Calculus 1
Syllabus
Office Hours
Office Hours are 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 course material, go over some problems together with you, check your assignment work, review together for an exam, or discuss any course content you may have questions about.
Textbook
No textbook required. Course material, practice problems and review sheets are on this website. The material of this course (as well of Calculus 2 and Calculus 3) matches Calculus by James Stewart.
Technology
All students are required to have a graphing calculator. Instructions will be given for TI83/84. It is possible to borrow a graphing calculator from the Math Department for a semester.
Topics Covered
1. Limits2. Infinite Limits, Limits at Infinity, Horizontal and Vertical Asymptotes
3. Continuity. Squeeze Theorem. Applications of Limits
4. The Derivative, the Rate of Change
5. Finding and Using Derivative
6. Higher Derivatives. Differentiability
(Exam 1)
7. The Product, Quotient, and Chain Rules
8. Derivatives of Exponential, Logarithmic and Trigonometric Functions
9. Linear Approximation. Differentials
10. Implicit Differentiation
11. L'Hopital's Rule.
12. Related Rates
(Exam 2)
13. Increasing/Decreasing Test. Extreme Values and the First Derivative Test
14. Concavity and Inflection Points. The Second Derivative Test
15. Absolute Extrema and Constrained Optimization
(Exam 3)
16. Antiderivatives and the Indefinite Integral
17. Substitution
18. Integrals of Exponential and Trigonometric Functions. Integrals Producing Logarithmic Functions
19. Definite Integral. Left and Right Sums
20. Fundamental Theorem of Calculus. The Total Change Theorem.
21. Areas between Curves
Tentative exam dates
Exam 1: during the 4th week of classes.Exam 2: during the 7th week of classes.
Exam 3: during the 11th week of classes.
Final Exam: during the finals week.
Grading
Exams 1, 2 and 3 | 20% each |
Final Exam | 22% |
Assignments | 18% |
TOTAL | 100% |
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
4
Prerequisites
Precalculus or permission of instructor
This is a rigorous course. You should plan to spend a minimum of twice the number of class hours on reading, homework assignments, and practice problems. The assigned homework is the minimum amount of practice you should complete. It is your responsibility to come to class prepared to ask questions on any covered concept.
Attendance
It 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.Exams
There will be three in-class exams plus a two hour comprehensive 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
There will be four homework assignments. There will be no makeup assignments. Assignments turned in after their due date will receive an automatic reduction in grade. No assignment grade will be dropped.Course Objectives
- Students will obtain a well rounded introduction to the area of limits, differentiation, optimization, and basic integration techniques.
- Students will develop basic knowledge of calculus problem formulation, problem solving and modeling techniques required for successful application of mathematics.
- Students will competently use appropriate technology to model data, implement mathematical algorithms, and solve mathematical problems.
- Students will cultivate the analytical skills required for the efficient use and understanding of mathematics.
Learning outcomes
- Students will demonstrate knowledge of the analytical methods used within a specific mathematical field, and distinguish between effective and faulty reasoning.
- Students will formulate problems, obtain their solutions, and be familiar with modeling techniques required for successful application of mathematics to a variety of fields.
- Students will develop an understanding of differentiation, optimization, and integration and their uses.
- Students will be able to use calculus to modela and solve problems from other disciplines.
- Students will be able to use appropriate technology to solve calculus problems.