Foundations of Physics: Units, Measurements, and Vector Algebra

Every journey into physics and engineering begins with understanding how we measure the universe and describe physical quantities. Mastering units, dimensions, and vectors is the critical first step to solving complex mechanics problems with ease. This text-based course guides you from absolute beginner concepts to a practical working knowledge of physical quantities and vector mathematics. You will build the analytical skills necessary to approach physics problems systematically and eliminate common calculation errors. What you'll learn: Understand the international system of units (SI) and modern standards of measurement; Apply dimensional analysis to verify physical equations and derive relationships between variables; Master scientific notation, significant figures, and basic error analysis in experimental data; Perform vector operations including addition, subtraction, dot products, and cross products; Resolve vectors into components in both two-dimensional and three-dimensional space; Practice solving foundational mechanics problems using systematic mathematical frameworks. You will start with the core definitions of physical quantities, units, and dimensions before progressing to coordinate systems and vector algebra. Through clear written explanations and step-by-step mathematical breakdowns, you will develop a strong intuitive grasp of these essential tools. This course is designed for beginners, high school physics students, and pre-engineering or pre-medical aspirants looking to build a rock-solid foundation in physical mathematics. No prior advanced physics knowledge is required. Start reading today to master the core mathematical language of physics.