Calculus I (MATH 1610) – Course Overview and Study Guide

Course Overview

Introduction to Calculus I

This course provides a comprehensive introduction to differential calculus, focusing on the foundational concepts, techniques, and applications necessary for further study in mathematics, science, and engineering. Students will explore the properties and behaviors of functions, limits, derivatives, and their applications.

• Credits: 4

• Prerequisite: Placement in MATH 1610

• Delivery Mode: LRON (Live Remote Online)

• Instructor: Bujar Konjusha

Main Topics

Functions and Their Properties

Functions are mathematical relationships that assign each input exactly one output. Understanding their properties is essential for calculus.

• Definition: A function f is a rule that assigns to each element x in a set D exactly one element, called f(x), in a set E.

• Types of Functions: Polynomial, rational, exponential, logarithmic, trigonometric, and piecewise-defined functions.

• Domain and Range: The set of all possible inputs (domain) and outputs (range) for a function.

• Example: The function $f(x) = x^2$ has domain $(-\infty, \infty)$ and range $[0, \infty)$.

Limits and Continuity

Limits are fundamental to calculus, describing the behavior of functions as inputs approach specific values.

• Definition of a Limit: $\lim_{x \to a} f(x) = L$ means that as $x$ approaches $a$, $f(x)$ approaches $L$.

• Continuity: A function is continuous at $x = a$ if $\lim_{x \to a} f(x) = f(a)$.

• Example: $\lim_{x \to 2} (3x + 1) = 7$.

Differentiation

Differentiation is the process of finding the derivative, which measures the rate of change of a function.

• Definition of Derivative: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Basic Rules: Power rule, product rule, quotient rule, chain rule.

• Example: If $f(x) = x^3$, then $f'(x) = 3x^2$.

Applications of Derivatives

Derivatives are used to solve problems involving rates of change, optimization, and motion.

• Critical Points: Points where $f'(x) = 0$ or $f'(x)$ does not exist; used to find local maxima and minima.

• Optimization: Finding the maximum or minimum values of a function in a given interval.

• Related Rates: Problems involving two or more quantities that change with respect to time.

• Example: If $s(t) = t^2$, then the velocity $v(t) = s'(t) = 2t$.

Mathematical Modeling and Problem Solving

Students will apply calculus concepts to model and solve real-world problems in science, engineering, and other fields.

• Modeling: Using functions and derivatives to represent and analyze physical phenomena.

• Example: Modeling population growth with exponential functions.

Course Structure and Assessment

Assessment Components

Student performance is evaluated through a combination of online assignments, quizzes, exams, and participation.

Assessment	Weight	Description
Homework & Math Review	5%	Online assignments in MyMathLab, including section homework and review problems.
Chapter Quizzes	25%	Quizzes on MyMathLab covering multiple chapters; best score out of two attempts is counted.
Midterm Exam	20%	Online exam covering chapters 1-3; best score out of two attempts is counted.
Cumulative Final Exam	30%	Comprehensive online exam; best score out of two attempts is counted.
Coursework Expectations	20%	Completion of all assigned work and participation in online sessions.

Calculator Policy

• Recommended calculators: TI-83+, TI-84+, TI-84.

• Calculators with QWERTY keyboards or those capable of symbolic manipulation are not allowed on quizzes and exams.

Course Materials

• Textbook: Calculus, Early Transcendentals by Briggs, Cochran, Gillett, and Schulz, 4th Edition (Pearson, 2023).

• Online Platform: MyMathLab for assignments and quizzes.

Academic Engagement and Important Dates

• Academic Engagement Deadline: Students must complete the first online assignment by Wednesday, 09/24/25.

• Withdrawal Deadline: Last day to withdraw is Wednesday, 11/12/25.

Resources and Support

• Office Hours: Scheduled times for individual help and questions.

• Group Work: Collaborative sessions to reinforce learning.

• Online Resources: MyMathLab, course website, and the Academic Success Center (ASC).

Best Practices for Online Learning (LRON)

• Participate in live sessions and group work.

• Attend office hours for additional support.

• Check your equipment and internet connection before class.

• Eliminate distractions and actively engage in class activities.

• Communicate with your instructor and peers regularly.

Summary Table: Key Calculus I Concepts

Concept	Definition	Example
Function	Rule assigning each input one output	$f(x) = 2x + 3$
Limit	Value a function approaches as input approaches a point	$\lim_{x \to 1} (x^2) = 1$
Derivative	Instantaneous rate of change	$f'(x) = 2x$ for $f(x) = x^2$
Critical Point	Where $f'(x) = 0$ or undefined	$f(x) = x^2$ at $x = 0$

Additional info: These notes are based on the course syllabus and structure for Calculus I (MATH 1610), including assessment breakdowns, textbook requirements, and online learning best practices. For detailed content on each calculus topic, refer to the assigned textbook chapters and MyMathLab modules.