MATH 2760  Analytic Geometry & Calculus 3 Credit Hours: 4.00 Prerequisites: MATH 1770 with grade C or better; or an equivalent college course; or an acceptable score on a placement or prerequisite exam
MATH 2760 is part of a sequence of courses required for most engineering, science, and mathematics majors and includes concepts and procedures from vector algebra, vector calculus, quadric surfaces, calculus of functions of two and three variables, multiple integrals, line integrals, surface integrals, and calculus with vector fields including the theorems of Stokes and Gauss.
Billable Contact Hours: 4
Search for Sections Transfer Possibilities Michigan Transfer Network (MiTransfer)  Utilize this website to easily search how your credits transfer to colleges and universities. OUTCOMES AND OBJECTIVES Outcome 1: Upon completion of this course, the student will be able to demonstrate competency with vectors and vector algebra in the plane and in space, and to apply these tools to various geometric measurements.
Objectives: Students will:
 Add and subtract vectors and be able to geometrically represent these operations.
 Find a scalar multiple of a vector and be able to represent it graphically.
 Calculate a dot product of two vectors.
 Calculate the work done by a force as it moves an object.
 Find the angle between two vectors.
 Find the scalar projection and vector projection of one vector onto another.
 Use projections to find the distances between: a point and a line, a point and a plane, two lines.
 Calculate a cross product of vectors and demonstrate knowledge of its geometric interpretation.
 Find the equation of a line in R2 and R3 in vector nonparametric form.
 Find the symmetric equations of line in R3.
 Find the equation of a plane in vector nonparametric form.
 Be able to rewrite a vector equation in Cartesian nonparametric form.
 Calculate a box product and demonstrate knowledge of its geometric interpretation.
Outcome 2: Upon completion of this course, the student will be able to perform calculus on vector valued functions and obtain measurements in geometry and kinematics.
Objectives: Students will:
 Express the equation of a line in vector parametric form and scalar parametric form.
 Differentiate a vectorvalued function.
 Find the velocity, speed and acceleration vectors of a particle in space given its position function.
 Find the length of an arc described parametrically or as a vectorvalued function.
Outcome 3: Upon completion of this course, the student will be able to recognize quadric surfaces and their equations, graph quadric surfaces, and obtain traces of quadric surfaces.
Objectives: Students will:
 Recognize the equation of the following quadric surfaces: ellipsoids, hyperboloids of one sheet, hyperboloids of two sheets, elliptic cones, elliptic paraboloids, and hyperbolic paraboloids.
 Graph the following quadric surfaces: ellipsoids, hyperboloids of one sheet, hyperboloids of two sheets, elliptic cones, elliptic paraboloids, and hyperbolic paraboloids.
 Find the traces of a quadric surface.
 Find the cross section of a quadric surface with a plane perpendicular to one of the coordinate axes.
Outcome 4: Upon completion of this course, the student will be able to find the domain and range, calculate limits, and perform differential calculus on functions of two or three variables, as well as to use differential calculus to analyze the shape of a graph and to solve optimization problems.
Objectives: Students will:
 Graph a function of 2 variables and identify its domain and range.
 Find the limit of a function of several variables.
 Find the partial derivatives of a function of several variables and interpret the derivative geometrically.
 Find the total differential of a function of several variables and use it in an application
 Use the chain rule for function of several variables to find a partial derivative of a function.
 Find the directional derivative of a function of two or three variables in any direction.
 Find the gradient of a function in two or three variables.
 Find the maximum value of the directional derivative and a unit vector in the direction of the maximum directional derivative at a given point for a function of two or three variables.
 Find the equation of a line normal to and the line tangent to a level curve at a given point.
 Find the equation of a line normal to and the plane tangent to a level surface at a given point.
 Find critical points of a function in two or three variables.
 Classify relative extrema of functions of two variables using the second derivative test.
 Use second derivative test to find the optimum solution of an applied problem.
 Use the method of Lagrange multipliers to solve constrained optimization problems.
 Use the method of Lagrange multipliers to solve applied constrained optimization problems.
Outcome 5: Upon completion of this course, the student will be able to evaluate double and triple integrals in rectangular, polar, cylindrical, and spherical coordinates, and to apply these tools to calculate areas and volumes.
Objectives: Students will:
 Evaluate an iterated integral.
 Change the order of integration of an iterated integral.
 Convert a double integral to an iterated integral.
 Use a double integral to find the area of a region in the plane.
 Use a double integral to find the volume of a solid.
 Use polar coordinates to evaluate a double integral.
 Use an iterated integral to evaluate a triple integral
 Use a triple integral to find the volume of a solid.
 Use cylindrical coordinates to evaluate a triple integral.
 Use spherical coordinates to evaluate a triple integral.
 Use a double integral to calculate the area of a surface.
Outcome 6: Upon completion of this course, the student will be able to perform calculus on vector fields, with topics including divergence, curl, line integrals, and surface integrals, as well as to manipulate integrals using the fundamental theorem, Green’s theorem, the divergence theorem, and Stokes’ theorem.
Objectives: Students will:
 Evaluate a line integral over a curve described in scalar parametric form.
 Use the dot product to evaluate a line integral on a curve given in scalar Cartesian form.
 Use a line integral to calculate the work done by a force moving a particle along a curve.
 Use Green’s theorem to evaluate an appropriate line integral.
 Evaluate a line integral using the fundamental theorem.
 Calculate the divergence and the curl of a vector field.
 Find the area of a parametric surface.
 Evaluate a surface integral.
 Use Stokes’ theorem.
 Use the divergence theorem.
COMMON DEGREE OUTCOMES (CDO)
 Communication: The graduate can communicate effectively for the intended purpose and audience.
 Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue.
 Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives.
 Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task.
 Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments.
 Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.
CDO marked YES apply to this course: Critical Thinking: YES Quantitative Reasoning: YES COURSE CONTENT OUTLINE
 Vectors
 Vector operations
 Addition/subtraction
 Scalar multiplication
 Dot Product
 Cross product
 Box product
 Analytic Geometry
 The angle between two vectors
 The projection of one vector onto another
 Equations of a line in both parametric and nonparametric forms
 Equations of a plane in both parametric and nonparametric forms
 Using the projection to find the distance between two objects in the plane or in space.
 Vector valued functions and parametric equations
 Graphs of parametric equations and vector valued functions
 Limits of vector valued functions
 Continuity of vector valued functions
 Differentiation of vector valued functions
 Velocity, speed and acceleration of a particle in space
 The length of an arc described parametrically or by a vector valued function
 Surfaces in space
 Intercepts, traces, and cross sections
 Cylinders
 Quadric surfaces
 Graphs of functions of 2 variables
 Functions of several variables
 Domains of functions of more than one variable
 Limits of functions of more than one variable
 Continuity of functions of 2 or 3 variables
 Partial derivatives
 Total Differential
 Chain rule for functions of several variables
 Directional derivatives and gradients
 Tangent Planes and normal lines
 Extrema for functions of 2 variables
 Lagrange multipliers
 Multiple integration
 Iterated integrals
 Double integrals
 Areas and volumes
 Using polar coordinates to evaluate a double integral
 Triple integrals
 Volumes
 E Using spherical and cylindrical coordinates to evaluate a triple integral
 Surface area
 Vector calculus
 Line integrals of conservative and nonconservative vector fields over closed and nonclosed curves
 The fundamental theorem of line integrals
 Green’s Theorem
 Divergence and Curl
 Parametric surfaces and their areas
 Surface integrals
 Stokes’ theorem
 Divergence theorem
Primary Faculty Williams, Paul Secondary Faculty Friday, David Associate Dean McMillen, Lisa Dean Pritchett, Marie
Primary Syllabus  Macomb Community College, 14500 E 12 Mile Road, Warren, MI 48088
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