Law of Sines with simple derivations and diagrams, showing how they are used to solve any triangle and how the Pythagorean Theorem appears as a special case.

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Change of Base Formula in Logarithms
This post explains the Change of Base Formula for logarithms in a clear and simple way. It helps convert logarithmic expressions from one base to another, which is essential for solving algebraic and higher-level mathematics problems efficiently.

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Classification of Ordinary, Regular Singular, and Irregular (Essential) Points
This post explains the classification of points in second-order differential equations in a clear and structured way. It covers ordinary (non-singular) points, regular (non-essential) singular points, and irregular (essential) singular points, which are fundamental for understanding series solutions of ODEs. These concepts are especially important for Bessel, Legendre, Laguerre, and Hermite equations.

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Second Order Linear Differential Equations | Fuchs’ Theorem | Frobenius Series Method
A concise and clear explanation of second order linear differential equations covering homogeneous forms, constant & variable coefficients, Fuchs’ theorem, and the Frobenius (series) method.
Ideal for BS, MSc, MPhil Mathematics students and competitive exam preparation.

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🔷 Title
Linear & Non-Linear Differential Equations
Classification, General Form & Linear Combination Theorem
🔷 Description
In this post, you will learn the core theory of Linear and Non-Linear Differential Equations, including:
✔ Proper classification of differential equations
✔ General form of linear differential equations
✔ Difference between linear and non-linear equations
✔ Theorem on linear combination of solutions
These notes are designed for BSc, ADS, MSc, BS, and entry test students who want to build strong mathematical foundations with clarity and precision.
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📌 Title:
Order & Degree of Differential Equations — Explained Simply
📝 Short Description:
Confused about order and degree?
This post gives a clean, step-by-step explanation with well-chosen examples — perfect for BS, MSc, MPhil, and PhD entry test preparation.
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📌 Title:
Solving a Triangle – Complete Guide
📝 Short Description:
This chart explains how to solve a triangle using SSS, SSA, ASA, AAS, and SAS cases with the correct use of the Law of Sines and Law of Cosines. Very helpful for FSC, ICS, A Level, and BS Mathematics students.
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📌 Title (Short):
Monomials, Polynomials & Coefficients
📝 Description (Point-wise):
• This post explains monomials, polynomials, and coefficients with clear definitions.
• Learn how variables, constants, and numerical factors form algebraic expressions.
• Understand binomials and trinomials through simple classification.
• Helpful for Matric, Intermediate, and O-Level students to build strong algebra basics.
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📌 Title:
Classification of Polynomial by Degree
📝 Short Description:
This post explains how polynomials are classified based on their degree, from constant to quintic, with clear examples for better understanding.
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📌 Title:
Average vs Instantaneous Rate of Change | Calculus Basics
📝 Description:
Confused between average and instantaneous rate of change?
This post explains both concepts with clear definitions, formulas, and diagrams—perfect for intermediate and BS students.
💬 Comment “YES” if you want more calculus concepts.
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