 Mathematics in Science

The curriculum of Ergopedia's science textbooks embeds 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. The mathematical concept of slope is directly connected with velocity in the equation of motion. Geometry and trigonometry are connected to a pulley problem when separating force vectors into their components.
Mathematics integrated into Essential Physics:
• 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; 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: solving the equations of motion in an inclined plane; and resolving a force vector into its components.
• Vector mathematics, such as: resolving the components of forces; adding and subtracting vectors in motion; and deriving the equations of projectile motion.  Advanced vector mathematics is introduced on an intuitive level, such as: the dot product, when understanding work and power; and 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, such as 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.