# 14: Fundamentals of Engineering

- Page ID
- 43060

### First a helpful suggestion

The Schaum's outline series is a series of outlines (more then 200 inexpensive books started in the 1930s) with solved problems that cover many of the subjects in engineering, science, mathematics, and other disciplines that the student might want to invest in at some point in their career.

## Now the introduction to this chapter

This chapter consists of the academic core of engineering with a skim of the mathematics, science, and discipline specific ideas. This chapter while seeming purely academic is meant to give engineers a taste of the hard core portion of engineering. While someone might desire to become an engineer, the high-level of mathematics and science might discourage a possible engineer. This chapter gives a taste of what is to come. This chapter is another piece of the puzzle on what an engineer is and will hopefully help a student make a decision on whether they wish to become an engineer. Some topics might be difficult, but don't let that discourage you, it takes time to learn complex ideas (even for geniuses).

- 14.1: The importance of Units
- This is just a review of units...more about how to use them, not a list of them. For a list of them it is just better to go to the NIST site.

- 14.2: Arithmetic
- Arithmetic is basically all math considered essential for all careers going from the basics of adding and subtracting to pseudo algebra that is generally referred to just as algebra in classrooms.
- 14.2.1: Powers and Roots
- 14.2.1.1: Algebraic Expressions and Formulas
- 14.2.1.2: Rules of Exponents and Scientific Notation
- 14.2.1.3: Roots and Radicals
- 14.2.1.4: The Binomial Theorem
- 14.2.2: Partial Fractions
- 14.2.3: Matrices and how to use them
- 14.2.3.1: Matrices and Matrix Operations
- 14.2.3.2: System of equations and Matrices
- 14.2.4: Combinations and Permutations
- 14.2.5: Complex Numbers
- 14.2.6: Sequences and Series
- 14.2.6.1: Prelude to Sequence and Series
- 14.2.6.2: Sequences
- 14.2.6.3: Infinite Series
- 14.2.7: Power Series
- 14.2.7.1: Prelude to Power Series
- 14.2.7.2: Power Series and Functions
- 14.2.7.3: Taylor and Maclaurin Series
- 14.2.7.4: Working with Taylor Series
- 14.2.7.5: Fourier Series and Transform
- 14.2.7.6: The Laplace Transform

- 14.3: Geometry
- Functions of circles and related items

- 14.5: Scalars, vectors, and tensors
- Vectors are one of the most important concepts for engineers and scientists and this section will give a quick preview of them. It is not a substitute for math course.

- 14.6: Calculus
- A quick introduction to calculus as a theory, the techniques are in later sections. This is not a substitute for calculus class.

- 14.7: Infinitesimal calculus for derivatives
- A quick preview on derivatives and some application...note the student does not need to be taking calculus for this review as this acts as a quick introduction to prepare the student. This is not meant to substitute for an actual calculus course. It's just a preview. To repeat it is just a preview. Calm.

- 14.8: Infinitesimal Calculus for integration
- A quick preview of the integration and how it is used...note the student does not need to be taking calculus for this review as this acts as a quick introduction to prepare the student. This is not meant to substitute for an actual calculus course. It's just a preview. To repeat it is just a preview. Calm.
- 14.8.1: Table of Integrals
- 14.8.2: Substitution
- 14.8.3: Applications of Integration
- 14.8.3.1: Prelude to Applications of Integration
- 14.8.3.2: Volumes of Revolution - Cylindrical Shells
- 14.8.3.3: Arc Length of a Curve and Surface Area
- 14.8.3.4: Physical Applications of Integration
- 14.8.3.5: Moments and Centers of Mass

- 14.9: Statistics and Probability
- A quick preview of statistics and probability. This is not meant as a substitute for an actual math course. Engineers are expected to take a calculus-based statistics and probability course in a number of disciplines (though not all of them).

- 14.10: Differential equations
- This is a quick preview of differential equations. See parachute person.

- 14.11: Mechanics
- This is a preview of statics, dynamics, and solids. These topics are important to mechanical and civil engineers in particular, but it is good for other disciplines to have at least a rudimentary understanding of statics, dynamics, and solids.

- 14.12: Thermodynamics (Statistical Physics)
- This is a preview of thermodynamics through a small amount of statistical physics.

- 14.13: Electrical Circuits
- This is a preview of analysis of electrical circuit. This topic is important to electrical engineering in particular, but it is good for other disciplines to have at least a rudimentary understanding of electric circuits.

- 14.14: Signals and Systems (Control systems)
- This is a preview of signals and systems which sometimes is referred to as control systems (especially electrical engineers). The topics associated with this topic are important to all engineers.

- 14.15: Optics
- This is a preview of optics. This topic is important to optical engineers and electrical engineers in particular, but it is good for other disciplines to have at least a rudimentary understanding of optics. This is not a full description. Physics class should give you a much better description.

- 14.16: Chemistry
- Just a quick review of chemistry for engineering for introduction to engineering. All engineering programs should have a dedicated chemistry for engineering as outlined here and implemented in the Chemistry for Engineering course linked in this "chapter."