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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.