IC162211 Calculus I
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IC162211 Calculus I
COURSE INFORMATION
. Credits: 4
. Semester: 2026summer
. Teaching Methods: Online
. Time: May18-July31,2026
COURSE DESCRIPTION
Differential and integral calculus are introduced in this course, covering fundamental concepts such as limits, continuity, derivatives, and integrals. Through analytical and problem-solving exercises, students will learn to apply calculus in real-world contexts, including science, engineering, and economics. The focus is on understanding mathematical principles and their applications rather than solely on computation.
PREREQUISITES
None
COURSE OBJECTIVES
By the end of this course, students should be able to:
1. Understand the concept of limits and continuity and their role in calculus.
2. Compute derivatives of algebraic, trigonometric, exponential, and logarithmic functions.
3. Apply differentiation techniques to solve problems related to rates of change, optimization, and motion.
4. Understand and apply the Fundamental Theorem of Calculus.
5. Compute definite and indefinite integrals using various techniques.
6. Apply integration techniques to problems involving areas, volumes, and other applications.
7. Develop a strong foundation for further studies in mathematics, physics, and engineering.
REQUIRED TEXTBOOKS AND MATERIALS
. Required Text: James Stewart, Calculus: Early Transcendentals, 8th Edition, 2015, Brooks Cole.
. Recommended Texts & Other Readings: N/A
COURSE CONTENTS
|
Unit 1 Functions and Models: Four Ways to Represent a Function, Mathematical Models: A Catalog of Essential Functions, New Functions from Old Functions, Exponential Functions, Inverse Functions and Logarithms Assessments: Homework #1 |
|
Unit 2 Limits and Derivatives: The Tangent and Velocity Problems, The Limit of a Function, Calculating Limits Using the Limit Laws, The Precise Definition of a Limit, Continuity, Limits at Infinity; Horizontal Asymptotes, Derivatives and Rates of Change, The Derivative as a Function Assessments: Homework #2 |
|
Unit 3 Differentiation Rules: Derivatives of Polynomials and Exponential Functions, The Product and Quotient Rules, Derivatives of Trigonometric Functions, The Chain Rule,Implicit Differentiation, Derivatives of Logarithmic Functions, Rates of Change in the Natural and Social Sciences, Exponential Growth and Decay, Related Rates, Linear Approximations and Differentials, Hyperbolic Functions Assessments: Quiz #1 |
|
Unit 4 Applications of Differentiation: Maximum and Minimum Values, The Mean Value Theorem, How Derivatives Affect the Shape of a Graph, Indeterminate Forms and l'Hospital's Rule, Summary of Curve Sketching, Graphing with Calculus and Calculators, Optimization Problems, Newton's Method, Antiderivatives Assessments: Midterm Exam |
|
Unit 5 Integrals: Areas and Distances, The Definite Integral, The Fundamental Theorem of Calculus, Indefinite Integrals and the Net Change Theorem, The Substitution Rule Assessments: Homework #3 |
|
Unit 6 Applications of Integration: Areas Between Curves, Volumes, Volumes by Cylindrical Shells, Work, Average Value of a Function Assessments: Homework #4 |
|
Unit 7 Techniques of Integration: Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Integration of Rational Functions by Partial Fractions, Strategy for Integration, Integration Using Tables and Computer Algebra Systems, Approximate Integration, Improper Integrals Assessments: Quiz #2 |
|
Unit 8 Further Applications of Integration: Arc Length, Area of a Surface of Revolution, Applications to Physics and Engineering, Applications to Economics and Biology, Probability Assessments: Final Exam |
ASSESSMENT AND GRADING
|
Assessment |
Percentage |
Format/Grading |
|
2 Quizzes |
30% |
Computer/Instructor |
|
4 Homework |
20% |
Computer/Instructor |
|
Midterm Exam |
20% |
Computer/Instructor |
|
Final Exam |
30% |
Computer/Instructor |
|
Total |
100% |
|
|
Grade |
Percentage |
|
A |
93-100% |
|
A- |
90-92% |
|
B+ |
87-89% |
|
B |
83-86% |
|
B- |
80-82% |
|
C+ |
77-79% |
|
C |
73-76% |
|
C- |
70-72% |
|
D+ |
67-69% |
|
D |
60-66% |
|
F |
0-59% |
*Since there is no physical class attendance in online courses, it is crucial to regularly log in to the course platform, submit assignments on time, take exams, or communicate with instructors. You must engage in these activities to ensure that your participation is properly recognized and documented.
COURSE POLICIES
Technology Policy
You need to have access to a personal computer or laptop with a working webcam and microphone in order to access all features of the course. Exams are proctored remotely using Zoom, which records you and your environment during the exam. You must install Zoom to take an exam. Any student who accesses a phone or any internet-capable device during an exam for any reason automatically receives a score of zero. All such devices must be turned off, put away, and made inaccessible during the exam. Since there is no physical class attendance in an online class, online instructors will certify last days attended/participated based on verifiable participation only, such as submitted assignments, exams taken, participation in online discussions, or communicating with the instructor by email.
Academic Honesty
Academic integrity is of utmost importance. All students are expected to adhere to the university's policies on academic honesty. Plagiarism, cheating, and other forms of academic misconduct will not be tolerated and will result in disciplinary action, which may include failure of the assignment, failure of the course, or further action by the university.
Course Withdrawal
Students may withdraw from the course according to the university's withdrawal policy. It is the student's responsibility to be aware of the deadlines and procedures for withdrawing from a course. Withdrawal forms must be submitted by Withdrawal Deadline.
Late Work Policy
Assignments are expected to be submitted on time. Late submissions will incur penalties as follows: a 10% deduction per day for submissions 1-3 days late, a 20% deduction per day for submissions 4-7 days late, and submissions more than 7 days late will not be accepted without prior arrangement. Students are allowed one 48-hour grace period for one assignment per semester, provided they notify the instructor before the original deadline. Extensions may be granted for documented emergencies, and students observing religious or cultural events should notify the instructor in advance to arrange alternative deadlines.
Special Needs or Assistance
Students with disabilities or who require special accommodations should contact the instructor as early as possible. The university provides resources and support for students with special needs, and the instructor will work with the university's disability services to ensure that appropriate accommodations are made.
2026-03-09