College in the Schools - Course Offerings

MATH 1371 - Calculus I

(Four University of Minnesota semester credits)

Student prerequisites:

Before enrolling in Math 1371 (Calculus I), students should have demonstrated an understanding of the topics covered in the University of Minnesota’s Pre-calculus courses Math 1051 and 1151, including algebra, analytic geometry, exponentials, logarithms, trigonometry, and complex numbers beyond usual coverage found in three-year high school mathematics program. This usually means that they have earned an A or A- in a rigorous pre-calculus class. 

Although the Math 1371 course allows for the use of a calculator, one of the exams in the course must be taken without a calculator. Before enrolling in Math 1371, students should be able to think through and manipulate complex algebraic expressions without relying on a calculator. 

Length of the course:

Math 1371 should be taught over an entire high school academic year. 

High school grades:

Teachers have the option of giving students two grades: one for the high school transcript and one for the University transcript. 

Testing and assessments:

The University of Minnesota Mathematics Department will provide required examinations (all 1371 classes on the Twin Cities campus take these departmental exams). High school teachers have the option of designing additional assessments that can be used to calculate the high school grade.

Class size:

The maximum class size for Math 1371 is 25 students. 

Web site for information about how Calculus 1 classes are taught at the U.

You can visit the following Web site for more information about how Calculus I classes are taught at the U.

http://www.math.umn.edu/~voronov/1271/index.html

The Web site is for Calculus 1271, rather than 1371. The 1271 info can be applied to 1371 except that the prohibition mentioned on the Web site about using calculators during exams will not apply to the CIS course, with the exception of a “gateway” exam. The sample exams on the Web site indicate the approximate level of difficulty of the exam questions, but some exam questions on the Web would not be suitable for a course (such as the CIS course) in which graphing calculators are allowed.

You will note by looking at the Web site that a few sections from the text (see below) are omitted from the University course because of time constraints. The University math professors would recommend including most of these topics in the CIS course as they are often included in the University course if time permits.

Textbook and topics covered:

Schools are required to use the same text or a text comparable to the one used in the on-campus 1371 course (Stewart, Calculus Early Transcendentals, 6^th Ed. If you are ordering new texts please order the custom two-semester version that includes chapters 1 – 13, ISBN number: 0495466468 from Thompson, Brooks, and Cole publishers.). NOTE: Schools will not, however, be required to change texts every time that the publisher issues a new edition of the text. 

If you want to use something other than Stewart, Calculus Early Transcendentals, 5^th or 6^th Ed., you must be certain that the text will allow for all of the topics listed below to be taught, and to be taught in the order presented below.  It is important to teach the topics in this order so that your students are ready for the departmental exams, or common exams, that all students are required to take. 

Topics

• Review of precalculus
• The Tangent and velocity problem
• Limit of a function
• Limits using Limit Laws
• Continuity
• Limits and Infinity; Asymptotes

First COMMON EXAM will cover the above topics.

• Tangents, velocity, other rates of change
• Derivatives
• Derivative as a function
• Derivatives of Polynomials and exponentials
• Product and Quotient rules
• Rates of Change in the Natural & Social Sciences
• Derivatives of trig functions
• Chain Rule
• Implicit Differentiation
• Higher Derivatives
• Derivatives of Log functions

Second COMMON EXAM will cover the above topics, with emphasis on those topics discussed since the first common exam.

• Hyperbolic functions (can be omitted)
• Related rates
• Linear Approximation and Differentials
• Max and Min

FALL FINAL EXAM will cover all of the above topics.

• Mean Value Theorem
• How derivatives affect the shape of a graph
• Indeterminate forms and L'Hospital's rule
• Summary of curve sketching
• Graphing with calculus and calculators
• Optimization Applications
• Newton's method

Third COMMON EXAM will cover the above topics, with emphasis on those topics discussed since the fall final exam.

• Antiderivatives
• Areas and Distances
• Definite Integral
• Fund Theorem of calc
• Indefinite Integrals
• Substitution Rile
• Areas between curves

Fourth COMMON EXAM will cover the above topics, with emphasis on those topics discussed since the third common exam.

• Volumes
• Volumes by Shells
• Work
• Average value of a function
• Direction fields
• Exponential growth

SPRING FINAL EXAM will cover all of the above (including topics from fall semester).