In engineering, mathematics is the tool used in applying physics to engineering.
Physics is not applied math in the same sense that engineering is applied physics. In fact, math supports both engineering and physics, A principle or discovery of physics is applied by engineering to the conditions of the real world by using mathematics on the properties of the materials of the real world (physics defines a lever and the ratio of forces involved, engineering picks a material like steel and checks to see whether the forces involved will damage a particular design in steel including a safety factor. One aspect of math allows the definition of a lever (or the forces of an explosion in mining) in physics while other aspects of math allow making choices (will we save money with a heavier steel lever bar or is the bigger but lighter aluminum bar with the same strength okay - how many holes are best to drill for installing 500 pounds of explosive to break up 200 square feet of iron ore)
let me answer that with a different type of statement and see if that helps. In engineering you need mathematics to be able to determine what can/can't be done. Once you get into the field you wont use the mathematics as much as in your scholastic career. However, the courses will repeatedly reinforce logical linear thinking, which is essential in engineering. they are more brain training exercises than anything else. essentially engineering and mathematics use the same logical processess in order to accomplish the desired goal.
I would suggest that your statement could be amended to state that engineering is applied physics and chemistry, as both are needed to understand our physical world.
Mathematics is a study that allows asignment of numerical quantities and magnitudes to physical properties and processes, which can be used to predict and quantify physical relationships.
In the sciences, including physics and chemistry, the goal is to understand and make predictions of the outcomes of physical processes. The outcomes are analyzed both qualitatively and quantitatively. Qualitative analysis is a descriptive analysis of the initial and final states of a particular process. Quantitive analysis uses mathematics to quanitify the process. For example, if you combine hydrogen with oxygen and apply heat, one can qualitatively predict that parts of the oxygen and hydrogen will combine to yield water possibly along with some free oxygen and/or hydrogen. The quantitative analysis is a prediction of the actual quantities of water, hydrogen and oxygen that will be yielded, given specific amounts of intitial constituents and heat. The quantitative analysis in this case, requires a certain type of mathematics referred to as stoichiometry.
Likewise, a structural element, such as a beam, which is comprised of specific metallic alloys, can be combined into a structure to support a load. Based on the physical and chemical properties of the beam, along with rigorous testing, engineers can make predictions as to how much the beam will sag due to application of loads, based on mathematics. Engineers can also mathematically predict modes of failure and determine safety and longevity of the structural system.
Sorry about this again but what I meant in my question is, if engineering is applied physics and physics is applied mathematics, where does this leave engineering and mathematics?
