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.

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.

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