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Essential Objectives

Course Syllabus


Revision Date: 02-Jan-24
 

Calculus I




Credits:
Semester Dates: Last day to drop without a grade: 02-11-2024 - Refund Policy
Last day to withdraw (W grade): 03-24-2024 - Refund Policy
This course has started, please contact the offering academic center about registration

Faculty

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Course Description

This course is a review of analytical geometry and introduction to the calculus of one variable. Topics include limits, derivatives of algebraic, transcendental, and trigonometric functions, rates of change, optimization, curve sketching, elements of integration of algebraic, transcendental, and trigonometric functions, area, volume, and practical applications in many fields. Students must take a math assessment for placement purposes prior to registration. Prerequisite: Pre-Calculus or equivalent skills.


Essential Objectives

1. Use the Cartesian Coordinate system to graph linear and other functions.
2. Define and recognize functions.
3. Apply concepts of limits and continuity.
4. Define and apply the concept of derivative.
5. Apply the appropriate process to find the derivative to include product, quotient, and chain rules.
6. Use derivatives to find solutions to maximum and minimum problems.
7. Find derivatives of algebraic, exponential, logarithmic, and trigonometric functions.
8. Use the appropriate process to find the integral of algebraic, exponential, logarithmic, and trigonometric functions.
9. Use the definite integral to solve area and other applied problems.
10. Employ the graphing calculator for the numerical and graphical solution of problems.
11. Demonstrate proficiency in understanding, interpreting, evaluating, and applying quantitative data and information.
12. Apply mathematical reasoning to analyze social justice problems in a variety of different contexts and consider whether these approaches are just and equitable.


Required Technology

More information on general computer and internet recommendations is available on the CCV IT Support page. https://support.ccv.edu/general/computer-recommendations/

Please see CCV's Digital Equity Statement (pg. 45) to learn more about CCV's commitment to supporting all students access the technology they need to successfully finish their courses.


Required Textbooks and Resources

This course only uses free Open Educational Resources (OER) and/or library materials. For details, see the Canvas Site for this class.


Methods

Students learn math by doing math. My preferred teaching method is to provide a brief verbal explanation with lots of in class practice. This in class practice will consist of individual and group learning activities.


Evaluation Criteria

Your final grade will be calculated as follows:

10% Classroom Engagement
20% Online Homework
20% Paper and Pencil Homework
20% Weekly Quizzes
30% Tests

Grading Criteria

CCV Letter Grades as outlined in the Evaluation System Policy are assigned according to the following chart:

 HighLow
A+10098
A Less than 9893
A-Less than 9390
B+Less than 9088
B Less than 8883
B-Less than 8380
C+Less than 8078
C Less than 7873
C-Less than 7370
D+Less than 7068
D Less than 6863
D-Less than 6360
FLess than 60 
P10060
NPLess than 600


Weekly Schedule


Week/ModuleTopic  Readings  Assignments
 

1

Functions Part 1: Functions in general. Linear Functions, quadratics and higher order polynomials. Trigonometric functions.

  

1.1 Review of functions

1.2 Basic classes of functions

1. 3 Trigonometric Functions

  

3 Sofia Assignments

 

2

Inverse Functions

Exponential and logarithmic functions

  

1.4 Inverse functions

1.5 Exponential and logarithmic functions

  

Sofia Assignments

 

3

Limits and Continuity -- What is a limit? Why it matters, how to find limits numerically graphically and algebraically

  

2.2 The Limit of a function

2.3 The Limit Laws

2.4 Continuity

  

Sofia Assignments

Problem Set 1: Chapters 1 and 2

 

4

What is derivative? The derivative is a limit. Average change vs. Instantaneous change. Finding the derivative function.

  

3.1 Defining the derivative

3.2 The Derivative as a function

  

Sofia Assignments

 

5

Differentiation

  

3.3 Differentiation Rules

  

Sofia Assignments

Quiz 1

 

6

Differentiation Rules: Basic Rules, power rule, addition rule, product rule, quotient rule

  

3.3 Differentiation Rules

3.4 Derivative as a rate of change

3.5 Derivatives of the trigonometric functions

  

Sofia Assignments

Pencil and Paper homework 5

 

7

The Chain rule

  

3.6 The chain rule

3.7 Derivatives of Inverse Functions

  

Sofia Assignments

Pencil and Paper homework 6

Wednesday: Quiz on Week 6 - Basic Rules

 

8

Implicit Differentiation

Derivatives of exponential and logarithmic functions

Logarithmic differentiation

  

3.8 Implicit Differentiation

3.9 Derivatives of Exponential and Logarithmic Functions

  

Sofia Assignments

Pencil and Paper homework 7

Wednesday Quiz on Week 7

 

9

Graphing with Calculus

  

4.3 Maxima and Minima

4.5 Derivatives and the Shape of a Graph

4.6 Limits at infinity and Asymptotes

  

Sofia Assignments

Pencil and Paper homework 8

Wednesday: Quiz on Week 8

 

10

Test 2

  

Wrap up loose ends from weeks 6 - 9

In class review and practice for Test 2

Wednesday: Test 2

  

Test 2

 

11

Applications of the Derivative

  

4.1 Related Rates

4.7 Applied optimization problems

  

Sofia Assignments

Pencil and Paper homework 9

 

12

Antiderivatives and Areas

  

4.10 Anti derivatives

5.1 Approximating Area

5.2 Definite Integral

  

Sofia Assignments

Pencil and Paper homework 10

Wednesday Quiz on Week 11

 

13

The fundamental Theorem of Calculus

  

5.3 The fundamental Theorem of Calculus

5.4 Integration formulas and the Net Change Theorem

  

Sofia Assignments

Pencil and Paper homework 11

Wednesday: Quiz on Week 12

 

14

Substitution Method

  

5.5 Substitution

5.6 Integrals involving Exponential and Logarithmic Functions

6.1 Area Between Curves

  

Sofia Assignments

Pencil and Paper 12

Wednesday: Quiz on Week 13 material

 

15

Test 3

  

Wrap up loose ends

In class practice and review for Test 3

  

Test 3

 

Attendance Policy

Regular attendance and participation in classes are essential for success in and are completion requirements for courses at CCV. A student's failure to meet attendance requirements as specified in course descriptions will normally result in a non-satisfactory grade.

  • In general, missing more than 20% of a course due to absences, lateness or early departures may jeopardize a student's ability to earn a satisfactory final grade.
  • Attending an on-ground or synchronous course means a student appeared in the live classroom for at least a meaningful portion of a given class meeting. Attending an online course means a student posted a discussion forum response, completed a quiz or attempted some other academically required activity. Simply viewing a course item or module does not count as attendance.
  • Meeting the minimum attendance requirement for a course does not mean a student has satisfied the academic requirements for participation, which require students to go above and beyond simply attending a portion of the class. Faculty members will individually determine what constitutes participation in each course they teach and explain in their course descriptions how participation factors into a student's final grade.


Participation Expectations

You will receive a classroom engagement grade for each class period. To get full points:

  • Be Present
  • Be on time
  • Ignore your phone except for emergencies
  • Engage in all learning activities.


Missing & Late Work Policy

  • Pay attention to all due dates in Canvas.
  • Sofia assignments are assigned each class and due 11:59 pm the day of the subsequent class. pm.
  • Paper and Pencil assignments are available on Wednesdays and are due the subsequent Wednesday.
  • You will have a weekly quiz each Wednesday based on the Pencil and Paper assignment. .
  • All homework (Sofia and Pencil and Paper) are reduced 2.86% for each day late. This is the equivalent of two letter grades per week.
  • You are responsible for materials and information should you miss class. All assignments, handouts, notes are available in Canvas.

Accessibility Services for Students with Disabilities:


CCV strives to mitigate barriers to course access for students with documented disabilities. To request accommodations, please
  1. Provide disability documentation to the Accessibility Coordinator at your academic center. https://ccv.edu/discover-resources/students-with-disabilities/
  2. Request an appointment to meet with accessibility coordinator to discuss your request and create an accommodation plan.
  3. Once created, students will share the accommodation plan with faculty. Please note, faculty cannot make disability accommodations outside of this process.


Academic Integrity


CCV has a commitment to honesty and excellence in academic work and expects the same from all students. Academic dishonesty, or cheating, can occur whenever you present -as your own work- something that you did not do. You can also be guilty of cheating if you help someone else cheat. Being unaware of what constitutes academic dishonesty (such as knowing what plagiarism is) does not absolve a student of the responsibility to be honest in his/her academic work. Academic dishonesty is taken very seriously and may lead to dismissal from the College.