I. General Information
1. Course Title:
Multivariable Calculus
2. Course Prefix & Number:
MATH 2458
3. Course Credits and Contact Hours:
Credits: 4
Lecture Hours: 4
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Vectors, dot and cross products, surfaces. Vector-valued functions and curves. Functions of several variables, partial and directional derivatives, double and triple integration, line and surface integrals. Applications to extrema, area, volume, moments, and centroids.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 2458 - Multivariable Calculus
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1478 | Calculus II | 5 cr. |
9. Co-requisite Courses:
MATH 2458 - Multivariable Calculus
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency - similar course from other regional institutions:
|
Name of Institution
|
Course Number and Title
|
Credits
|
|
St. Cloud State University
|
MATH 321. Vector and Multivariable Calculus
|
4
|
|
Bemidji State University
|
MATH 2480 MULTIVARIABLE CALCULUS
|
4
|
III. Course Purpose
Program-Applicable Courses – This course is required for the following program(s):
|
Name of Program(s)
|
Program Type
|
|
Engineering
|
AS
|
MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning
IV. Learning Outcomes
1. College-Wide Outcomes
| College-Wide Outcomes/Competencies |
Students will be able to: |
| Assess alternative solutions to a problem |
Examine differing methods in solving problems, e.g. find the volume of a solid. |
| Apply abstract ideas to concrete situations |
Apply concepts and methods to solve application problems |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
|
Clearly express mathematical ideas in writing.
|
|
Explain what constitutes a valid mathematical argument.
|
|
Apply higher-order problem-solving strategies.
|
|
Apply appropriate technology.
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
Ia. Vectors in the Plane
|
|
Ib. Space Coordinates and Vectors in Space
|
|
Ic. The Dot Product of Two Vectors
|
|
Id. Cross Product
|
|
Ie. Lines and Planes in Space
|
|
If. Surfaces
|
|
Ig. Cylindrical and Spherical Coordinates
|
|
IIa. Vector-Valued Functions
|
|
IIb. Differentiation and Integration of Vector-Valued Functions.
|
|
IIc. Velocity and Acceleration
|
|
IId. Tangent Vectors and Normal Vectors
|
|
IIe. Arc Length and Curvature
|
|
IIIa. Functions of Several Variables
|
|
IIIb. Limits and Continuity
|
|
IIIc. Partial Derivatives
|
|
IIId. Differentials
|
|
IIIe. Chain Rules
|
|
IIIf. Directional Derivatives and Gradients
|
|
IIIg. Tangent Planes and Normal Lines
|
|
IIIh. Extrema of Functions of Two Variables
|
|
IIIi. Applications of Extrema
|
|
IIIj. Lagrange Multipliers
|
|
IVa. Iterated Integrals and Area
|
|
IVb. Double Integrals and Volume
|
|
IVc. Polar Coordinates
|
|
IVd. Center of Mass and Moments of Inertia
|
|
IVe. Surface Area
|
|
IVf. Triple Integrals
|
|
IVg. Triple Integrals in Cylindrical and Spherical Coordinates
|
|
IVh. Change of Variables: Jacobians
|
|
Va. Vector Fields
|
|
Vb. Line Integrals
|
|
Vc. Conservative Vector Fields and Independence of Path
|
|
Vd. Green’s Theorem
|
|
Ve. Parametric Surfaces
|
|
Vf. Surface Integrals
|
|
Vg. Divergence Theorem
|
|
Vh. Stokes’s Theorem
|
I. General Information
1. Course Title:
Multivariable Calculus
2. Course Prefix & Number:
MATH 2458
3. Course Credits and Contact Hours:
Credits: 4
Lecture Hours: 4
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Vectors, dot and cross products, surfaces. Vector-valued functions and curves. Functions of several variables, partial and directional derivatives, double and triple integration, line and surface integrals. Applications to extrema, area, volume, moments, and centroids.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 2458 - Multivariable Calculus
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1478 | Calculus II | 5 cr. |
9. Co-requisite Courses:
MATH 2458 - Multivariable Calculus
There are no corequisites for this course.
II. Transfer and Articulation
1. Course Equivalency - similar course from other regional institutions:
|
Name of Institution
|
Course Number and Title
|
Credits
|
|
St. Cloud State University
|
MATH 321. Vector and Multivariable Calculus
|
4
|
|
Bemidji State University
|
MATH 2480 MULTIVARIABLE CALCULUS
|
4
|
III. Course Purpose
1. Program-Applicable Courses – This course is required for the following program(s):
|
Name of Program(s)
|
Program Type
|
|
Engineering
|
AS
|
2. MN Transfer Curriculum (General Education) Courses - This course fulfills the following goal area(s) of the MN Transfer Curriculum:
Goal 4 – Mathematical/Logical Reasoning
IV. Learning Outcomes
1. College-Wide Outcomes
| College-Wide Outcomes/Competencies |
Students will be able to: |
| Apply abstract ideas to concrete situations |
Apply concepts and methods to solve application problems |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
|
Clearly express mathematical ideas in writing.
|
|
Explain what constitutes a valid mathematical argument.
|
|
Apply higher-order problem-solving strategies.
|
|
Apply appropriate technology.
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
Ia. Vectors in the Plane
|
|
Ib. Space Coordinates and Vectors in Space
|
|
Ic. The Dot Product of Two Vectors
|
|
Id. Cross Product
|
|
Ie. Lines and Planes in Space
|
|
If. Surfaces
|
|
Ig. Cylindrical and Spherical Coordinates
|
|
IIa. Vector-Valued Functions
|
|
IIb. Differentiation and Integration of Vector-Valued Functions.
|
|
IIc. Velocity and Acceleration
|
|
IId. Tangent Vectors and Normal Vectors
|
|
IIe. Arc Length and Curvature
|
|
IIIa. Functions of Several Variables
|
|
IIIb. Limits and Continuity
|
|
IIIc. Partial Derivatives
|
|
IIId. Differentials
|
|
IIIe. Chain Rules
|
|
IIIf. Directional Derivatives and Gradients
|
|
IIIg. Tangent Planes and Normal Lines
|
|
IIIh. Extrema of Functions of Two Variables
|
|
IIIi. Applications of Extrema
|
|
IIIj. Lagrange Multipliers
|
|
IVa. Iterated Integrals and Area
|
|
IVb. Double Integrals and Volume
|
|
IVc. Polar Coordinates
|
|
IVd. Center of Mass and Moments of Inertia
|
|
IVe. Surface Area
|
|
IVf. Triple Integrals
|
|
IVg. Triple Integrals in Cylindrical and Spherical Coordinates
|
|
IVh. Change of Variables: Jacobians
|
|
Va. Vector Fields
|
|
Vb. Line Integrals
|
|
Vc. Conservative Vector Fields and Independence of Path
|
|
Vd. Green’s Theorem
|
|
Ve. Parametric Surfaces
|
|
Vf. Surface Integrals
|
|
Vg. Divergence Theorem
|
|
Vh. Stokes’s Theorem
|