Mathematics
_The curriculum of Ergopedia's science textbooks embed the teaching of
mathematics in context. Most chapters include one or more mathematical
concepts or techniques introduced alongside, or directly within, their
physical applications. Indexing through hyperlinks in the e-book
provides immediate access to the mathematical tools introduced in each
chapter.
_Examples:
- Algebra is used to solve a diverse variety of physical problems, such as: conceptualizing slope in the equations of motion; locating an image formed by a lens or the calculating the effective resistance of parallel resistors; solving simultaneous equations with multiple unknowns for tension problems in ropes and pulleys; and solving quadratic equations in the equations of motion.
- Geometry and trigonometry--including Pythagorean's Theorem--such as when solving the equations of motion in an inclined plane, or in resolving a force vector into its components.
- Vector mathematics, such as resolving the components of forces, adding and subtracting vectors in motion, and the equations of projectile motion. Advanced vector mathematics is introduced on an intuitive level, such as the dot product (when understanding work and power) or the cross product (when using the right-hand rule for angular momentum or motion of a charged particle in a magnetic field).
- Volume and density are reinforced by measuring them directly and indirectly for a variety of materials, including metals.
- Basics of pre-calculus
are introduced through an intuitive understanding of the relationship between position
and velocity, as well as the difference between average and instantaneous
velocity.
- Mathematics, logic, and scientific inquiry are stressed through the formulation and testing of hypotheses and models.