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Summary. Calculus is the study of continuous change. Building upon knowledge of functions, algebra, and trigonometry, this course introduces the fundamental calculus concept of a limit and its application to definition of derivatives and integrals. These calculus constructs are subsequently applied to a large variety of problems from the sciences.
Times |
TuTh 9:30-10:45AM, Phillips 215 |
Office hours |
We 3:30-4:30PM Chapman 451, Th 3:30-4:30PM, Fr 2:30-3:30PM, Zoom |
Instructor |
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| Assistants | Jake Grdadolnik, Kaitlyn Hohmeier, Aaron Jacobson |
(The instructor reserves the right to make changes to the syllabus. Any changes will be announced as early as possible.)
Students must have satisfied at least one of the following in order to enroll in MATH 231:
Score of at least 640 on the SAT 2 Subject Test, Mathematics Level 2
Score of at least 29 on the ACT Mathematics Test
Score of at least 4 on the International Baccalaureate Mathematics High Level
Score of at least 5 on the International Baccalaureate Mathematics Standard Level
Grade of at least C- in MATH 130
MATH 231L is a one-hour course that offers just-in-time instruction and practice on algebra and trigonometry to support MATH 231 students. Students who meet the prerequisite above but are near the cut-off scores, should strongly consider enrolling in the corequisite course.
Upon course completion students should acquire the following concepts and skills:
the need for a framework for infinite number of operations;
the idea of a limit and its application to limits of functions;
relationship between function graphs and function limits at a point;
derivatives of functions and their applications;
integrals of functions and their applications;
geometric significance of derivatives and integrals;
relationship between derivatives and integrals expressed in the Fundamental Theorem of Calculus
Course textbook: Calculus: Early Transcendentals (3rd edition) by S. Briggs, L. Cochran, B. Gillet, E. Schulz.
MyLab Math student registration instructions.
Course activities are meant to ensure understanding of calculus concepts and are detailed in Tabel 1. Students should:
read relevant textbook sections before each class;
self-assess understanding of concepts through recommended exercises;
complete homework meant to build proficiecy in calculus techniques;
study practical applications of calculus by drafting solutions to recitation problems;
demonstrate mastery of both concepts and technqiues in scheduled tests and final examination.
Late homework is not accepted, except for university-approved absences.
All tests are in-class, 45 minutes, closed-book, and with no calculation aids. Test dates are posted in the leson plan below. If unable to attend due to an university-approved absence, taking the test early is possible.
Active participation in all course activities (lectures, recitations, office hours) is required to attain course outcomes. There is no need to inform instructors of absences due to personal circumstances. Students are required to inform themselves of topics covered during absences. Various extra credit activities are announced to encourage active class participation.
Unless explicitly stated otherwise, all work is individual. You may discuss various approaches to homework problems with students, instructors, but must draft your answers by yourself. Students implicitly accept this honor code by submission of any work for grading.
A total of 104 assignment/test grade points are offered to allow sufficient flexibility for personal circumstances that might require student absence from courses activities, e.g., two recitation and two homework assignments can be missed. Also, the point total formula for the course allows a missed or failed test to be substituted with good performance in the final examination (see Table 1). Course points are mapped to grades as shown in Table 2. Various in-class course participation activities are rewarded with up to 6 grade points for a total of 110 possible grade points.
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Students are required to have a laptop, that conforms to CCI minimal standards. Software investigation of calculus concepts will be interspersed throughout the course.
Test dates are indicated in bold red. Practice tests and solutions:
All students are offered the chance to retake Test1-3 on Nov. 29. These make-up or re-tests will be 35 minutes long, allowing students to attempt two tests during class time. Tests will not be returned, but the higher of your original test or the retest will be used for grade calculations. Grade calculations are sent to students on 12/06 to include final examination. Any errors noticed in grade calculations must be signaled by email by noon 12/07. Grades are sent to Registrar at 3:00PM on 12/07.
Week |
Notes |
Date |
Textbook |
Topic |
01 |
08/16 08/18 |
§2.1 §2.2 |
Limit concept Limit techniques |
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02 |
08/23 08/25 |
§2.3 §2.4-5 |
MyLab Math. Limit techniques Infinity & limits |
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03 |
08/30 09/01 |
§2.6-7 §3.1-2 |
Continuity Derivative |
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04 |
- 09/08 |
§3.2-3 |
Derivative function Differentiation rules |
|
05 |
09/13 09/15 |
§3.4 §3.5 |
Derivatives of products, quotients Derivatives of trigonometric functions |
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06 |
09/20 09/22 |
§3.6 §3.7 |
Test 1 (§2.1-6, §3.1-3). Rate of change Differentiation chain rule |
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07 |
09/27 09/29 |
§3.8 §3.9 |
Implicit differentiation Derivatives of logarithm/exponentials |
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08 |
10/04 10/06 |
§3.10 §3.11 |
Derivatives of inverse functions Related rates |
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09 |
10/11 10/13 |
§4.1-2 §4.3 |
Extrema, mean value theorem Derivatives information |
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11 |
10/18 - |
§4.4
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Function graphs
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12 |
10/25 10/27 |
§4.5 §4.6 |
Test 2 (§3.4-11, §4.1-3). Optimization Linear approximation |
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13 |
11/01 11/03 |
§4.7-8 §4.9 |
L'Hôpital rule. Newton method Anti-derivative |
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14 |
11/08 11/10 |
§5.1 §5.2 |
Areas under curve Definite integral |
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15 |
11/15 11/17 |
§5.3 §5.4-5 |
Test 3 (§4.4-9, §5.1) Fundamental theorem of calculus Integral techniques |
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16 |
11/22 11/29 |
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Final preparation Test1-3 retake (you may retake 2) |
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12/05 |
4:00PM |
Common Final Examination (Coker Hall-0201) Sections: §2.1 to §5.5 |
Homework is generally assigned and graded through the online MyLab Math system at 5PM on Tuesdays, and due the following Tuesday. The schedule is modified for UNC holidays. Thirteen homework assignments are scheduled.
Nr. |
Issue Date |
Due Date |
Problems |
Solution |
HW00 |
08/22 |
09/20 |
Algebra review |
Not graded |
HW01 |
08/23 |
08/30 |
§2.2: 4, 5, 23, 33, 34, 36, 38, 39, 41, 53 |
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HW02 |
08/30 |
09/06 |
§2.4: 26, 27, 34, 35, 54 §2.5: 37, 39, 57, 59, 71 |
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HW03 |
09/06 |
09/13 |
§3.2: 25, 29, 36, 49, 59 §3.3: 27, 28, 33, 68, 71 |
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HW04 |
09/14 |
09/20 |
§3.4: 20, 22, 25, 46, 55 §3.5: 26, 29, 40, 48, 59 |
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HW05 |
09/19 |
09/27 |
§3.6: 15, 18, 19, 37, 39 §3.7: 17, 20, 23, 44, 49 |
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HW06 |
09/26 |
10/04 |
§3.8: 15, 17, 18, 45, 46 §3.9: 36, 37, 40, 77, 78 |
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HW07 |
10/3 |
10/11 |
§3.10: 15, 19, 21, 23, 29 §3.11: 11, 13, 23, 29, 35 |
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HW08 |
10/11 |
10/18 |
§4.1: 25, 27, 31, 39, 72,73 §4.2: 25, 26, 39, 45, |
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HW09 |
10/20 |
10/27 |
§4.3: 15, 22, 25, 48, 50 §4.4: 7, 8, 17, 19, 23 |
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HW10 |
10/28 |
11/03 |
§4.5: 22, 27, 33, 40, 45 §4.7: 21, 25, 31, 35, 39 |
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HW11 |
11/03 |
11/10 |
§5.1: 7, 9, 15, 19, 27, 31, 40, 45, 49, 64 |
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HW12 |
11/10 |
11/17 |
§5.2: 26, 28, 34, 43, 51, 69, 71, 72, 75, 94 |
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HW13 |
11/17 |
11/29 |
§5.3: 5, 13, 18, 24, 41, 46, 52, 64, 67, 78 |
One handwritten problem will be submitted in recitation in weeks 2-15, excepting UNC holidays and wellness days for a total of 13 recitation problems. Model solutions will be posted that show:
proper problem formulation
motivated solution procedure
calculation organization
procedure used by recitation leaders to grade the problem
Nr. |
Issue Date |
Due Date |
Choose 1 from problems |
Model Solution |
R01 |
08/23 |
08/29 |
§2.3: 73-76, 88-94 |
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R02 |
08/30 |
09/12 |
§2.5: 52-56, 72-81 |
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R03 |
08/30 |
09/12 |
§2.6: 42-48, 68-72 |
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R04 |
09/14 |
09/19 |
§3.4: 48-54, §3.5: 42-47 |
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R05 |
09/19 |
10/03 |
§3.6: 23-27, §3.7: 50-60 |
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R06 |
09/22 |
10/03 |
§3.8: 29-40 |
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R07 |
10/03 |
10/10 |
§3.11: 30-34, 36-45 |
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R08 |
10/11 |
10/17 |
§4.1: 30-34, 36-45 |
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R09 |
10/20 |
10/24 |
§4.4: 50-54 |
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R10 |
10/28 |
10/31 |
§4.5: 28-31, 50-53, Q01 |
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R11 |
10/31 |
11/7 |
§4.7: 84-86, §4.8: 9-12, Q02 |
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R12 |
11/7 |
11/14 |
§4.9: 30-34, §5.1: 18-21, Q03 |
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R13 |
11/14 |
11/21 |
§5.3: 34-40, §5.5: 24-28, Q04 |
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R14 |
11/27 |
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Practice Make-up Solutions |
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