MA 221 Calculus 2
Monday 1-2, Thursday 4-5, Friday 1-3 (no appointment necessary). Feel free to make an appointment if you cannot come to my regular office hours.
No textbook required. Handouts with new material and practice problems will be distributed for each teaching unit. Also Review Sheets will be distributed in class before every exam. The material of this course (as well of Calculus 1 and Calculus 3) matches Calculus by James Stewart.
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|
MA122 or MA102 or permission of instructor
AttendanceIt is imperative that students attend all classes. 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. 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.
- to obtain a well rounded introduction to the area of integration techniques, applications of integrals, differential equations and parametric and polar functions;
- to deepen students' knowledge of problem formulation, problem solving and modeling techniques required for successful application of mathematics obtained in previous calculus courses;
- to competently use the appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.
- to cultivate the analytical skills required for the efficient use and understanding of mathematics.
Learning outcomesStudents will:
- be able to demonstrate the 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;
- be able to demonstrate the use of calculus in problem solving;
- know how to use appropriate technology to solve problems applying calculus techniques;
- demonstrate a proficiency in using mathematical software.