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…
Rodrigo Ribeiro, Ph.D 