Calculus I (MA 1021-A23)

Course Objectives

At the conclusion of this course, students will be able to:

• State the domain and range of a function and be able to sketch a qualitative graph of the function.

• Determine if a particular limit of a function exists, and if it does, be able to find that limit.

• State the definition of continuity, and be able to find the domain where a function is continuous.

• State the definition of the derivative, and be able to find the derivative of a function, if it exists, based on this definition.

• State the derivatives of polynomials, trigonometric functions, exponential functions, and logarithmic functions.

• Be fluent in the application of the product rule, the quotient rule, the chain rule.

• Be able to use implicit differentiation in finding the derivatives of inverses of functions.

• Use the derivative to find the extrema of functions, such as maximum and minimum values.

• Be able to convert word problems into a mathematical formulation appropriate for this course, solve this mathematical formulation, and then interpret the solution in terms of the original question.

• Pass a Basic Skills test administered by the Mathematics Department

Course Organization

The class typically meets 5 times per week: 4 lectures on MTRF, 1 discussion section (M or T), and 1 laboratory section. Students are responsible for all material presented in lecture and discussion for exams. My expectations for these activities are

• Lectures: This is the first opportunity for a student to see the material, and my expectation of students after a lecture is to have an introduction of the material, not to demonstrate mastery (i.e. Lehr). The goal is to give a high-level description of the main points of the topics, and to provide some examples illustrating the topic. These lectures are recorded via Echo 360, and these videos can be accessed through the course Canvas page.

• Practice Problems: For each section, there is a list of suggested problems from the text for students to learn the concepts through doing (i.e. Kunst). Solutions to these problems are neither collected nor graded, but they form the main topics of discussion during the Discussion section. The problem selection is a combination of examples of the types of problems to be found on the exams and quizzes, along with problems that are more detailed and which enhance learning the topics at a deeper level.

• Discussions: Students have an opportunity to sit down and work through the practice problems on a topic with an instructor and have their individual questions addressed. It is through the Discussion that the student can get major questions asked so that after Discussion, the student can continue to work through the practice problems to develop mastery.  Attendance is required to take the weekly "quiz" in Discussion, described below.

• Canvas: Course materials can be found on the Canvas page. The material is organized by the section number of the topic in the text. In the event that lectures need to be delivered remotely, they will take place through Zoom.

Students are expected to spend an additional 8-12 hours per week studying outside of class: reading the text, organizing notes, and solving problems. In previous years, the average time, self-reported, spent outside of class on this course is 10 hours