Hawaii Pacific University
MATH 2214 Calculus I Section ____
Semester and year, meeting times
Instructor: Name, contact information and other relevant information about the instructor.
Course description: A course in single variable calculus which emphasizes limit, continuity, derivative,
and integral. Primary focus is on the derivative with an introduction to the integral and elementary
applications of the integral. Differentiation topics include: chain rule, implicit differentiation, curve
sketching and maxima and minima problems. Integration topics include: fundamental theorem of calculus,
method of substitution, area between curves, and volumes of revolution.
Course prerequisite: MATH 1140 or higher (or placement into the course)
General Education Requirement: This course is classified under the Research and Epistemology Theme
and meets the requirement for a course in Research & Epistemology B: Numeracy and Quantitative
Reasoning.
General Education Student Learning Outcomes and the Five Themes: HPU’s general education
curriculum is focused around five themes. This course emphasizes the Research and Epistemology
Theme and provides students with opportunities to achieve the following related general education
student learning outcomes.
Students will understand the concept of epistemology, i.e., that there are various systems of
gather/organizing/analyzing/evaluating in the process of constructing knowledge as well as
multiple ways to solve a problem. Mathematics depends on multiple ways of evaluating a
process and solving problems. In Calculus we will study the graphic solution in addition to
algebraic and numeric solutions for a number of problems, and discuss the advantages of
different strategies for solving problems. Students will build on what they learned in precalculus courses to solve problems choosing from a variety of approaches, including the
application of limits, the use of derivatives and the application of differentiation, and the use
of integrals and the application of integration.
Students will seek and achieve understanding of numerical data. In Calculus students are
constantly working with numeric data. This is done in order to generate equations, construct
graphs and interpret the results. Students must be able to understand the techniques used to
generate numeric data in addition to asking the important questions “What does this mean?”
and “Do my results make sense in the context of this problem?” Students will learn that
calculus is much more than an obscure mathematical language involving the techniques of
differentiation and integration. As calculus has evolved through the ages, beginning in the
late 17th Century, it has been used in a wide variety of applications to find maximum and
minimum quantities. It has direct application to economics, engineering, social sciences,
business and industry.
Students will recognize the multiple interpretations numerical data permit and
ways that they can be manipulated. In this calculus class, students will find that numerical
data related to mathematical functions and operations can be interpreted in different ways.
For example, data presented might indicate that an investment approach has unlimited profit
opportunities. When examined more closely, however, students may find that the investment
cannot be maximized as efficiently as previously assumed. Another example is the analysis of
an economic operation using techniques of differentiation. Students may assume that as a
company makes and sells more product, the profits will continue to increase exponentially.
Students may not initially understand that the production of an item using a cost-benefit
analysis may have a minimal point where the cost of production actually outweighs the profit
until a point of equilibrium is reached. These critical data points can be found using
techniques of differentiation.
Students will utilize methods and technologies appropriate to the discipline to
investigate research questions, generate predictions, test hypotheses and/or solve
problems. Students will use verbal (written or oral), numerical (data table), symbolic
(mathematical formula), and graphical representations of functions to solve problems. In the
lessons provided, problem-solving techniques are presented that employ the use of a
graphing calculator. For example, students might address problems such as controlling the
flow from a draining tank, or calculating the distance between ships at sea
Note: Purple text shows places where specific course information must be filled in. Red text contains
explanatory notes to the instructor which should be deleted before using the syllabus. Blue explanations
above should be rephrased by the individual instructor if necessary to reflect the specific approach in that
section of the course. Course specific outcomes below are an example and may also be rephrased or
modified by the instructor.
Student Learning Outcomes for MATH 2214 Calculus I
Upon the successful completion of this course, students should be able to:
1. Calculate or estimate limits of functions given by formulas, graphs, or tables; also using
properties of limits and L’Hopital’s Rule.
2. Determine whether a function given by a graph or formula is continuous or differentiable at a
given point or on a given interval.
3. Distinguish between average and instantaneous rate of change, and interpret the definition of
the derivative graphically.
4. Calculate derivatives of polynomial, rational, common transcendental functions, combinations
of these functions, and implicitly defined functions.
5. Apply the power rule, product rule, quotient rule and the chain rule to functions explicitly and
implicitly for finding derivatives.
6. Find extreme values of modeling functions given by formulas or graphs:
a. predict, construct and interpret the shapes of graphs,
b. solving equations (i.e. Newton’s Method),
c. find linear approximations of functions (differentials).
7. Estimate a slope, a rate of change and the reasonableness of a result.
8. Sketch a possible graph of a function given the graph of its derivatives.
9. Use derivatives in practical applications, such as distance, velocity, acceleration and related
rates. Use first and second derivative tests to optimize functions and to find critical numbers,
inflection points, extreme points, and the shape of the graph.
10. Interpret solutions to applied problems, attaching the appropriate units to an answer.
11. Distinguish assumptions and conclusions in mathematical statements
12. Estimate areas beneath function curves with finite sums.
13. Compute definite integrals as limits of finite sums.
14. Evaluate definite integrals using the linearity property.
15. Compute definite integrals using the Fundamental Theorem of Calculus.
16. Evaluate indefinite integrals using the substitution rule
17. Compute the area between curves as a definite integral using substitution.
For the rest of these required syllabus items see the details in the faculty handbook. Delete this note
once the syllabus is complete. For online courses there are some additional requirements given at this
link.
Texts List textbooks with ISBN’s and include this language as well
All textbook information (pricing, ISBN #, and e-books) for this course can be found on the HPU
Bookstore website: hpu.edu/bookstore.
If you have any questions regarding textbooks, please contact the HPU Bookstore at:
Phone:
808-544-9347
Or e-mail:
jyokota@hpu.edu
mmiyahira@hpu.edu
Assignments and mode of evaluation
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not given with the description of the assignments).
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