Math 109. Calculus 1b

Spring 2023


No class on Wednesday March 8 and Friday March 10.

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

Course Description

(Calculus Ib: Transcendental Calculus.) This course is a continuation of Math 108 that further develops the concepts of calculus, such as differentiation and integration, to exponential, logarithm and trigonometric functions. Related topics in exponentiation and analytic geometry are covered as needed. Satisfactory completion of both Math 108 and Math 109 is equivalent to the satisfactory completion of Math 110. (Credit cannot be earned in both Math 109 and Math 110.) Prerequisite: Completion of Math 108 with a grade of C- or better, or permission of the instructor. This course is being offered on a pilot basis for the 2019-2020 academic year. (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 7: Exponential and Logarithmic Functions
7.1 Exponential Functions and Their Graphs
7.2 Logarithmic Functions and Their Graphs
7.3 Using Properties of Logarithms
7.4 Exponential and Logarithmic Equations
7.5 Exponential and Logarithmic Models

Chapter 8: Exponential and Logarithmic Functions and Calculus
8.1 Exponential Functions: Differentiation and Integration
8.2 Logarithmic Functions and Differentiation
8.3 Logarithmic Functions and Integration
8.4 Differential Equations: Growth and Decay

Chapter 9: Trigonometric Functions
9.1 Radian and Degree Measure
9.2 Trigonometric Functions: The Unit Circle
9.3 Right Triangle Trigonometry
9.4 Trigonometric Functions of Any Angle
9.5 Graphs of Sine and Cosine Functions
9.6 Graphs of Other Trigonometric Functions
9.7 Inverse Trigonometric Functions
9.8 Applications and Models

Chapter 10: Analytic Trigonometry
10.1 Using Fundamental Trigonometric Identities
10.2 Verifying Trigonometric Identities
10.3 Solving Trigonometric Identities
10.4 Sum and Difference Formulas
10.5 Multiple-Angle and Product-to-Sum Formulas

Chapter 11: Trigonometric Functions and Calculus
11.1 Limits of Trigonometric Functions
11.2 Trigonometric Functions: Differentiation
11.3 Trigonometric Functions: Integration
11.4 Inverse Trigonometric Functions: Differentiation
11.5 Inverse Trigonometric Functions: Integration
11.6 Hypoerblic Functions

Chapter 12: Topics in Analytic Geometry
12.1 Introduction to Conics: Parabolas
12.2 Ellipses and Implicit Differentiation
12.3 Hyperbolas and Implicit Differentiation
12.4 Parametric Equations and Calculus
12.5 Polar Coordinates and Calculus
12.6 Graphs of Polas Coordinates
12.7 Polar Equations of Conics

Chapter 13: Additional Topics in Trigonometry
13.1 Law of Sines
13.2 Law of Cosines
13.3 Vectors in the Plane
13.4 Vectors and Dot Products
13.5 Trigonometric Form of a Complex Number

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 Fridays. 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 Wednesday February 22.

The second midterm will be on Friday March 22.

The third midterm will be on Wednesday April 19.

The final exam will be a cumulutive three hour exam.

The date for the final exam is Monday May 8 from 1:30pm to 4:30pm.


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.


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.

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. 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:

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Kara Fifield.

Last modified on April 14, 2023.