Math 1710 – Calculus I
University of North Texas
Text: Calculus, by Briggs, and Cochran (First edition)
Text adopted Spring2011, Outline adopted Fall 2011.
Section / Suggested number of weeks per chapter / Topic/Comments2.1* / 2 ½ weeks / The Idea of Limits (Optional)
Mention briefly how the idea of limits arises. This section merges nicely into section 3.1. You can essentially do both at once, or you can do each separately.
2.2 / Definitions of Limits
This is an introduction to limits. It may take longer than one period if you spend too much time making tables. Mathematica or Maple demonstrations can help students “see” limits. One-sided limits usually come easily to students once they understand two-sided limits
2.3 / Techniques for Computing Limits
This section is short. Limit laws make perfect sense to students when they see examples. The Squeeze (Sandwich) Theorem usually takes some explanation and examples.
2.4, 2.5 / Infinite Limits, Limits at infinity
It is best not to get hung up on the technical definition. The emphasis should be on infinite limits and asymptotes. Students may use a graphing calculator to check their answer, but they should know how to evaluate limits analytically.
2.6 / Continuity
Many examples are helpful for students to understand the concept of continuity.
2.7* / Precise Definition of Limits (Optional: except TAMS)
There are different levels at which this section may be covered. The extremes are to skip the formal definition of limits (not recommended) and to expect students to prove limits (also not recommended). In between, you have the options of convincing them that the definition is reasonable, having them memorize the definition, or have them find delta for linear functions. Don’t get hung up on this section or else you will not be able to cover required material at the end.
3.1 / 3 weeks / Introducing the Derivative
Expect students to calculate the derivative, not using the derivative’s rule but the definition of the derivative. It is a good exercise to learn how to write mathematics logically and neatly.
3.2 / Rules of Differentiation
Don’t rush this. It typically takes time for students to figure out how to use the rules. Many examples are helpful.
3.3, 3.4 / The product and Quotient Rules, Derivatives of Trigonometric Functions
Expect that students often forget about trigonometric functions. Quick review might be helpful.
3.5 / Derivatives as Rations of Change
In addition to introducing the instantaneous rate of change, this section gives students an opportunity to see and practice more differentiation.
3.6 / The Chain Rule,
Students often have trouble with the chain rule. You may have to spend more than one hour if the class has trouble with it.
3.7 / Implicit Differentiation,
Implicit differentiation reinforces the chain rule. This section is very important for students who will take Calculus II.
3.8 / Related Rates,
This section gives good reinforcement of the chain rule. You can cover the material in an hour, but expect questions the day after.
4.1 / 2 ½ weeks / Maxima and minima,
Don’t get too hung up on Theorem 1.
4.2 / What Derivatives Tell Us,
Encourage students to discover what derivatives tell us.
4.3 / Graphing Functions,
Graphing by hand (without a graphing calculator or computer) is something that many high schools students do not see. So, even basic graphing may be difficult for the students.
4.4 / Optimization Problems,
This section brings excitement to engineering students. You can cover the material in an hour, but expect questions the day after.
4.5* / Linear Approximations and Differentials (Optional: Except TAMS)
This is an ideal topic for the use of Mathematica or Maple.
4.6 / Mean Value Theorem,
If you choose to do a careful proof of Rolle’s Theorem and the MVT, you will need two hours for this section. If you do a more intuitive proof, this section can be done in one hour.
4.7 / L’Hopital’s Rule,
You may teach L’Hopital’s rule immediately after section 3.4.
4.8 / Antiderivatives,
Antidifferentiation can be covered in one day, but there may be questions the second.
5.1, 5.2, / 2 ½ weeks / Approximating Areas under Curves, Definite Integrals
Sections will probably take two hours if you carefully do examples of computing integrals as limits of Riemann sums. A more intuitive approach would take 1.5 hours.
5.3 / Fundamental Theorem of Calculus,
Clarify the difference between indefinite and definite integrals.
5.4 / Working with Integrals,
If you wish to prove several properties, it will take two hours.
5.5 / Substitution Rule,
Do a lot of examples and make sure the students do a lot of exercises. This section is very important for Calculus II.
6.1* / 2 ½ weeks / Velocity and Net Change (Optional)
6.2 / Regions Between Curves,
Do a lot of examples and make sure the students do a lot of exercises.
6.3 / Volume by Slicing,
This is an ideal topic for the use of Mathematica or Maple.
6.4* / Volume by Shells(Optional)
6.5 / Length of Curves,
Briefly explain the idea for the definition of arc length.
6.6 / Physical Application,
Work is part of the catalog description, so please cover this topic.
From the 20011-20012 Undergraduate Catalog:
MATH 1720 - Calculus I
(MATH 2313 or MATH 2413 or MATH 2513)
4 hours
Limits and continuity, derivatives and integrals; differentiation and integration of polynomial, rational, trigonometric, and algebraic functions; applications, including slope, velocity, extrema, area, volume and work.
Prerequisite(s):MATH 1650; or both MATH 1600 and MATH 1610.