Engineering Calculus

MAEC: Engineering Calculus

MAEC.A: Multidimensional Engineering Analysis

MAEC.B: Differentiation In Engineering

MAEC.C: Multidimensional Integration in Engineering Systems

MAEC.A.1: apply knowledge of mathematics, science, and engineering design to solve problems; determine the equations of lines and surfaces using vectors and 3D graphing; apply dot and cross products of vectors to express equations of planes, parallelism, perpendicularity, angles; describe the role of vectors in engineering applications, such as modeling the velocity of moving objects or static forces on structures and objects

MAEC.A.2: learn to evaluate matrices and apply their properties to solve engineering problems; calculate determinants of matrices; express systems of linear equations in matrix equation form; use Gaussian elimination to compute solution sets of linear systems

MAEC.A.3: investigate functions of two and three independent variables to model engineering systems; compute limits of scalar and vector-valued functions; identify, interpret and graph level curves of multivariate functions; calculate regions of continuity of such functions

MAEC.A.4: use visual and written communication to express basic design elements in the appropriate mathematics notation; demonstrate fundamentals of technical sketching using computer-generated visuals by using the appropriate mathematics scale; present a technical design, using computer-generated model, for an assigned design project utilizing the appropriate scientific units (US standards and SI units)

MAEC.B.5: evaluate and apply partial differentiation of multivariable functions with two or more independent variables; compute the first and second partial derivatives of a function; use the general chain rule to determine the partial derivatives of composite functions; compute and apply the gradient of multivariable functions; solve engineering optimization problems by applying partial differentiation or Lagrange multipliers; utilize partial derivatives in developing the appropriate system balances (e.g., mass balance) in engineering problems

MAEC.C.6: apply the techniques of double and triple integration to multivariable scalar- and vector-valued functions; manipulate integrals by changing the order of integration, introducing variable substitutions, or changing to curvilinear coordinates; evaluate and apply line integrals that are independent of path; apply properties of integrals to calculate and represent area, volume, or mass; 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