Muhammad Danish Mathematics, Physics
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Expertise in mathematics, particularly in algebra, trigonometry, calculus, matrices, and equations, encompasses a comprehensive understanding and proficient application of concepts within these domains.

Algebra
Algebra involves the study of symbols and rules for manipulating these symbols. Expertise in algebra includes:
Linear Equations and Inequalities: Solving single-variable and multi-variable equations and inequalities, understanding their graphical representations.
Polynomials: Operations with polynomials, factoring, and solving polynomial equations.
Functions: Knowledge of different types of functions (linear, quadratic, exponential, logarithmic), their properties, and transformations.
-Systems of Equations: Methods for solving systems, including substitution, elimination, and matrix methods.
Abstract Algebra: Understanding structures such as groups, rings, and fields, and their properties and applications.

Trigonometry
Trigonometry focuses on the relationships between angles and sides of triangles. Expertise in trigonometry includes:
Trigonometric Functions: Deep knowledge of sine, cosine, tangent, and their reciprocals, including their graphs and properties.
Identities and Equations: Proficiency in proving and using trigonometric identities, solving trigonometric equations.
Applications: Applying trigonometric concepts to solve real-world problems, such as in physics and engineering.
Inverse Trigonometric Functions: Understanding and applying the inverses of trigonometric functions.

Calculus
Calculus is the study of change and motion, divided into differential and integral calculus. Expertise in calculus includes:
Differential Calculus: Understanding and applying concepts of limits, continuity, derivatives, and their applications in finding slopes, rates of change, and optimization problems.
Integral Calculus: Mastery of antiderivatives, definite and indefinite integrals, and techniques of integration, including their applications in calculating areas, volumes, and solving differential equations.
Multivariable Calculus: Extending concepts to functions of several variables, partial derivatives, multiple integrals, and vector calculus.

Matrices
Matrices involve the study of rectangular arrays of numbers and their manipulation. Expertise in matrices includes:
Matrix Operations: Proficiency in addition, subtraction, multiplication, and scalar multiplication of matrices.
Determinants and Inverses: Understanding the calculation and interpretation of determinants, finding inverses of matrices.
Linear Transformations: Applying matrices to represent and solve linear transformations.
Eigenvalues and Eigenvectors: Finding and applying eigenvalues and eigenvectors in various contexts, such as stability analysis and diagonalization.

Equations
Solving equations is a fundamental aspect of mathematics. Expertise in equations includes:
Linear Equations: Solving single and systems of linear equations using various methods, including algebraic and graphical approaches.
Quadratic Equations: Solving quadratic equations using factoring, completing the square, and the quadratic formula.
Higher-Order Polynomials: Techniques for solving cubic and quartic equations, understanding the fundamental theorem of algebra.
Differential Equations: Solving ordinary differential equations (ODEs) and partial differential equations (PDEs) using analytical and numerical methods.

General Skills
Problem-Solving: Applying mathematical principles to solve complex and abstract problems.
Proof Techniques: Constructing rigorous mathematical proofs using direct, indirect, and contradiction methods.
Applications: Utilizing mathematical theories in various fields such as physics, engineering, economics, and computer science.
Computational Tools: Using software and programming languages to perform complex calculations and simulations.

Mathematical expertise in these areas requires not only theoretical knowledge but also practical application skills, continuous learning, and the ability to communicate complex ideas effectively.

Subjects

  • Math & Reasoning for Competitive Exams Beginner-Expert

Experience

  • Controlling Officer (Feb, 2024–Present) at Philip Morris International
    Monitoring & Reporting of Factory KPI's.
    Monitoring the PDR's.
    Handling Asset Count.

Education

  • Mechanical Engineering (Sep, 2017–Aug, 2021) from UET LAHORE

Fee details

    Rs500–1,500/hour (US$1.79–5.38/hour)

    My availability is from 6 PM to 12 AM.

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