# Fundamentals of Calculus

### Syllabus

handouts syllabus pdf flier photographs

## Fall 2023

The classes will be held on the University City campus.
Class times and place: Tue and Th 2:00–3:15 pm in STC 147.

## Office Hours

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 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.

## Learning Platforms

Canvas: You should be able to access the course page on Canvas. After the hand-in assignments and exams are graded, their solutions will be emailed to you and posted on Canvas.
Mobius: An online learning platform called Mobius is used instead of a texbook for this course. On Mobius, the course material is presented in a gradual way and there are step-by-step examples and practice problems. You can access Mobius here and here you can find more information on how to set up an account o Mobius and access the course material.
This website: In addition to Mobius, there are handouts on this website here.

## Technology

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

## Topics Covered

1. Limits
2. Infinite Limits, Limits at Infinity, Horizontal and Vertical Asymptotes
3. Continuity. 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. Implicit Differentiation
10. Related Rates
(Exam 2)

11. Increasing/Decreasing Test. Extreme Values and the First Derivative Test
12. Concavity and Inflection Points. The Second Derivative Test
13. Absolute Extrema and Constrained Optimization
(Exam 3)

14. Antiderivatives and the Indefinite Integral
15. Substitution
16. Integrals of Exponential and Trigonometric Functions. Integrals Producing Logarithmic Functions
17. Definite Integral. Left and Right Sums
18. Fundamental Theorem of Calculus. Total Change and applications
19. 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.

 Exams 1, 2 and 3 17% each Final Exam 24% Hand-in Assignments 15% Mobius Assignments 10% TOTAL 100%
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

3

## Prerequisites

MAT 120, placement, or permission of instructor

This is a rigorous course. You should plan to spend a minimum of twice the number of class hours on going over the lectures, understand concepts, and doing the 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.

## Hand-in Assignments

There will be four homework assignments. The purpose of these assignments is to prepare you for the coming exams. 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.

## Mobius Assignments

There will be 12 Mobius assignments during the semester. Two lowest Mobius assignment grades will be dropped. The purpose of these assignments is to ensure you are on track with the material and to prepare you for the hand-in assignments and exams. There will be no makeup Mobius assignments.

## 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

• to obtain a well rounded introduction to the area of limits, differentiation and basic integration techniques;
• to develop basic knowledge of calculus problem formulation, problem solving and modeling techniques required for successful application of mathematics;
• to competently use 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 outcomes

Students will:
• know the basic concepts of differential and integral calculus;
• demonstrate proficiency in differentiation and integration techniques;
• be able to interpret and critique graphs using calculus techniques;
• be able to understand and solve multidisciplinary application problems using calculus;
• demonstrate proficiency in using mathematical software;
• know how to use appropriate technology to solve problems applying calculus techniques.