Course Information
Mathematics
Calculus I
Math 170
Jayce Bell
jbell@basinschools.net
208-392-4183 ext 1278
Course Description
This is the first course in the calculus sequence. It covers algebraic and transcendental functions; rate of change; limits; continuity; differentiation of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions; differentials; applications of differentiation; definite and indefinite integrals; area between curves; volumes; and other applications of integration, indeterminate forms, and L'Hôpital's rule. PREREQ: MATH 147 (or MATH 143 and MATH 144) or equivalent placement score. (This CWI course meets Idaho State Board of Education GEM competency requirements for GEM 3 - Mathematical Ways of Knowing.). (5 lecture hours, 0 lab hours, 5 credits)
Schedule
Class will meet Monday through Fridays in Room 1 at Idaho City High School.
Hybrid/online instruction options are available depending on the status of the school due to COVID-19.
Instructor Availability
Mr. Bell is available in his office from 8:00 am until 3:30 pm, Mondays through Fridays.
Course Learning Outcomes
The Course Objective is to provide students with the mathematical foundation necessary (1) for students majoring in the mathematical and physical sciences, engineering, mathematics education, and related fields, and (2) to be able to develop strong mathematical reasoning skills, clear conceptual understanding, and the ability to think critically.
Students completing this course are expected to acquire the ability and skills to:
A. Graph functions, including trigonometric functions.
1. Find the domain and range of functions and graph functions, including polynomial functions, absolute-value functions, rational functions, square root and cube functions, power functions, algebraic functions, exponential functions, logarithmic functions, and trigonometric functions.
2. Find sums, differences, products, quotients, and compositions of functions.
3. Shift, scale, and reflect graphs of functions.
4. Evaluate trigonometric functions for special angles.
5. Use trigonometric identities, including the Pythagorean identity, the Addition formulas, the Double-Angle formulas, the Half-Angle formulas, and the Law of Cosines.
6. Understand the limitations of using a graphing utility, such as choosing an appropriate window and obtaining a complete graph.
7. Find inverse functions.
8. Use properties of logarithms.
9. Graph arcsine and arccosine and identify their domains and ranges.
B. Find limits and determine whether a function is continuous.
1. Calculate average and instantaneous rates of change.
2. Find limits from graphs.
3. Use the limit laws to calculate limits.
4. Eliminate common factors to find limits of rational functions.
5. Find limits of average rates of change.
6. Use the Sandwich Theorem (aka Squeeze Theorem) to find limits of functions.
7. Use the formal definition of a limit to prove limit statements.
8. Find one-sided limits graphically and algebraically.
9. Use the fact that the limit of the ratio of and is , to find limits.
10. Apply the Continuity Test to determine whether a function is continuous at a point.
11. Find limits of continuous composite functions.
12. Apply the Intermediate Value Theorem for continuous functions to find solutions to equations.
13. Use limits involving infinity to find asymptotes.
C. Calculate derivatives of functions.
1. Find the tangent to the graph of a function.
2. Find the derivative of a function at a given point using the limit of the difference quotient.
3. Use the alternative formula for the derivative to calculate derivatives.
4. Identify cases when the derivative does not exist.
5. Understand the relationship between differentiability and continuity.
6. Apply differentiation rules for constant functions, powers, sums, differences, products, and quotients of functions.
7. Calculate higher-order derivatives.
8. Solve problems involving motion along a line, such as find displacement, average velocity, speed, and acceleration.
9. Calculate derivatives of trigonometric functions.
10. Apply the chain rule to find derivatives.
11. Use implicit differentiation to find derivatives.
12. Apply the Derivative Rule for Inverses to find derivatives of inverse functions.
13. Find derivatives of logarithms.
14. Use logarithmic differentiation to find the derivative.
15. Find derivatives of inverse trigonometric functions.
16. Solve related rates problems.
17. Approximate functions using linearization.
18. Use differentials to estimate change.
D. Use derivatives to solve application problems.
1. Find the absolute extrema of a continuous function.
2. Find values that satisfy the conclusion of the Mean Value Theorem.
3. Use the first derivative to determine the local extrema of a function.
4. Use the second derivative to test for concavity and for local extrema.
5. Use derivatives to graph functions.
6. Apply L’Hopital’s Rule to find limits of rational functions having appropriate indeterminant forms.
7. Solve applied optimization problems, such as minimize perimeter or cost, or maximize volume or profit.
8. Apply Newton’s Method to approximate roots.
E. Evaluate integrals.
1. Find antiderivatives.
2. Approximate area with finite sums.
3. Find limits of finite sums.
4. Use properties of definite integrals to evaluate integrals.
5. Use definite integrals to find area of nonnegative functions.
6. Find the average value of a continuous function using a definite integral.
7. Use the Fundamental Theorem of Calculus to find derivatives of integrals and to evaluate definite integrals using antiderivatives.
8. Apply the Substitution Method to evaluate indefinite integrals.
9. Find the area between two curves.
F. Solve application problems involving definite integrals.
1. Find the volume of a solid by slicing with parallel planes.
2. Find the volume of a solid of revolution using the Disk Method
3. Find the volume of a solid of revolution using the Washer Method.
4. Find the volume of a solid of revolution using cylindrical shells.
5. Find work done by a variable force.
6. Find the work done to pump liquids from containers.
G. Solve problems involving integrals and transcendental functions.
1. Evaluate integrals that result in a logarithmic function.
2. Evaluate integrals that result in an exponential function.
3. Solve separable differential equations involving exponential change, such as unlimited population growth, radioactivity, and heat transfer.
4. Find derivatives of hyperbolic and inverse hyperbolic functions.
5. Compare the growth rates of functions.
Outcomes Assessment
Student outcomes will be assessed using Quizzes, Unit Tests, Projects and Finals.
Grading Policy
· Grading scale (What defines an A, B, C, etc.?)
· Methods used to evaluate student performance (required assignments, quizzes, group work, participation, presentations, exams, essays, skills tests, etc.) and percentage or points breakdown.
· Sample policy (modify as needed): Your overall grade for the course will be calculated using the following weights and categories:
Category
Weight
Homework
15%
Quizzes
20%
5-8 Exams
45%
Final Exam
20%
TOTAL:
100%
Letter grades will be determined as follows:
A:
90-100%
B:
80-89%
C:
70-79%
D:
60-69%
F:
59% or below
Per departmental policy, a student must earn at least a 60% on the common final exam to be eligible to pass the class with a grade of C or better. Students whose overall average is 70% or better after failing the common final, will be given a letter grade of D and will be offered the opportunity to take a challenge exam.
o Challenge Exam: This exam is available for a limited time after the end of the semester. Students who can earn a 60% or better on the challenge exam will have their grade changed from the D given based on the departmental policy to the letter grade that matches their original semester average. Students eligible for this challenge opportunity will be notified by their instructor of their eligibility along with details regarding dates of availability and the timeframe for grade changes. Please note: This opportunity is not available to all students who fail the final exam. It is only available to students who fail the final exam whose semester average stays at 70% or above after having done so.
Textbooks and Required Materials
The textbook for the course is Calculus, 8th Edition, by Larson, Hostetler, and Edwards, 2006.
A scientific calculator is needed for this course. A graphing calculator is encouraged.
Instructional Conversation
[Reference the Instructional Conversation guide for additional language or clarification]
Learning is an active exchange between faculty and student.
As a faculty, I will
· Instruct through varied methods including lecture, activities, guided discovery and video feedback.
· Assess through standard tests, quizzes and homework.
· Inform through Lumen, Google Classroom, and Blackboard
As a student, you will
· Attend class and be ready to actively participate
· Submit assignments on time and communicate prior to the due date if that is an issue.
· Participate by actively engaging in class discussions.
Course Calendar
Please refer to the running course calendar in your Google Classroom stream.
Course Expectations
· The hourly expectation involved in this class is as follows:
o A student can expect to spend on an average approximately 8 hours per week in total on this class (reading, homework, participating/attendance, etc.). Some students may need more time, and some may need less time each week. Please make sure that you are using the amount of time that is right for you to be successful in this class.
· Please refer to the ICHS student handbook for safety requirements and guidelines
· There is to be no smoking, drinking or eating in class under any circumstances
· Late work policy, definition of attendance and attendance policy, cell phone use
· Any guests/children to be brought to class need to be cleared by the front office.
· Any scheduling issues, as well as grade updates will be posted in Lumen.
Personal Technical Skills
This course will not provide information on how to use a computer, use Blackboard, navigate the web or manage electronic files. Students who are having difficulty should contact their instructor, IT Help Desk or Tutoring Services. Please use the resources listed above or speak with the instructor before dropping a course.
Students must be able to do the following with or without accommodation:
· Use an internet browser to navigate the internet and Blackboard.
· Download, upload, create, save, edit and open documents using Microsoft Office applications, such Word, Excel and PowerPoint.
· Download and upload audio and video files.
Civility and Behavioral Expectations
The College of Western Idaho is committed to educational excellence and recognizes that to achieve that excellence, students, faculty, and staff have a right to be in a safe environment, free of disturbance and civil in all aspects of human relations. Membership in the CWI learning community places a special obligation on all members to preserve the safe learning environment, regardless of the medium of the environment. It is the responsibility of instructors to determine, maintain, and enforce the standards of behavior required to preserve that safe environment.
Behavior that has a negative impact on the learning environment is prohibited. Such behavior may include, but is not limited to, rude, sarcastic, obscene, or disrespectful and/or disruptive behavior. Instructors will determine the appropriate response to problematic behavior in line with the procedures stated in the CWI Student Handbook. Problematic behavior may result in a student being removed from the class session and/or referred to the CWI Academic Conduct Process. For information on how problematic behavior will be managed, see the CWI Student Handbook. It is the student’s responsibility to check their email to receive notification of any scheduled appointments or other urgent communications.
Any student or other member of the learning community may report a violation of the Student Code of Conduct here.
Academic Integrity
One of the College’s Core Themes is Instructional Excellence, and in order to achieve instructional Excellence, academic integrity must be upheld. Academic Integrity is the “commitment to five fundamental values: honesty, trust, fairness, respect, and responsibility. … these five values, plus the courage to act on them even in the face of adversity, are truly foundational to the academy” (The Fundamental Values of Academic Integrity, 2013). These values are especially important in how students represent their own learning, ideas, and work. Practicing academic integrity includes, but is not limited to, non-participation in the following behaviors: cheating, plagiarism, falsifying information, unauthorized collaboration, facilitating academic dishonesty, and violating program policies and procedures.
For additional information on academic integrity expectations, see the Student Code of Conduct. Violations may result in disciplinary action ranging from failure of the assignment to failure of the entire course. Acts of academic dishonesty, especially when sanctions are given, are reported and run through the Academic Conduct Process. Repeated acts of academic dishonesty have more severe institutional consequences.
Title IX & A Respectful Community
Title IX guarantees all students the right to an education free from discrimination on the basis of sex. This includes the right to an education free from sexual harassment, including sexual assault. This may include unwelcome conduct of a sexual nature in class, or in online discussion boards or through chat or video conferences. This law also protects students from discrimination based on pregnancy or being a parent and provides support options as well. If you, or someone you know, may have been experienced sexual harassment or discrimination of any kind, you are encouraged to report it to the College Title IX Coordinator by completing a report here, or by e-mailing respectfulcommunity@cwi.edu. Filing a report allows the College to provide supportive measures to those involved. It does not obligate a student to go forward with an investigation, and all information reported is protected under federal law. For more information, click here.
Student Services
CWI provides a number of offices and services to assist students on their academic journey. Below is a list of the services most commonly accessed by students:
· One Stop Service Centers – Provides assistance with admissions, advising, registration, financial aid, and most other common needs you may have. They are a good first stop for any questions.
· Student Disability Services – Provides accommodations and support for students with a range of disabilities.
· Counseling Services – Short-term counseling for students provided free of charge.
· Library & Research Support – Assists students with research, study skills, textbook reserves and other services key to academic success.
· Tutoring Center – Free tutoring services on a range of academic subjects, available to all enrolled students.
· Writing Center – Provides strategies to help students identify opportunities to improve the quality of their writing, free of charge.
· Assessment & Testing – Proctoring services for a range of course exams, accommodated testing, and outside certification tests.
· Student Affairs – Provides a range of engagement opportunities, including professional and interest organizations, student government, support for veteran students & families, and CARE Services to support students through unexpected life events.
CWI COVID-19 Response
CWI is committed to providing a safe learning environment for all of our students. We will be monitoring the class environment and delivery to ensure continued compliance with CDC and State of Idaho guidelines. Any change to course delivery will be communicated directly to students.
Emergency Procedures [Required for In-person, Hyflex and Hybrid Courses]
CWI posts instructions for evacuation in all rooms and encourages everyone on campus to review the CWI Emergency Handbook.
Emergency Procedures for Idaho City High School are posted by each classroom door.
Idaho General Education Matriculation (GEM) Competency
This course meets the Idaho State Board Gen Ed Matriculation (GEM) course competencies for Mathematical Ways of Knowing courses. For more information see the State Board competencies.
Signature Assignments
This course meets the Gen Ed Program Outcome of Solve Problems through its Signature assignment. For more information see the CWI Gen Ed Program Outcomes