Calculus has been historically called "calculus of infinitesimals" or "infinitesimal calculus". Though it was known to be done by Issac Newton and Gottfired Leibniz as early as 1666, the first book of solid definitions and proofs was published by Augustin Cauchy in 1840.

Calculus can be thought of as describing and calculating continuous change. Calculus has two main branches - Differential Calculus adn Integral Calculus. Differential Calulus involves the study of rates of change (including slopes of tangent lines) and Integral Calculus concerns the accumulation of quantities (such as areas under a curve of volumes of a solid). All of these are first introduced and defined with the notion of a "limit" - the idea of approaching a number/quanity, rather than "plugging in" or "being at" a certain number/quanitity. Limits are the theoretical foundation of both derivatives and integrals. Investigating properties of derivatives and integrals (via their description by a limit) leads to amazingly beautiful and simple formulas that are used for calculations, such as the the derivative rules and the Fundamental Theorem of Calculus.

This course will begin with a study of limits from an intuitive point of view, continue with a thorough study of differential calculus, and end with some work on definite integrals. Calculus II (Math 231) includes more work on integrals and their applications, as well as the study of infinite sequences and series. Students in this course (1) will study calculus concepts from a theoretical point of view, (2) will learn techniques of calculation, and (3) will apply calculus to model scientific problems.

We will cover Chapters 2 - 6 in

- James Stewart,
*Calculus: Early Transcendentals*,**8th edition**, with Enhanced WebAssign.

For most people, calculus is the most challenging math
class they have encountered so far. There are a larger number of interrelated
concepts than before, and solving a single problem can require
thinking about one concept or object in several different ways.
Because of this, conceptual understanding is more important than ever,
and it is not possible to learn a short list of “problem
templates” in lecture that will allow you to do all the HW and
exam problems. Thus, while lecture and section will include many
worked examples, you will still often be asked to solve a HW problem
that doesn’t match up with one that you’ve already seen.
The goal here is to get a solid understanding of vector calculus so
you can solve *any* such problem you encounter in mathematics,
the sciences, or engineering. That requires trying to solve new
problems from first principles, if only because the real world is sadly complicated.

These are all posted online in the course diary.

There will be 3 midterms held in lecture (314 Altgled) on the following Thursdays: September 26th, October 24th, and November 21st. You MUST bring your I-card to the exam. All material covered during Lecture, Discussion, or Homework may be on the exam.

You should expect regular weekly quizzes on Friday (mostly)s. In addition, several take-home quizzes will be assigned during the semester. The schedule of quizzes can be found in the course diary.

Solutions to groupwork assignments will be posted the next class day following discussion.

These problems are not for turning in, and should be completed by students after the section is covered during lecture. Solutions can be found on our moodle page.

Staring Wednesday August 28th, teaching Assistants will be available in 341 Altgeld at the following dates/times for walk-in tutoring