## I. General Information

1. Course Title:

Honors Calculus I

2. Course Prefix & Number:

MATH 1480

3. Course Credits and Contact Hours:

**Credits:** 5

**Lecture Hours:** 5

4. Course Description:

This honors course is a first course in calculus, covering topics with greater depth than the traditional course. Course topics include: the definition of a limit and processes for determining limits; the definition of the derivative; rules of differentiation using algebraic, trigonometric, exponential and logarithmic functions; applications of the derivative; anti-differentiation, elementary differential equations, and the Fundamental Theorem of Calculus. Students enrolled in this course will be required to do supplementary reading of articles pertaining to calculus, study substantial problems involving calculus theory and/or application, and present the results of their investigations to the class. Communicating mathematically, whether through in-class presentation, tutoring on-campus, or tutoring in the wider community, will be strongly encouraged.
Courses in the Honors Program emphasize independent inquiry, informed discourse, and direct application within small, transformative, and seminar-style classes that embrace detailed examinations of the material and feature close working relationships with instructors. In addition, students learn to leverage course materials so that they can affect the world around them in positive ways.

5. Placement Tests Required:

**Accuplacer (specify test):** |
College Mathematics |
**Score:** |
86 |

6. Prerequisite Courses:

MATH 1480 - Honors Calculus I

All Credit(s) from the following...
Course Code | Course Title | Credits |

MATH 1472 | Precalculus | 5 |

9. Co-requisite Courses:

MATH 1480 - Honors Calculus I

There are no corequisites for this course.
## II. Transfer and Articulation

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

University of Minnesota (Duluth), MATH 1596 - Honors: Calculus I, 5 credits

University of Minnesota (Twin Cities), MATH 1571H - Honors Calculus I, 5 credits

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):

This course will provide a strong background in differential calculus for mathematics, physics, and engineering students. It is an alternative to MATH 1477 Calculus I as a prerequisite for the Engineering A.S. degree.

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 |
Find the derivative of a function using the product rule, quotient rule, or chain rule. |

Apply abstract ideas to concrete situations |
Determine the solution of a differential equation with a slope field. |

Utilize appropriate technology |
Use a graphing calculator or computer application to solve calculus problems. |

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 (MnTC Goal 4);
- Determine whether a function is continuous at a point and/or on a given interval (MnTC Goal 4);
- Demonstrate an understanding of the definition of a limit (MnTC Goal 4);
- 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 (MnTC Goal 4);
- Find derivatives of algebraic, trigonometric, and composite functions, using basic differentiation rules, the product and quotient rules, and the chain rule (MnTC Goal 4);
- Use implicit differentiation to find derivatives (MnTC Goal 4);
- Solve difficult problems involving applications of the derivative, including solving related rates problems, finding extreme values, determining concavity, sketching curves, determining differentials, and using Newton’s Method (MnTC Goal 4);
- Demonstrate an understanding of the integral as an antiderivative and as a measure of the area under a curve (MnTC Goal 4);
- Use Riemann sums and the Trapezoidal and Simpson’s Rules to approximate the area under a curve (MnTC Goal 4);
- Find definite integrals using basic integration rules and substitution (MnTC Goal 4);
- Differentiate and integrate functions of the natural logarithm and
*e* as well as functions involving bases other than *e* (MnTC Goal 4);
- Solve problems involving applications of the natural logarithm and
*e* (MnTC Goal 4); and
- Present the results of an investigation into a challenging problem to an audience of peers (MnTC Goal 4).

## V. Topical Outline

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

1. Lecture Sessions

- 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
- The history of the development of 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
- 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
- Differentiation and integration of the natural exponential function
- Applications
- Bases other than
*e*