Rodrigo Ribeiro, Ph.D.
Professor
IMPA Tech
Sala 02
Calculus I [Summer Course]
July 1, 2023 August 1, 2023
University of Denver
Undergraduate
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.
Sep 12 – Sep 16
|
0 – History of Calculus
1.1 – Review of Functions (optional)
1.2 – Basic Classes of Functions (optional)
2.1 – A Preview of Calculus
2.2– The Limit of a Function
Assignment 1 (Sep 16)
Sep 19 – Sep 23
| 2.3 – Limit Laws
2.4 – Continuity
2.5 – The Precise Definition of a Limit*
Assignment 2 (Sep 23)
Sep 26 – Sep 30
| 3.1 – Defining the Derivative
3.2 – The Derivative as a Function
3.3 – Differentiation Rules
Assignment 3 (Sep 30)
Oct 3 – Oct 7
|
3.4 – Derivatives as Rates of Change
3.5 – Derivatives of Trigonometric Functions
Assignment 4 (Oct 7)
MIDTERM 1 (Oct 7)
Oct 10 – Oct 14
| 3.6 – The Chain Rule
3.8 – Implicit Differentiation
3.9 – Derivatives of Exponential and Logarithmic Functions
Assignment 4 (Oct 14)
Oct 17 – Oct 21
| 4.1 – Related Rates
4.2 – Linear Approximations and Differentials
Assignment 5 (Oct 21)
Oct 24 – Oct 28
| 4.3 – Maxima and Minima
4.4 – The Mean Value Theorem
Assignment 6 (Oct 28)
Oct 31 – Nov 4
| 4.5 – Derivatives and the Shape of a Graph
4.6 – Limits at Infinity and Asymptotes
4.8 – l’Hopital’s Rule (0/0, infty/infty only)
Assignment 7 (Nov 4)
MIDTERM 2 (Nov 4)
Nov 7 – Nov 11
| 4.7 – Applied Optimization Problems
4.9 – Newton’s Method
Assignment 8 (Nov 11)
Nov 14 – Nov 18
| Curve Sketching
More on Optimization Problems
Review
Assignment 9 (Nov 18)
Nov 20
|
FINAL EXAM
|
0 – History of Calculus
1.1 – Review of Functions (optional)
1.2 – Basic Classes of Functions (optional)
2.1 – A Preview of Calculus
2.2– The Limit of a Function
Assignment 1 (Sep 16)
Sep 19 – Sep 23
| 2.3 – Limit Laws
2.4 – Continuity
2.5 – The Precise Definition of a Limit*
Assignment 2 (Sep 23)
Sep 26 – Sep 30
| 3.1 – Defining the Derivative
3.2 – The Derivative as a Function
3.3 – Differentiation Rules
Assignment 3 (Sep 30)
Oct 3 – Oct 7
|
3.4 – Derivatives as Rates of Change
3.5 – Derivatives of Trigonometric Functions
Assignment 4 (Oct 7)
MIDTERM 1 (Oct 7)
Oct 10 – Oct 14
| 3.6 – The Chain Rule
3.8 – Implicit Differentiation
3.9 – Derivatives of Exponential and Logarithmic Functions
Assignment 4 (Oct 14)
Oct 17 – Oct 21
| 4.1 – Related Rates
4.2 – Linear Approximations and Differentials
Assignment 5 (Oct 21)
Oct 24 – Oct 28
| 4.3 – Maxima and Minima
4.4 – The Mean Value Theorem
Assignment 6 (Oct 28)
Oct 31 – Nov 4
| 4.5 – Derivatives and the Shape of a Graph
4.6 – Limits at Infinity and Asymptotes
4.8 – l’Hopital’s Rule (0/0, infty/infty only)
Assignment 7 (Nov 4)
MIDTERM 2 (Nov 4)
Nov 7 – Nov 11
| 4.7 – Applied Optimization Problems
4.9 – Newton’s Method
Assignment 8 (Nov 11)
Nov 14 – Nov 18
| Curve Sketching
More on Optimization Problems
Review
Assignment 9 (Nov 18)
Nov 20
|
FINAL EXAM