MATH 160
Calculus I
Summer Term 2026 |
Instructor: Staff |
Total sessions: 35 Sessions |
Office Hours: TBA |
Session Length: 145 Minutes |
Classroom: TBA |
Credits: 3 Units |
Class Length: 7 Weeks |
Language: English |
Course Overview:
This course introduces the main ideas of calculus, focusing on how functions change and how these changes can be measured and applied. Students will learn how to analyze limits, compute derivatives, and evaluate integrals, building both technical skills and intuitive understanding. Throughout the course, we explore how calculus can be used to describe real-world situations, such as motion, growth, and optimization. Emphasis is placed on developing problem-solving strategies and understanding the connections between formulas, graphs, and applications.
Required Material:
Gilbert Strang and Edwin “Jed” Herman, Calculus Volume 1, OpenStax College, 2016.
Learning Objectives:
1. Evaluate limits and analyze continuity using algebraic and graphical methods
2. Compute derivatives of algebraic, trigonometric, exponential, and logarithmic functions
3. Apply derivatives to solve problems involving rates of change, optimization, and curve analysis
4. Evaluate definite integrals and use them to interpret area and other applications
Course Outline:
Week 1:
Lecture 1-5: Functions & Review
Lecture 1: Functions and Graphs
o Function notation and evaluation
o Graphs and basic transformations
Lecture 2: Exponential and Logarithmic Functions
o Properties of exponential functions
o Logarithmic functions
Lecture 3: Trigonometric Functions
o Definitions and graphs
o Basic identities
Lecture 4: Inverse Functions
o Inverse trig functions
o Properties
Lecture 5: Review of Algebra
o Algebraic manipulation
o Function composition
Assignment 1
More specific requirements (e.g., formatting requirements, deadlines, etc.) will be provided in the course.
Week 2:
Lecture 6-10: Limits & Continuity
Lecture 6: Introduction to Limits
o Intuitive definition
o Limit notation
Lecture 7: Limit Laws
o Algebraic limit rules
o Direct substitution
Lecture 8: Limits at Infinity
o Behavior at infinity
o Asymptotes
Lecture 9: Continuity
o Definition of continuity
o Types of discontinuities
Lecture 10: Infinite Limits
o Vertical asymptotes
o Divergence
Week 3:
Lecture 11-15: Derivatives
Lecture 11: Definition of Derivative
o Limit definition
o Tangent lines
Lecture 12: Differentiation Rules
o Power rule
o Sum and product rules
Lecture 13: Chain Rule
o Composite functions
o Applications
Lecture 14: Implicit Differentiation
o Differentiating implicitly
o Applications
Lecture 15: Higher-Order Derivatives
o Second derivative
o Concavity
Midterm Exam: multiple choice and problem-solving questions
(Contains topics in Lecture 1-15)
Week 4:
Lecture 16-20: Applications of Derivatives
Lecture 16: Related Rates
o Setup and interpretation
o Applications
Lecture 17: Linear Approximation
o Tangent line approximation
o Differentials
Lecture 18: Extreme Values
o Critical points
o Max/min
Lecture 19: Curve Sketching
o First and second derivative tests
o Graph behavior
Lecture 20: Optimization
o Modeling problems
o Solving optimization
Week 5:
Lecture 21-25: Advanced Derivatives
Lecture 21: Logarithmic Differentiation
o Differentiating complex functions
o Applications
Lecture 22: Derivatives of Trig Functions
o All trig derivatives
o Inverse trig derivatives
Lecture 23: L’Hôpital’s Rule
o Indeterminate forms
o Applications
Lecture 24: Review of Derivatives
o Mixed problems
o Strategy
Lecture 25: Antiderivatives
o Basic integration
o Indefinite integrals
Assignment 2
More specific requirements (e.g., formatting requirements, deadlines, etc.) will be provided in the course.
Week 6:
Lecture 26-30: Integration
Lecture 26: Definite Integrals
o Riemann sums
o Area interpretation
Lecture 27: Fundamental Theorem of Calculus
o Statement and meaning
o Applications
Lecture 28: Substitution Rule
o u-substitution
o Practice
Lecture 29: Area Between Curves
o Setting up integrals
o Applications
Lecture 30: Numerical Integration
o Approximation methods
o Interpretation
Week 7:
Lecture 31-35: Applications of Integration
Lecture 31: Volumes of Solids
o Disk and washer method
o Applications
Lecture 32: Arc Length (Intro)
o Setup
o Interpretation
Lecture 33: Average Value of Functions
o Definition
o Applications
Lecture 34: Review of Integrals
o Mixed problems
o Strategy
Lecture 35: Applications Summary
o Real-world modeling
o Course wrap-up concepts
Final Exam: multiple choice and Problem-solving questions
(Contains topics in All Lectures)
Grading Assessment:
Assignment 1 |
15% |
Assignment 2 |
15% |
Midterm |
30% |
Final exam |
30% |
Seminar Participation |
10% |
Total |
100% |
Assignments:
Students are required to complete two assignments during the semester, each assignment will consist of a set of problems that align with the topics discussed in lectures, offering students the opportunity to apply the theories and techniques learned in a practical setting. The problems will focus on areas such as limits, derivatives, and integrals, along with their applications. Students are expected to present clear, well-structured solutions with logical reasoning and proper mathematical notation. Step-by-step explanations should be included to demonstrate understanding, and graphs or diagrams may be used where appropriate. Assignments must be submitted as written documents. Late submissions will incur a penalty unless prior arrangements have been made.
Attendance:
Students are required to attend a weekly seminar led by TA to focus on the week's topic and deepen understanding. Seminar time assigned by TA. Seminar attendance counts toward the final grade.
Exams:
The examinations in this course consist of multiple choice and Problem-solving questions. The final exam is cumulative.
Final Evaluation:
Letter Grade |
Percentage (%) |
Letter Grade |
Percentage |
A+ |
≥95 |
C+ |
64-67 |
A |
89-94 |
C |
60-64 |
A- |
84-88 |
C- |
56-59 |
B+ |
79-83 |
D+ |
54-56 |
B |
73-78 |
D |
50-53 |
B- |
68-72 |
F |
≤50 |
General Policies:
Academic integrity
Academic integrity is the cornerstone of academia and requires students and researchers to maintain honesty, fairness, trust and responsibility in all academic activities. It includes not only avoiding dishonest behaviors such as plagiarism, cheating, and falsifying data, but also requires taking responsibility for one's own academic actions and ensuring that all work is done independently and accurately cites the research of others. Violations of academic integrity can result in severe academic penalties, such as zero grades, suspension or even expulsion, and can cause serious damage to an individual's reputation and future career. Upholding academic integrity is therefore essential to promoting a fair academic environment and facilitating the authentic dissemination of knowledge.
Accessible Resources Policy
The policy ensures that all students, especially those with disabilities, are able to participate equally in school learning and activities. The school provides a wide range of accessibility resources including, but not limited to, specialized classrooms, hearing aids, Braille textbooks, assistive technology, and flexible testing arrangements. Students are required to apply to the school in advance and provide appropriate medical or psychological evaluations so that an individualized support plan can be developed for them. This policy is designed to remove barriers in the academic environment and to ensure that every student has access to equitable learning opportunities.
Withdrawal Policy
Students may choose to withdraw from a course within a specified period of time, and may not be able to do so after the expiration date. When withdrawing from a course, students are required to fill out a withdrawal form with a reason, which will be reviewed and processed on a case-by-case basis. Withdrawal from a course may not affect the student's academic performance. If a student withdraws from a course with incomplete requirements, a “W” may be assigned instead of a grade, depending on the course.
