I. General Information
1. Course Title:
Calculus II
2. Course Prefix & Number:
MATH 1478
3. Course Credits and Contact Hours:
Credits: 5
Lecture Hours: 5
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Math 1478 is a second course in the Calculus of one variable. Topics include differentiation and integration of inverse trigonometric function and hyperbolic function. This course also includes slope fields and first order linear differential equations. Applications of integration will be used to calculate the area between curves, volume using the disk and shell method, arc length and surfaces of revolution, work, moments and centers of mass. It incorporates integration by parts, trigonometry integration, trigonometric substitution, partial fraction, indeterminate forms, L’hopital’s Rule and improper integrals. Math 1478 also works with Infinite series, p-series, test for convergence and divergence, Taylor Polynomials and the representation of functions by power series and applications of calculus to parametric and polar equations.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 1478 - Calculus II
A total of 1 Course(s) from...
7. Other Prerequisites
9. Co-requisite Courses:
MATH 1478 - Calculus II
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
|
|
Bemidji State University
|
Math 2472 Calculus II
|
5
|
|
Saint Cloud State Universtiy
|
Math 222 Calculus and Analytic Geometry II
|
4
|
3. Prior Learning - the following prior learning methods are acceptable for this course:
Advanced Placement (AP)
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: |
| Demonstrate written communication skills |
Writing mathematics using correct
mathematic syntax
|
| Assess alternative solutions to a problem |
Solving problems using pencil and paper,
Graphing calculator, Computer Algebra Systems
|
| Analyze and follow a sequence of operations |
Solving Calculus problems involve using a sequence of math operation. |
| Apply abstract ideas to concrete situations |
Looking at a solution of a differential equation with a slope field |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
MnTC
Goal Area
|
|
Clearly express mathematical/logical ideas in writing
|
4
|
|
Explain what constitutes a valid mathematical argument
|
4
|
|
Apply higher-order problem-solving and/or modeling strategies
|
4
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
I. Inverse Trigonometric Functions
A. Integration
B. Differentiation
II. Hyperbolic Functions
A. Integration and differentiation of hyperbolic functions
B. Integration and differentiation of inverse hyperbolic functions.
|
|
III. Differential Equations
A. Slope fields.
B. Differential equations applied to growth and decay.
C. Solving of differential equations.
|
IV. Applications of Integration
A. Area between to curves.
B. Volume using the disk and shell method.
C. Arc length and surface of revolution.
D. Work and centers of mass.
|
V. Integration Techniques, L’Hopital’s Rule and Improper Integrals.
A. Integration by parts
B. Trigonometric integrals
C. Trigonometric substitution
D. Partial fractions.
E. Indeterminate forms and l’Hopital’s Rule
|
VII. Infinite Series
A. Sequences, series and convergence/divergence.
B. The integral test and p-series, harmonic series, alternating series.
C. Test for convergence and divergence.
D. Taylor Polynomials
E. Power Series and representation of functions by a power series.
|
VII. Parametric Equations and Polar Coordinates
A. Plane curves and parametric equations and application of calculus to parametric equations.
B. Polar coordinates and polar graph and the application of calculus to polar equations.
|
I. General Information
1. Course Title:
Calculus II
2. Course Prefix & Number:
MATH 1478
3. Course Credits and Contact Hours:
Credits: 5
Lecture Hours: 5
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Math 1478 is a second course in the Calculus of one variable. Topics include differentiation and integration of inverse trigonometric function and hyperbolic function. This course also includes slope fields and first order linear differential equations. Applications of integration will be used to calculate the area between curves, volume using the disk and shell method, arc length and surfaces of revolution, work, moments and centers of mass. It incorporates integration by parts, trigonometry integration, trigonometric substitution, partial fraction, indeterminate forms, L’hopital’s Rule and improper integrals. Math 1478 also works with Infinite series, p-series, test for convergence and divergence, Taylor Polynomials and the representation of functions by power series and applications of calculus to parametric and polar equations.
5. Placement Tests Required:
6. Prerequisite Courses:
MATH 1478 - Calculus II
A total of 1 Course(s) from...
7. Other Prerequisites
9. Co-requisite Courses:
MATH 1478 - Calculus II
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
|
|
Bemidji State University
|
Math 2472 Calculus II
|
5
|
|
Saint Cloud State Universtiy
|
Math 222 Calculus and Analytic Geometry II
|
4
|
3. Prior Learning - the following prior learning methods are acceptable for this course:
Advanced Placement (AP)
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: |
| Demonstrate written communication skills |
Writing mathematics using correct
mathematic syntax
|
| Analyze and follow a sequence of operations |
Solving Calculus problems involve using a sequence of math operation. |
| Apply abstract ideas to concrete situations |
Looking at a solution of a differential equation with a slope field |
2. Course Specific Outcomes - Students will be able to achieve the following measurable goals upon completion of
the course:
|
Expected Outcome
|
MnTC
Goal Area
|
|
Clearly express mathematical/logical ideas in writing
|
4
|
|
Explain what constitutes a valid mathematical argument
|
4
|
|
Apply higher-order problem-solving and/or modeling strategies
|
4
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
I. Inverse Trigonometric Functions
A. Integration
B. Differentiation
II. Hyperbolic Functions
A. Integration and differentiation of hyperbolic functions
B. Integration and differentiation of inverse hyperbolic functions.
|
|
III. Differential Equations
A. Slope fields.
B. Differential equations applied to growth and decay.
C. Solving of differential equations.
|
IV. Applications of Integration
A. Area between to curves.
B. Volume using the disk and shell method.
C. Arc length and surface of revolution.
D. Work and centers of mass.
|
V. Integration Techniques, L’Hopital’s Rule and Improper Integrals.
A. Integration by parts
B. Trigonometric integrals
C. Trigonometric substitution
D. Partial fractions.
E. Indeterminate forms and l’Hopital’s Rule
|
VII. Infinite Series
A. Sequences, series and convergence/divergence.
B. The integral test and p-series, harmonic series, alternating series.
C. Test for convergence and divergence.
D. Taylor Polynomials
E. Power Series and representation of functions by a power series.
|
VII. Parametric Equations and Polar Coordinates
A. Plane curves and parametric equations and application of calculus to parametric equations.
B. Polar coordinates and polar graph and the application of calculus to polar equations.
|