1. Understanding the difference between an engineer and a scientist There are many similarities and differences

2. Academic engineering is narrow while science is broad Academic majors in engineering are discipline specific based on the type of designs associated with the work Science is very broad like physics, biology, and social science, for example. However, sub-set specialization may or may not be the declared major.

3. Similar and Different? Scientists tend to explore the natural world and discover new knowledge about the universe and how it works. Engineers apply that knowledge to solve practical problems, often with an eye toward optimizing cost, efficiency, or some other parameters. There is considerable overlap between science and engineering, so you will find scientists who design and construct equipment and engineers who make important scientific discoveries.

4. Two Major Content Knowledge Disciplines Mathematics is the language of science and engineering. Physics is the conceptual and calculated language of science and engineering.

5. Mathematics for Engineers and Scientists Algebra Trigonometry Calculus 1 Calculus 2 Calculus 3 Differential Equations

6. Algebra: briefly and conceptually Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables. The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations (mathematical statements containing letters or symbols to represent numbers). Before we use algebra to find information about these kinds of relationships, it is important to first cover some basic terminology. In this unit we will first define terms, expressions, and equations. In the remaining units in this book we will review how to work with algebraic expressions, solve equations, and how to construct algebraic equations that describe a relationship. We will also introduce the notation used in algebra as we move through this unit.

7. Trigonometry: briefly and conceptually Angle measurement and tables Trigonometry began as the computational component of geometry. For instance, one statement of plane geometry states that a triangle is determined by a side and two angles. In other words, given one side of a triangle and two angles in the triangle, then the other two sides and the remaining angle are determined. Trigonometry includes the methods for computing those other two sides. The remaining angle is easy to find since the sum of the three angles equals 180 degrees (usually written 180°). If there is anything that distinguishes trigonometry from the rest of geometry, it is that trig depends on angle measurement and quantities determined by the measure of an angle. Of course, all of geometry depends on treating angles as quantities, but in the rest of geometry, angles aren’t measured, they’re just compared or added or subtracted. Trigonometric functions such as sine, cosine, and tangent are used in computations in trigonometry. These functions relate measurements of angles to measurements of associated straight lines as described later in this short course. Trig functions are not easy to compute like polynomials are. So much time goes into computing them in ancient times that tables were made for their values. Even with tables, using trig functions takes time because any use of a trig function involves at least one multiplication or division, and, when several digits are involved, even multiplication and division are slow. In the early 17th century computation sped up with the invention of logarithms and soon after slide rules. With the advent of calculators computation has become easy. Tables, logarithms, and slide rules aren’t needed in trigonometric computations. All you have to do is enter the numbers and push a few buttons to get the answer. One of the things that used to make learning trig difficult was performing the computations. That’s not a problem anymore!

8. Calculus 1: briefly and conceptually The branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects. A formula for the derivative of the composition of two functions in terms of their derivatives.

9. Calculus 2: briefly and conceptually Basic skills of calculus 2 – Techniques of Integration – Approximate integrals using numerical integration – Evaluate integrals using integration by parts – Evaluate integrals of trigonometric forms – Evaluate integrals by trigonometric substitution – Evaluate integrals by the method of partial fractions – Evaluate Improper Integrals Major Topics of Calculus 2 Infinite Series Parametric Equations, Polar Coordinates and Conic Sections Vectors Calculus of Vector Valued Functions Partial Derivatives

10. Calculus 3: briefly and conceptually Investigate higher dimensional geometry using the concept of a vector. Understand the concept of a function when extended to multiple inputs and outputs. Learn about and compute limits in higher dimensions. Learn about and compute derivatives in higher dimensions (partial, directional, total, gradient, divergence, curl, etc.). Learn about and compute integrals in higher dimensions (area, volume, path, surface, flux, etc.). Communicate mathematically, including understanding, making, and critiquing mathematical arguments.

11. Differential Equations First Order Differential Equations Second Order Constant Coefficient Linear Equations Fourier Series and Laplace Transform First Order Systems

12. Discussion and Homework Do you feel there are important distinctions between scientists and engineers? Count off by 4 and get into 4 teams to discuss what similarities and differences exist between scientists and engineers. You're assignment is to research each and write one page about the similarities and another page about the differences.