Math 111. Calculus II

Spring 2023


No class on Wednesday March 8 and Friday March 10.

Solving an integral using a series expansion.


Course Description

The calculus of functions of one variable. Integration, applications of integration, sequences, and series. Prerequisite: Mathematics 110. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)


Calculus Volume 2 by Strang, Herman, et. al., Open Stax.

The book is free online. You can find it here.

Topics to be covered

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

Chapter 1: Integtration
1.1 Approximating Areas
1.2 The Definite Integral
1.3 The Fundamental Theorem of Calculus
1.5 Substitution
1.6 Integrals Involving Exponential and Logarithmic Functions
1.7 Integrals Resulting in Inverse Trigonometric Functions

Chapter 2: Applications of Integration
2.1 Areas between Curves
2.2 Determining Volumes by Slicing
2.3 Volumes of Revolution: Cylindrical Shells
2.4 Arc Length of a Curve and Surface Area

Chapter 3: Techniques of Integration
3.1 Integration by Parts
3.2 Trigonometric Integrals
3.3 Trigonometric Substitution
3.4 Partial Fractions
3.6 Numerical Integration
3.7 Improper Integrals

Chapter 5: Sequences and Series
5.1 Sequences
5.2 Infinite Series
5.3 The Divergence and Integral Tests
5.4 Comparison Tests
5.5 Alternating Series
5.6 Ratio and Root Tests

Chapter 6: Power Series
6.1 Power Series and Functions
6.2 Properties of Power Series
6.3 Taylor and Maclaurin Series
6.4 Working with Taylor Series

Student Learning Outcomes

Some main learning outcomes include: In general, the goal is for the student to be able to learn Calculus in a way that it allows the student to apply it in science courses or higher level Mathematics courses.

The course grade will be based on:
Homework   10%
Midterm 1   20%,
Midterm 2   20%,
Midterm 3   20%
Final Exam   30%.


There will be written homework daily. 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 should submit your homework in class. 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:


On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.
The following dates are tentative:  

The first midterm will be on Wednesday February 22.

The second midterm will be on Wednessday March 29.

The third midterm will be on Wednessday April 26.

The final exam will be a cumulative three hour exam. It will be on Saturday May 6 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 policy

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 March 1, 2023.