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.

5. Placement Tests Required:

Accuplacer (specify test):	Calculus College Level	Score:
Other (specify test):	ACT Math component 24	Score:

6. Prerequisite Courses:

9. Co-requisite Courses:

There are no corequisites for this course.

II. Transfer and Articulation

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 is required 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. 1.  Preparation for Calculus
• Linear models and graphs of lines
• Functions and their graph
2. Limits
• Finding limits graphically and numerically
• The  definition of a limit
• Evaluating limits analytically
• Continuity
• One-sided limits
• Infinite limits
3. 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
4. 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
5. 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
6. 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