This is a first course in calculus, covering limits, differentiation and integration. The course begins with a brief review of the concept, properties, and graph of a function, which students are expected to have mastered previously. The definition of a limit is introduced, and processes for determining limits are developed. The derivative of a function is defined and applied to algebraic and trigonometric functions. Several applications of differentiation are covered, including optimization and related rates. Anti-differentiation and elementary differential equations are introduced, and then students see the definite integral as a limit of a Riemann sum and as an antiderivative via the Fundamental Theorem of Calculus. Finally, the course explores differentiation and integration of exponential and logarithmic functions.

1. Course Equivalency - similar course from other regional institutions:

Bemidji State University, Math 247 Calculus I, 5 credits St Cloud State University, Math 221 Calculus and Analytic Geometry, 5 credits

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 fulfills a requirement for the following program(s):

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

Solve problems using pencil and paper,
a graphing calculator, and computer algebra systems.

Analyze and follow a sequence of operations

Solve calculus problems involving a sequence of mathematical operations.

Apply abstract ideas to concrete situations

Determine the 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:

Find limits graphically, numerically, and analytically.

Determine whether a function is continuous at a point and/or on a given interval.

Demonstrate an understanding of the derivative 1) as the limit of the slope of a secant line through a function, and 2) as an instantaneous rate of change of the function.

Find derivatives of algebraic, trigonometric, and composite functions, using basic differentiation rules, the product and quotient rules, and the chain rule.

Use implicit differentiation to find derivatives.

Solve problems involving applications of the derivative, including: related rates, finding extreme values, finding concavity, curve sketching, determining differentials, and Newton’s Method.

Demonstrate an understanding of the integral as an antiderivative and as a measure of the area under a curve.

Use Riemann sums and the Trapezoidal and Simpson’s Rules to approximate the area under a curve.

Find definite integrals using basic integration rules and substitution.

Differentiate and integrate functions of the natural logarithm and e, as well as functions involving bases other than e.

Solve problems involving applications of the natural logarithm and e.

V. Topical Outline

Listed below are major areas of content typically covered in this course.

1. Lecture Sessions

1. Preparation for Calculus

Linear models and graphs of lines

Functions and their graph

Limits

Finding limits graphically and numerically

The definition of a limit

Evaluating limits analytically

Continuity

One-sided limits

Infinite limits

Differentiation

The tangent line problem and the derivative

Basic differentiation rules

Rates of change

The product and quotient rules for differentiation

Higher order derivatives

The chain rule

Implicit differentiation

Applications of Differentiation

Related rates

Extrema on an interval

Rolle’s Theorem and the Mean Value Theorem

The First Derivative Test

Concavity and the Second Derivative Test

Limits at infinity

Curve sketching

Optimization applications

Newton’s Method

Differentials

Integration

Antiderivatives and indefinite integration

Definite integration and area

Riemann sums

The Fundamental Theorem of Calculus

Integration by substitution

The Trapezoidal Rule and Simpson’s Rule

Exponential and Logarithmic Functions

Differentiation and integration of the natural logarithmic function

Inverse functions

Differentiation and integration of the natural exponential function

Applications

Bases other than e

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

4. Course Description:

This is a first course in calculus, covering limits, differentiation and integration. The course begins with a brief review of the concept, properties, and graph of a function, which students are expected to have mastered previously. The definition of a limit is introduced, and processes for determining limits are developed. The derivative of a function is defined and applied to algebraic and trigonometric functions. Several applications of differentiation are covered, including optimization and related rates. Anti-differentiation and elementary differential equations are introduced, and then students see the definite integral as a limit of a Riemann sum and as an antiderivative via the Fundamental Theorem of Calculus. Finally, the course explores differentiation and integration of exponential and logarithmic functions.

1. Course Equivalency - similar course from other regional institutions:

Bemidji State University, Math 247 Calculus I, 5 credits St Cloud State University, Math 221 Calculus and Analytic Geometry, 5 credits

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 fulfills a requirement for the following program(s):

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:

Analyze and follow a sequence of operations

Solve calculus problems involving a sequence of mathematical operations.

Apply abstract ideas to concrete situations

Determine the 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:

Find limits graphically, numerically, and analytically.

Determine whether a function is continuous at a point and/or on a given interval.

Demonstrate an understanding of the derivative 1) as the limit of the slope of a secant line through a function, and 2) as an instantaneous rate of change of the function.

Find derivatives of algebraic, trigonometric, and composite functions, using basic differentiation rules, the product and quotient rules, and the chain rule.

Use implicit differentiation to find derivatives.

Solve problems involving applications of the derivative, including: related rates, finding extreme values, finding concavity, curve sketching, determining differentials, and Newton’s Method.

Demonstrate an understanding of the integral as an antiderivative and as a measure of the area under a curve.

Use Riemann sums and the Trapezoidal and Simpson’s Rules to approximate the area under a curve.

Find definite integrals using basic integration rules and substitution.

Differentiate and integrate functions of the natural logarithm and e, as well as functions involving bases other than e.

Solve problems involving applications of the natural logarithm and e.

V. Topical Outline

Listed below are major areas of content typically covered in this course.

1. Lecture Sessions

1. Preparation for Calculus

Linear models and graphs of lines

Functions and their graph

Limits

Finding limits graphically and numerically

The definition of a limit

Evaluating limits analytically

Continuity

One-sided limits

Infinite limits

Differentiation

The tangent line problem and the derivative

Basic differentiation rules

Rates of change

The product and quotient rules for differentiation

Higher order derivatives

The chain rule

Implicit differentiation

Applications of Differentiation

Related rates

Extrema on an interval

Rolle’s Theorem and the Mean Value Theorem

The First Derivative Test

Concavity and the Second Derivative Test

Limits at infinity

Curve sketching

Optimization applications

Newton’s Method

Differentials

Integration

Antiderivatives and indefinite integration

Definite integration and area

Riemann sums

The Fundamental Theorem of Calculus

Integration by substitution

The Trapezoidal Rule and Simpson’s Rule

Exponential and Logarithmic Functions

Differentiation and integration of the natural logarithmic function

Inverse functions

Differentiation and integration of the natural exponential function