MATH 2110 - Calculus III

4 sem hrs cr

This course is a study of parametric and polar equations; vectors in the plane and in space; solid analytic geometry, including cylindrical and spherical coordinates; functions of several variables, including partial derivatives and their applications; multiple integrals with applications; selected topics from vector calculus. Prerequisite: MATH 1920  with a grade of “C” or better

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

This course may include proctored exams which must be completed on campus or at an instructor-approved proctoring center which may require additional costs to the student. Please consult your instructor for additional details.

  Formerly/Same As (Formerly MAT 2530)

Transfer (UT) or Non-Transfer Course (UN): UT

By the end of the course, students will be able to…

• acquire the ability to understand the definitions of the four conic sections, construct their graphs, and name their various parts.
• study plane curves in parametric and polar form as well as surfaces and curves in space.
• develop proficiency in the study and application of vectors in the plane and in space.
• develop skill in finding appropriate partial derivatives and apply this skill to application problems in multivariable calculus.
• evaluate multiple integrals and apply the results to finding volume, mass, and center of mass.
• further develop skills in calculus that are necessary for students to succeed in mathematics, science, and engineering courses that are part of their curriculum.

Student Objectives

Throughout the course, students will have the opportunity to…

• write the equation of a parabola in standard form; identify and locate the vertex, focus, directrix, and sketch.
• write the equation of an ellipse in standard form; identify and locate the center, foci, vertices, eccentricity, and sketch.
• write the equation of a hyperbola in standard form; identify and locate the center, foci, vertices, eccentricity, directrices, and sketch.
• classify equations, in general form, as the equation of a circle, parabola, ellipse, or hyperbola.
• use a graphing calculator to sketch certain equations in parametric form.
• eliminate the parameter and sketch by hand certain equations in parametric form.
• write the equations of certain conic sections in parametric form.
• use calculus to find the first and second derivatives of equations in parametric form.
• write the equations of tangent lines, and optionally, find arc length and surface areas of revolution for parametric curves.
• convert points and equations from polar to rectangular form and vice versa.
• recognize and sketch curves in polar form by hand and with the use of technology.
• calculate slopes of, and tangent lines to, the graphs of equations in polar form.
• find intersection points of graphs and use calculus to find appropriate areas, and optionally, arc lengths, and surface areas of revolution for given curves in polar form.
• write equations of conic sections in polar form and graph (optional).
• write the component form of a vector, perform vector operations and interpret the results geometrically, and write a vector as a linear combination of standard unity vectors, all in the plane.
• understand the three-dimensional rectangular coordinate system and analyze vectors in space.
• use the properties of the dot product of two vectors, find the angel between two vectors, find the direction cosines of a vector in space, and find the projection of one vector onto another.
• find the cross product of two vectors I space and apply properties of the cross product.
• write equations of lines and planes in space and sketch.
• find distances in space, including distance from a point to a line, between parallel and skew lines, from a point to a plane and between parallel planes.
• classify quadric surfaces from one of their six basic forms.
• sketch quadric surfaces and, optionally, certain surfaces of revolution.
• convert points and equations in cylindrical, spherical or 4rectangular coordinates from any one of the systems to another of these systems.
• understand basic concepts concerning functions of several variables.
• understand the basic ideas of limits and continuity in three dimensions (optional).
• determine specified partial derivatives of multivariable functions.
• interpret specified partial derivatives as the appropriate slopes of curves in space.
• find the total differential of a multivariable function.
• determine and compare the values of delta f and df for multivariable functions.
• determine how the total differential can be applied to absolute error and percent error (optional).
• write the appropriate chain rule form for multivariable function whose variables are defined in terms of other parameters.
• find and determine specified directional derivatives at indicated points.
• find, determine, and interpret the gradiant vector for multivariable function.
• given a point on a surface, write the equation of the tangent plane and normal line.
• find extrema for a multivariable function and test to determine if these extrema are maxima or minima.
• write the model for required optimization problems and determine the maximum or minimum value as appropriate (optional).
• evaluate iterated integrals.
• apply iterated integrals to finding areas.
• apply double integrals to finding volumes under surfaces.
• write and evaluate double integrals in polar form (optional).
• apply the polar form of double integrals to finding volumes of solids that can best be expressed in polar form (optional).
• use double integrals to find the mass, the center of mass, and the moment of inertia and radius of gyration for lamina with variable densities (optional).
• use double integrals to find the area of a surface over a region R (optional).
• evaluate triple integrals.
• apply triple integrals to finding volume, mass, center of mass and, optionally, moment of inertia.
• graph vector functions (optional).
• find and interpret the derivatives and integrals of vector functions (optional).
• write, sketch, and interpret models for projectiles in motion, including velocity and acceleration (optional).
• find tangent and normal vectors to graphs of vector functions (optional).
• find the arclength of the graph of a vector function and the curvature of a vector function at a specified point and interpret the concept of curvature and radius of curvature (optional).