MAC 2313 - Calculus with Analytic Geometry III

Mathematics Department

Credit(s): 4
Contact Hours: 62
Effective Term Summer 2019 (560)

Requisites

Prerequisite MAC 2312 with a minimum grade of C

Course Description

This course is a continuation of MAC 2312 with the study of vectors in two and three-dimensional space, as well as differentiation and integration of functions of several variables. Topics include vectors in the plane and space, three-dimensional surfaces, various coordinate systems, vector-valued functions, differential calculus of functions of several variables, gradients, directional derivatives, applications of partial derivatives, multiple integration, vector analysis, line integrals, surface integrals and applications.

Learning Outcomes and Objectives

  1. The student will apply geometric properties and calculus concepts involving surfaces, two- and three-dimensional vectors, vector-valued functions, planes, lines and the cylindrical and spherical coordinate systems by:
    1. computing the following when given two- or three-dimensional vectors: sum, difference, scalar product, magnitude, dot product, cross product (3-dim. only), vector projection, scalar projection.
    2. finding the equations of planes and the parametric and symmetric equations of a line when given sufficient information.
    3. finding the derivatives and integrals of vector-valued functions and applying these to applied problems concerning both the motion of a particle, and tangent and normal vectors.
    4. using vector dot products and cross products in order to compute distances between points, skew lines and planes.
    5. using cylindrical or spherical coordinates to solve problems dealing with three-dimensional geometry.
  2. The student will apply limits, continuity, differentiability and the chain rule to functions of several variables by:
    1. finding limits of functions of two or three variables if the limits exist; showing that a limit does not exist by using different paths.
    2. determining if a given function of two or three variables is continuous or differentiable at a point.
    3. determining the partial derivatives of functions of two or more independent variables.
    4. determining the partial derivatives of composite functions of two or more variables by using the chain rule.
    5. finding the first or second partial derivatives of functions of two variables at a given point by using the definition of partial derivative.
  3. The student will apply differential calculus on functions of several variables to applied problems by:
    1. using the differential to demonstrate the differentiability of a function of several variables.
    2. computing the directional derivative for a function of two or three variables and find the equations of the tangent plane and normal line to a point on a given surface.
    3. computing the gradient and using it in applied problems.
    4. computing the possible extrema for a function of two variables.
  4. The student will apply the definite integral of a function to a two- and three-dimensional setting and utilize Riemann sums by:
    1. approximating the value of an integrable function of two variables by using Riemann sums.
    2. computing the values of double and triple integrals by using iterated integrals in rectangular coordinates, polar coordinates, cylindrical coordinates and spherical coordinates.
  5. The student will compute double or triple integrals in rectangular, polar, and cylindrical coordinates to applied problems by:
    1. finding areas.
    2. finding volumes.
    3. finding surface areas.
  6. The student will utilize vector analysis to applied problems by:
    1. computing the line integral of a given 2 - or - 3 dimensional vector function by:
      1. parametric equations
      2. determining if a field is conservative and using the Fundamental Theorem of Line Integrals
      3. applying Green's Theorem
    2. computing the curl and divergence of a vector field.
    3. evaluating surface integrals.
    4. applying line integrals and surface integrals to applied problems.

Criteria Performance Standard

In order to earn a grade of C or better, the student will achieve at the 70% level or higher on classroom measures. Upon successful completion of the course the student will, with a minimum of 70% accuracy, demonstrate mastery of each of the above stated objectives through classroom measures developed by individual course instructors.

History of Changes

Revised 8/84 DBT 11/20/90 Effective Session 19911 3 YR C&I Review 8/94 C&I 3/17/98; DBT 4/20/98 Effective Session 19981 Effective Session 19981. 3-Year Review 2001. 3 Year Review 2005. 3-Year Review 2009. C&I Approval: 04/28/1998, BOT Approval: 05/29/1998, Effective Term: Fall 2009 (415).
C&I Approval: 02/14/2019, BOT Approval: 03/19/2019, Effective Term: Summer 2019 (560)

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