This lesson outlines the course objectives, structure, and assessment methods. It defines what is required for success and explains the critical importance of this material for any student of science or engineering.

This lesson provides a precise definition of physics. It is the fundamental science of matter and energy, distinguished by its reliance on mathematical models and precise measurement to describe reality. This quantitative approach is the basis for all physical science and engineering.

This lesson defines a physical quantity: any property that can be quantified by measurement. It establishes that every quantity consists of a numerical magnitude and a unit. This two-part structure is the fundamental basis for all quantitative science.

This lesson establishes why a single, coherent system of units is non-negotiable for science. It introduces the International System of Units (SI) as the required global standard, highlighting its advantages over other historical or regional systems.

This lesson defines the critical distinction between fundamental and derived quantities. We establish that all measurable properties are either defined independently or are constructed from a small set of base quantities. This hierarchy is the foundation of the SI system.

This lesson identifies the seven fundamental quantities that form the irreducible basis of the SI system. We will define each one in turn. Immediate recall of this complete set is a non-negotiable requirement for any work in the physical sciences.

Physical measurements span vast orders of magnitude. This lesson presents the standard methods for managing this scale: scientific notation (standard form) and SI prefixes. Correct application of these conventions is mandatory for all technical work.

This lesson defines mass as the quantitative measure of inertia. It establishes the kilogram (kg) as the SI base unit for mass and covers the principles of the balance instruments used for its accurate determination. This concept is distinct from weight.

This lesson defines length and establishes its SI base unit, the metre (m). It then covers the correct use and comparative precision of standard laboratory instruments, from the metre rule to the micrometer screw gauge.

This lesson defines time as the measure of the interval between events. It establishes the second (s) as the SI base unit and covers the practical use of timing instruments, like the stopwatch, for experimental work.

This lesson distinguishes the concept of a physical dimension from a unit. It establishes the fundamental dimensions – [M], [L], [T] – and demonstrates the method for deriving the dimensional formula for any quantity. This is the required first step for all analysis.

This lesson introduces the principle of dimensional homogeneity. This is the fundamental rule that for any physical equation to be valid, all its constituent terms must have the exact same dimensions. This concept is the basis for all dimensional checks.

This lesson establishes the critical distinction between scalar and vector quantities. We define scalars by magnitude alone and vectors by both magnitude and direction, providing clear, contrasting examples. This classification is non-negotiable for correct physical analysis.

Vectors do not add like scalars. This lesson covers the formal methods for vector addition, from the graphical head-to-tail rule for visualisation to the precise analytical method of adding components. Mastering this is essential for calculating any resultant vector.

This lesson covers the critical technique of resolving a vector into its perpendicular components using trigonometry. Mastering this process is the non-negotiable prerequisite for performing analytical vector algebra, particularly addition and subtraction.

This lesson introduces unit vectors – dimensionless vectors with a magnitude of one, used solely to specify direction. We will define the standard basis vectors, $\hat{i}$, $\hat{j}$, and $\hat{k}$, and use them to construct a concise and efficient notation for all vector algebra.

This lesson introduces the first method of vector multiplication: the scalar or dot product. We define this operation, which yields a scalar quantity, and cover the methods for its calculation using both vector components and the angle between them.

This lesson introduces the vector (cross) product, an operation that yields a new vector perpendicular to the original two. We will cover the calculation of the resultant vector's magnitude and the use of the right-hand rule to determine its direction, a process essential for analysing torque.

To analyse how vector quantities change with time, we must apply calculus. This lesson covers the differentiation of a vector function with respect to a scalar variable, a process performed on each component. This is the formal method for deriving velocity from position.

This lesson consolidates all course topics into a single, coherent framework. It serves as a final, high-level review of the essential mathematical tools – dimensional analysis, vector algebra, and vector calculus – that you are now expected to command.

This lesson provides a forward look into kinematics, the formal study of motion. It demonstrates how the vector and calculus toolkit you have acquired is immediately applied to describe displacement, velocity, and acceleration. This is the first critical application of these foundational tools.