Students will learn the basics of algebra and functions in two or more dimensions to prepare for the study of differentiation and integration of functions of several variables. In addition, students will explore and summarize the educational requirements and professional expectations associated with engineering career paths and solve problems related to various engineering disciplines.
MECA1 Students will apply knowledge of mathematics, science, and engineering design to solve problems.
a Determine the equations of lines and surfaces using vectors and 3D graphing.
b Apply dot and cross products of vectors to express equations of planes, parallelism, perpendicularity, angles.
c Describe the role of vectors in engineering applications, such as modeling the velocity of moving objects or static forces on structures and objects.
MECA2 Students will learn to evaluate matrices and apply their properties to solve engineering problems.
a Calculate determinants of matrices.
b Express systems of linear equations in matrix equation form.
c Use Gaussian elimination to compute solution sets of linear systems.
MECA3 Students will investigate functions of two and three independent variables to model engineering systems.
a Compute limits of scalar and vector-valued functions.
b Identify and graph level curves of multivariate functions.
c Calculate regions of continuity of such functions.
MECA4 Students will use visual and written communication to express basic design elements in the appropriate mathematics notation.
a Demonstrate fundamentals of technical sketching using computer-generated visuals by using the appropriate mathematics scale.
b Present a technical design, using computer-generated model, for an assigned design project utilizing the appropriate scientific units (US standards and SI units).
Differentiation in engineering
MECD1 Students will evaluate and apply partial differentiation of multivariable functions with two or more independent variables.
a Compute the first and second partial derivatives of a function.
b Use the general chain rule to determine the partial derivatives of composite functions.
c Compute and apply the gradient of multivariable functions.
d Solve engineering optimization problems by applying partial differentiation or Lagrange multipliers.
e Utilize partial derivatives in developing the appropriate system balances (ex: mass balance) in engineering problems.
Multidimensional integration in engineering systems
MECI1 Students will apply the techniques of double and triple integration to multivariable scalar- and vector-valued functions.
a Manipulate integrals by changing the order of integration, introducing variable substitutions, or changing to curvilinear coordinates.
b Evaluate and apply line integrals that are independent of path.
c Apply properties of integrals to calculate and represent area, volume, or mass.
d Use integrals of vectors to define and apply the gradient, divergence, or the curl
e Interpret the theorems of Green, Stokes, or Gauss and apply them to the study of real-world phenomena.
The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.
MECPS1 Students will solve engineering-based calculus problems (using appropriate technology).
a Build new mathematical knowledge through problem solving.
b Solve problems that arise in mathematics and in other contexts.
c Apply and adapt a variety of appropriate strategies to solve problems, such as considering realistic constraints relevant to the design of a system, component, or process.
d Monitor and reflect on the process of mathematical problem solving and interpret problem solutions.
MECPS2 Students will use visual and written communication to express basic design elements and will communicate mathematically.
a Organize and consolidate their mathematical thinking through communication.
b Communicate and use the language of mathematics to articulate their mathematical thinking coherently.
c Present a technical design, using computer-generated model, for an assigned design project.
MECPS3 Students will describe the history of technological advancement and make connections among mathematical ideas and to other disciplines.
a Recognize and use connections among mathematical and engineering ideas.
b Recognize and apply mathematics in contexts outside of mathematics.
c Explain the impact of key persons and historical events and their impact on engineering and society.
d Describe the issues of necessity that have influenced innovation and technological development.
MECPS4 Students will represent mathematics in multiple ways.
a Create and use representations to organize, record, and communicate mathematical ideas.
b Select, apply, and translate among mathematical representations to solve problems.
c Use representations to model and interpret physical, and mathematical phenomena.
MECPS5 Students will develop vocabulary and communication skills by reading text material and problem descriptions associated with engineering and technology education.
a Reading in all curriculum areas.
b Discussing articles or books.
c Building vocabulary knowledge.
MECPS6 Students will explore and summarize the educational requirements and professional expectations associated with engineering career paths.