Calculus 2


handouts videos syllabus pdf flier photographs

Fall 2023

The classes will be held on the University City campus.
Class times and place: Tue and Th 12:30–1:45, Fri 11:15–12:05 in STC 147.

Office Hours

are by appointment: Tue and Th 3:15 pm or at other times by appointment – email me and we will find a time for us to meet. I will be glad to answer all of your questions about the material, go over some problems together with you, check your assignment work, review together for an exam, or discuss any course material you may have questions about.


No textbook required. Handouts with course material, practice problems, and exam reviews are available on my website.


All students are required to have a graphing calculator. Instructions will be given for TI83/84.

Topics Covered

1. Review of Differentiation. Derivatives of Exponential and Logarithmic Functions.
2. Indefinite Integrals. Substitution.
3. Definite Integrals. Left and Right Sum
4. The Fundamental Theorem of Calculus
5. Areas between Curves
6. Volumes (cross-sections)
7. Volumes (shells)
8. Work. Average Value of a Function
9. Trigonometric, Inverse Trigonometric Functions and their Derivatives and Integrals
10. L'Hopital's Rule
(Exam 1)

13. Integration by Parts
14. Trigonometric Integrals
15. Partial Fractions
16. Improper Integrals
17. Approximate Integration: Trapezoidal and Simpson's Sum
18. Arc Length and Area of a Surface of Revolution
(Exam 2)

19. Differential Equations. Separable Equations
20. Direction Fields. Euler's Method
21. Autonomous Differential Equations and Population Dynamics
22. Modeling with Differential Equations. Applications
23. Linear Equations
24. Curves defined by Parametric Equations
25. Derivatives of Parametric Curves. Area
26. Arc Length and Surface Area of a Parametric Curve
(Exam 3)

27. Polar Coordinates
28. Areas and Lengths in Polar Coordinates
29. Taylor Polynomial

Tentative exam dates

Exam 1: during the 5th week of classes.
Exam 2: during the 9th week of classes.
Exam 3: during the 12th week of classes.
Final Exam: during the finals week.


Exams 1, 2 and 318% each
Final Exam24%
Grades are computed according to the following system:
A A- B+ B B- C+ C C- D+ D F
grade 93-100 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 60-66 0-59

Number of credits



MAT 155 or MAT 161 or permission of instructor


The class lectures will be delivered on campus (at the times listed above). Recordings of the lectures are available for students who miss some classes. To stay on track, it is highly recommended that students attend the classes and use the recordings just for reference.
Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.


There will be three semester exams and a cumulative final exam. No makeup exam will be given unless the excuse for missing the scheduled exam is acceptable to the instructor. Any makeup exam must be taken before the next regularly scheduled exam. No exam grade will be dropped.

Assignments and Projects

There will be four assignments and two Matlab projects during the semester (students will be able to install Matlab on their home computers or to use it from a web browser). There will be no makeup assignments. Assignments or projects turned in after their due date will receive an automatic reduction in grade. No assignment or project grade will be dropped.

Response time

The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.

Course Objectives

  • Obtain a well rounded introduction to the area of integration techniques, applications of integrals, differential equations and parametric and polar functions.
  • Deepen students' knowledge of problem formulation, problem solving and modeling techniques required for successful application of mathematics obtained in previous calculus courses.
  • Competently use appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.
  • Cultivate the analytical skills required for the efficient use and understanding of mathematics.

Learning outcomes

Students will:
  • demonstrate proficiency in integration techniques;
  • be able to use functions in parametric form and in polar coordinates;
  • model and solve problems using the first order differential equations;
  • demonstrate the use of calculus in problem solving;
  • demonstrate proficiency in using mathematical software;
  • know how to use appropriate technology to solve problems applying calculus techniques.

Academic integrity

Saint Joseph’s University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another’s individual and collective rights.

Student with Disabilities Statement

Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. If students have need of assistance or questions with this issue, they are encouraged to contact the Office of Student Disability Services (SDS) at or by phone at 610.660.1774. The Office of SDS also provides an appeal/grievance procedure for complaints regarding requested or offered reasonable accommodations. More information can be found at:

Health and Wellness Statement

Saint Joseph's University recognizes that physical and mental health strongly impact one's ability to do well in school and in life. As a result, there are many helpful campus resources designed to help students to care for their physical, mental, and spiritual health. Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. All of us benefit from support during times of struggle and challenges. If you are experiencing concerns, seeking assistance sooner rather than later is a courageous thing to do for yourself and those who care about you. The resources at can help you to cope with stress and to achieve your academic and personal goals.