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; antidifferentiation, 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 inclass presentation, tutoring oncampus, 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 seminarstyle 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 
Other (specify test): 
ACT Math component 
Score: 
24

6. Prerequisite Courses:
MATH 1480  Honors Calculus I
All Credit(s) from the following...
Course Code  Course Title  Credits 
MATH 1472  Precalculus  5 cr. 
7. Other Prerequisites
Accuplacer Reading score of 100 or greater, OR permission from the instructor or Honors Coordinator, or high school GPA of 3.5 or greater.
9. Corequisite 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. ProgramApplicable 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. CollegeWide Outcomes
CollegeWide 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
 Onesided 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