Math 108. Calculus 1a

Fall 2022


No class on Friday October 7.

No class on Wednesday September 14 and Friday September 16.

For your convenience, here's a link to the Homework page.

Course Description

(Calculus Ia: Introduction to Calculus.) The calculus of rational functions of one variable. Limits, continuity, differentiation, and applications; a brief introduction to integration. Related topics in college algebra also are reviewed, including pertinent aspects of functions, polynomials, and rational expressions. This courses is a required skills-building course for students desiring to complete Math 109. (Credit cannot be earned in Math 108 after satisfactory completion of Math 110.) Prerequisite: By placement only. Not open to students who have completed Math 110 with a grade of C- or better. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement.)


Calculus 1 with Precalculus (3rd edition) by Larson and Edwards.

Topics to be covered

The following is a tentative list of topics that will be covered:

Chapter P: Prerequisites
P.1 Solving Equations
P.2 Solving Inequalities
P.3 Graphical Representation of Data
P.4 Graphs of Equations
P.5 Linear Equations in Two Variables

Chapter 1: Functions and their Graphs
1.1 Functions
1.2 Analyzing Graphs of Functions
1.3 Transfomations of Functions
1.4 Combinations of Functions
1.5 Inverse Functions
1.6 Mathematical Modeling and Variation

Chapter 2: Polynomial and Rational Functions
2.1 Quadratic Functions and Models
2.2 Polynomial Functions of Higher Degree
2.3 Polynomial and Synthetic Division
2.4 Complex Numbers
2.5 The Fundamental Theorem of Algebra
2.6 Rational Functions

Chapter 3: Limits and Their Properties
3.1 A Preview of Calculus
3.2 Finding Limits Graphically and Numerically
3.3 Evaluating Limits Analytically
3.4 Continuity and One-Sided Limits
3.5 Infinite Limits.

Chapter 4: Differentiation
4.1 The Derivative and the Tangent Line Problem
4.2 Basic Differentiation Rules and Rates of Change
4.3 Product and Quotient Rules and Higher-Order Derivatives
4.4 The Chain Rule
4.5 Implicit Differentiation
4.6 Related Rates

Chapter 5: Applications of Differentiation
5.1 Extrema on an Interval
5.2 Rolle's Theorem and the Mean Value Theorem
5.3 Increasing and Decreasing Functions and the First Derivative Test
5.4 Concavity and the Second Derivative Test
5.5 Limits at Infinity
5.6 A Summary of Curve Sketching
5.7 Optimization Problems
5.8 Differentials

Chapter 6: Integration
6.1 Antiderivatives and Indefinite Integration
6.2 Areas
6.3 Riemann Sums and Definite Integrals
6.4 The Fundamental Theorem of calculus
6.5 Integration by Substitution
6.6 Numerical Integration

Student Learning Outcomes

Some main learning outcomes include: In general, the student should be able to understand most of the topics covered in the class and be able to use the tools to solve new problems.

The course grade will be based on:
Homework           10%
Quizzes               15%,
Midterm 1           15%,
Midterm 2           15%,
Midterm 3           15%
Final Exam         30%.


There will be written homework weekly. The homework will be turned in and will reinforce the matertial learned in class. Collaboration in the homework is permitted, however you must write your own solutions in your own words (or symbols). You must also support your answers with the intermediate steps you took to reach the answer.
You can find the homework assignments for this class below:


There will be a weekly quiz. The quiz will be at the beginning of class on the days that homework are due. The topics for each quiz come from the homework due the day of the quiz.


On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams. Also, no calculators or notes are permitted. I will provide simple calculators in the exam.
The first midterm will be on Friday September 30.

The second midterm will be on Friday November 4.

The third midterm will be on Wednesday November 30.

The final exam will be a cumulutive three hour exam.

The date for the final exam is Thursday December 15 from 8:30am to 11:30am.


Students are expected to come to every lecture and every exam. If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.


Accommodations Statement

If you are a student who needs an accommodation because of a disability or medical or psychological condition that limits your ability to fully participate in this course, please contact Kara Fifield (, Director of Disability Services, to document your disability with the College and with the professor of this course. Academic accommodations should be reasonable and not alter the fundamental nature of this course. Because it can take a week or more to arrange requested accommodations, you are encouraged to establish your semester accommodations as early in the semester as possible. Accommodations usually require a medical diagnosis. Some can be significant yet temporary in nature, such as a concussion, or a sprained wrist that impacts your ability to take notes. Others can last the entire term, such as PTSD or dyslexia. If you think you might have a condition that qualifies, please make an appointment with Kara Fifield as soon as possible. Contact Kara Fifield by email or phone, or 847-735-5167. For more information about services for students with disabilities at Lake Forest College, see the webpage. Students are expected to set up their own testing and notetaker accommodations. Please contact Stephanie Edgar, Coordinator of the Center for Academic Success,, for assistance.

Description of instructional time and expectations:

This course meets 3 times per week for 4.5 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Last modified on October 24, 2022.