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Active as of Fall Semester 2010
I. General Information
1. Course Title:
Calculus I
2. Course Prefix & Number:
MATH 1477
3. Course Credits and Contact Hours:
Credits: 5
Lecture Hours: 5
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Review of the concept and properties of a function. Emphasis on the graphing and behavior of a function. Limits are introduced and developed. The derivative of a function is defined and applied to algebraic and trigonometric functions. Anti-differentiation and elementary differential equations. Definite integral as a limit of a sum and as related to anti-differentiation via the Fundamental Theorem of Calculus. Applications to maximum, minimum and related rates. Differentiation and integration of exponential and logarithmic functions.
5. Placement Tests Required:
| Accuplacer (specify test): |
College Mathematics |
Score: |
86 |
6. Prerequisite Courses:
MATH 1477 - Calculus I
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1472 | Precalculus | 5 cr. |
9. Co-requisite Courses:
MATH 1477 - Calculus I
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 247 Calculus I
|
5
|
|
Saint Cloud State Universtiy
|
Math 221 Calculus and Analytic Geometry
|
5
|
3. Prior Learning - the following prior learning methods are acceptable for this course:
- Advanced Placement (AP)
- CLEP
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
|
|
Find limits graphically and analytically. Understand one sided limits and continuity of a function.
|
4
|
|
Understand the concept of a derivative as a rate of change. Understand basic differentiation rules, product and quotient rule, chain rule, implicit differentiation.
|
4
|
|
Apply differentiation extrema on an interval. Understand Rolle’s Theorem, Mean Value Theorem, First Derivative Test, Second Derivative Test. Understand limits at infinity, Newton’s method.
|
4
|
|
Understand antiderivatives, Riemann Sums and definite integrals, fundamental theorem of Calculus, integration by substitution, numerical integration.
|
4
|
|
Understand natural logarithmic differentiation and integration. Understand differentiation and integration of exponential functions of base e and other bases.
|
4
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
1. Preparation for Calculus
|
|
Graphs and Models, Linear Models and Rates of Change, Functions and Their Graphs
|
|
2. Limits and Their Properties
|
|
Preview of Calculus, Finding Limits Graphically and Numerically, Evaluating Limits Analytically, Continuity and One-Sided Limits, Infinite Limits
|
|
3. Differentiation
|
|
The Derivative and the Tangent Line Problem, Basic Differentiation Rules and Rates of Change, Product and Quotient Rules and Higher-Order Derivatives, The Chain Rule, Implicit Differentiation, Related Rates
|
|
4. Applications of Differentiation
|
|
Extrema on an Interval, Rolle’s Theorem and the Mean Value Theorem, Increasing and Decreasing Functions and the First Derivative Test, Concavity and the Second Derivative Test, Limits at Infinity, A Summary of Curve Sketching, Optimization Problems, Newton’s Method, Differentials
|
|
5. Integration
|
|
Antiderivatives and Indefinite Integration, Area, Riemann Sums and Definite Integrals, The Fundamental Theorem of Calculus, Integration by Substitution, Numerical Integration
|
|
6. Logarithmic and Exponential Functions
|
|
Differentiation of The Natural Logarithmic Function, Integration of The Natural Logarithmic Function, Inverse Functions, Differentiation and Integration of Exponential Functions, Bases Other Than e and Applications
|
I. General Information
1. Course Title:
Calculus I
2. Course Prefix & Number:
MATH 1477
3. Course Credits and Contact Hours:
Credits: 5
Lecture Hours: 5
Lab Hours: 0
Internship Hours: 0
4. Course Description:
Review of the concept and properties of a function. Emphasis on the graphing and behavior of a function. Limits are introduced and developed. The derivative of a function is defined and applied to algebraic and trigonometric functions. Anti-differentiation and elementary differential equations. Definite integral as a limit of a sum and as related to anti-differentiation via the Fundamental Theorem of Calculus. Applications to maximum, minimum and related rates. Differentiation and integration of exponential and logarithmic functions.
5. Placement Tests Required:
| Accuplacer (specify test): |
College Mathematics |
Score: |
86 |
6. Prerequisite Courses:
MATH 1477 - Calculus I
All Credit(s) from the following...
| Course Code | Course Title | Credits |
| MATH 1472 | Precalculus | 5 cr. |
9. Co-requisite Courses:
MATH 1477 - Calculus I
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 247 Calculus I
|
5
|
|
Saint Cloud State Universtiy
|
Math 221 Calculus and Analytic Geometry
|
5
|
3. Prior Learning - the following prior learning methods are acceptable for this course:
- Advanced Placement (AP)
- CLEP
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
|
|
Find limits graphically and analytically. Understand one sided limits and continuity of a function.
|
4
|
|
Understand the concept of a derivative as a rate of change. Understand basic differentiation rules, product and quotient rule, chain rule, implicit differentiation.
|
4
|
|
Apply differentiation extrema on an interval. Understand Rolle’s Theorem, Mean Value Theorem, First Derivative Test, Second Derivative Test. Understand limits at infinity, Newton’s method.
|
4
|
|
Understand antiderivatives, Riemann Sums and definite integrals, fundamental theorem of Calculus, integration by substitution, numerical integration.
|
4
|
|
Understand natural logarithmic differentiation and integration. Understand differentiation and integration of exponential functions of base e and other bases.
|
4
|
V. Topical Outline
Listed below are major areas of content typically covered in this course.
1. Lecture Sessions
|
1. Preparation for Calculus
|
|
Graphs and Models, Linear Models and Rates of Change, Functions and Their Graphs
|
|
2. Limits and Their Properties
|
|
Preview of Calculus, Finding Limits Graphically and Numerically, Evaluating Limits Analytically, Continuity and One-Sided Limits, Infinite Limits
|
|
3. Differentiation
|
|
The Derivative and the Tangent Line Problem, Basic Differentiation Rules and Rates of Change, Product and Quotient Rules and Higher-Order Derivatives, The Chain Rule, Implicit Differentiation, Related Rates
|
|
4. Applications of Differentiation
|
|
Extrema on an Interval, Rolle’s Theorem and the Mean Value Theorem, Increasing and Decreasing Functions and the First Derivative Test, Concavity and the Second Derivative Test, Limits at Infinity, A Summary of Curve Sketching, Optimization Problems, Newton’s Method, Differentials
|
|
5. Integration
|
|
Antiderivatives and Indefinite Integration, Area, Riemann Sums and Definite Integrals, The Fundamental Theorem of Calculus, Integration by Substitution, Numerical Integration
|
|
6. Logarithmic and Exponential Functions
|
|
Differentiation of The Natural Logarithmic Function, Integration of The Natural Logarithmic Function, Inverse Functions, Differentiation and Integration of Exponential Functions, Bases Other Than e and Applications
|