Fall Semester 2000-2001
Sudro 20, 8-8:50 MWF
Bill Martin, Assistant Professor
Department of Mathematics, Rm. 304B Minard, NDSU
Phone: 231-8480
Office hours: 9:30-10:30 Tuesday, 9-10 Wednesday and Friday (or by appointment)
University Calculus I is intended for students who require the regular science/engineering calculus sequence in their undergraduate program. With other courses in the sequence, it serves as a prerequisite for many advanced courses in science and mathematics. Math 165 is designed to develop quantitative skills that will be required for a variety of technical fields, including physical science, engineering, and mathematics.
Content: The focus of this first course in the calculus sequence is on foundations of calculus, especially limits, differential calculus, the fundamental theorem, and applications. It lays the foundation for the detailed study of the second main topic of calculus, integration, which is covered in Math 166.
To give students an understanding of and appreciation for the theory and applications of the differential and integral calculus of functions of one variable.
It develops student capabilities related to several of NDSU's General Education Objectives, including:
Grades in the course will reflect students' demonstrated attainment of course objectives. Grades will not be curved. As a guideline percentages in the 90s are A, 80s are B, 70s are C, 60s are D, and below 60% is unsatisfactory. The weighting of components will be as follows:
Class attendance will be noted and active participation in class, both in lecture and recitation, will be essential for success. Some graded work will be completed during class time. There will be weekly quizzes in recitations and regular quizzes in lectures. There will be no makeups for missed quizzes and homework. Makeup tests will only be given in the most exceptional circumstances (such as medical emergencies) and require prior approval of the instructor (unless impossible, in which case written excuses may be required). Even when approved, late work may not be graded until after the end of the semester, which could result in an "incomplete" grade for the course. Makeup tests tend to be more difficult, though this is not a deliberate policy. Students who are not regularly attending classes cannot expect special consideration in relation to their grades. Academic dishonesty will not be tolerated and will result in severe sanctions, such as failure of the course.
Group work: The lecture/discussion format of this course, which precludes extensive interaction with individuals during lectures, makes recitations and group work especially important. Research shows that working together cooperatively enhances learning and retention. Groups, to be formed during the first two weeks, will work together on homework, special assignments, and take-home portions of tests during the semester.
|
Topics |
Suggested Time | |
| 1 | Review of inequalities, functions and graphs. The concepts of limit and continuity. Applications. | 3 weeks |
| 2 | Derivatives and tangent lines. General differentiation rules including the chain rule. Applications of the chain rule. Derivatives of elementary functions (including polynomial, rational, radical, trigonometric, exponential, logarithmic, hyperbolic) and higher derivatives. | 4-5 weeks |
|
3 |
Applications of the derivative including monotonicity, concavity, curve sketching, optimization, approximation, numerical techniques, and l'Hospital's rule. | 4-5 weeks |
| 4 | Area and Riemann sums. The definite integral, the fundamental theorem of calculus, the indefinite integral and antiderivatives, and elementary substitutions. | 2-3 weeks |
| Week | Date | Topics |
| 1 | August 30, September 1 (WF) | Introduction to calculus: Sections 1.1-1.4, 2.1
Group Project 1 Assigned (Due in recitation Thursday September 14) |
| 2 | Sep 6, 8 (WF) (Labor Day Sep 4) | Limits: Sections 2.2, 2.3 |
| 3 | Sep 11, 13, 15 |
Formal limits, continuity: Sections 2.4, 2.5, 2.6
(Project 1 due in recitation Thursday September 14) |
| 4 | Sep 18, 20, 22 | The derivative: Sections 2.7, 2.8, 2.9
Project 2 assigned (Due in recitation Thursday October 5) |
| 5 | Sep 25, 27, 29 | Transcendental functions, review: Sections 1.5, 1.6
Test 1 September 28 (Thursday evening, 6-7:30 pm in Stevens Auditorium) |
| 6 | Oct 2, 4, 6 | Differentiation: Sections 3.1, 3.2, 3.3
(Project 2 due in recitation Thursday October 5) |
| 7 | Oct 9, 11, 13 | Differentiation techniques: Sections 3.4, 3.5, 3.6 |
| 8 | Oct 16, 18, 20 | Differentiation techniques: Sections 3.7, 3.8, 3.9
Project 3 Assigned (Due in recitation Thursday November 2) |
| 9 | Oct 23, 25, 27 | Applications of derivatives, review: Sections 3.10, 3.11
Test 2 October 26 (Thursday evening, 6-7:30 pm in Stevens Auditorium) |
| 10 | Oct 30; Nov 1, 3 | Integrals: Sections 5.1, 5.2
(Project 3 due in recitation Thursday November 2) |
| 11 | Nov 6, 8 (MW) (Veterans Day Nov 10) |
Fundamental theorem of calculus: Sections 5.3, 5.4, 4.10 |
| 12 | Nov 13, 15, 17 | Integration: Sections 5.5, 5.6
Project 4 Assigned (Due in recitation Thursday December 7) |
| 13 | Nov 20, 22 (MW) (Thanksgiving recess Nov 23, 24) |
Optimization, mean value theorem: Sections 4.1, 4.2 |
| 14 | Nov 27, 29, Dec 1 | Interpreting derivatives, review: Sections 4.3, 4.4
Test 3 November 30 (Thursday evening, 6-7:30 pm in Stevens Auditorium) |
| 15 | Dec 4, 6, 8 | Curve sketching, optimization: Sections 4.5, 4.6*, 4.7
(Project 4 due in recitation Thursday December 7) |
| 16 | Dec 11, 13, 15 | Applications of differentiation, review: Sections 4.8*, 4.9 |
| 17 | Dec 20 (Dec 18-22 Final Exams) |
Final Examination Wednesday Dec 20, 3-5 pm (Stevens Auditorium) |
*Starred sections may be treated lightly or omitted if there are disruptions, such as bad weather. The schedule is subject to change, if necessary. Check the "last modified" date on the website for the most recent update (below).