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.
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 Covered1. 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
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
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
27. Polar Coordinates
28. Areas and Lengths in Polar Coordinates
29. Taylor Polynomial
Tentative exam datesExam 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 3||18% each|
Number of credits
MAT 155 or MAT 161 or permission of instructor
AttendanceThe 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.
ExamsThere 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.
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.
- 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 outcomesStudents 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.