Limits, continuity, differentiation of functions of one variable, applications of the derivative. This course counts toward the Analytical Inquiry: The Natural and Physical World requirement. Prerequisite: MATH 1070 or equivalent.

Ongoing course

**Time:** M-F 02:00 PM – 02:50 PM**Location:** F.W. Olin Hall 205**Office hours:** TR 3:30 PM – 04:30 PM**TA:** Eden Ketchum – firstname.lastname@du.edu

Grading

**Homework:** 20% – Weekly homework (you must turn them in)**Participation in class:** 10%**Midterm I (10/07 ): ** 20% **Midterm II (11/04):** 20%**Final (11/20) :** 30%

Homework sets

*All problems refer to our textbook*

Textbook

Calculus is a well-established theory, and there are a lot of good books out there. We will be following Calculus Volume 1 from OpenStax, but you can use any other book you want. Just be aware that the exercises for the assignment will be selected from the textbook, okay?

Course notes

## Applications of derivative: Optimization Problems – MATH 1951

Using derivatives to optimization problems.

## Applications of derivative: Drawing the graph of a function – MATH 1951

Using first and second derivatives to sketch the graph of a function

## Applications of derivative: Concavity – MATH 1951

Concavity test and using second order derivatives to find local extrema.

## Applications of derivative: shape of a graph – MATH 1951

How derivatives shape the graph of a function.

## Applications of derivatives: Mean Value Theorem – MATH 1951

Second application of derivatives: Mean Value Theorem and its consequences. How to get back properties about the function knowing info about its derivative.

## Applications of derivatives: Maxima and Minima – MATH 1951

Second application of derivatives: maxima and minima. Finding critical points, finding extremum values of functions.

## Applications of derivatives: Related rates – MATH 1951

First application of derivatives: related rates. Examples to be discussed in class.

## Derivatives of Exponential and Logarithmic functions – MATH 1951

Derivatives of Exponential and Logarithmic functions.

## Derivative of Inverse Functions – MATH 1951

Using the chain rule to find the derivative of inverse functions.

## Derivative of Trigonometric Functions – MATH 1951

Finding the derivative of the main trigonometric functions.

## Differentiation Rules – MATH 1951

A lot of nice rules so you can compute derivatives faster!

## Derivative as a Function – MATH 1951

Derivative as a function itself, derivatives and continuity, higher-order derivatives.

## The Derivative of a Function – MATH 1951

Introducing the Concept of Derivative of a function together with some examples.

## Continuity – MATH 1951

Squeeze Theorem, indeterminate of the form K/0 and Continuity of functions.

## The Limit of a function – MATH 1951

Seeing limits in the real world. Definition limit of a function, table of functional values, and examples.

## Review: Special Types of Functions – MATH 1951

Working linear functions, quadratic and general polynomial functions

## Review of Functions – MATH 1951

Real functions, domain, ranges, graphs, zeros and other stuff…