Lecture Outlines - Calculus I Math 1141 Section 4

Class Meetings and Lectures

This is a (very) brief summary of what was (or will be) covered in each class.

December 10

The class met on Zoom. We went over 4 key definitions and related problems as a review for the final exam.
The Final Exam will be given from 3:00 - 6:00 p.m. on Monday, December 21. It will be given via Zoom, just like our exams during the semester. See Announcements for more information.
A Review Sheet for the Final Exam was sent by email and is available here. It contains key definitions and theorems we have covered in this course, and a list of review problems taken from the review sections of Chapters 2 - 5.

December 9

The class met on Zoom. Answered questions and worked out practice problems for Sections 5.4 and 5.5 of your text.
Problem Set 13 is due today, Wednesday, December 9. See Problem Sets for more information.
The Final Exam will be given from 3:00 - 6:00 p.m. on Monday, December 21. It will be given via Zoom, just like our exams during the semester. See Announcements for more information.

December 7

Group B met online via Zoom.
Introduced concepts and worked out practice problems related to Sections 5.4 and 5.5 of your text.
Problem Set 13 is due on Wednesday, December 9. See Problem Sets for more information.
Exam 3 was graded and posted on Blackboard. Solutions were sent by email. Please let me know if you cannot view your corrected exam paper or if you have questions about any of the problems.

December 3

Group A met online via Zoom.
Introduced concepts and worked out practice problems related to Sections 5.4 and 5.5 of your text.
Problem Set 13 is due on Wednesday, December 9. See Problem Sets for more information.

December 2

Exam 3 was administered over Zoom
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 5.4 The Indefinite Integral and Net Change: the indefinite integral is simply a notational convenience, using the integral sign to denote the general antiderivative of a function; the Net Change Theorem is a consequence of the Fundamental Theorem of Calculus: it states that the integral of the rate of change is the net change in a function; worked out an application to velocity, drawing a distinction between displacement and total distance traveled.
- Section 5.5 Substitution: introduces a technique of integration which allows us to find antiderivatives for some types of compositions; the technique resembles a reverse version of the chain rule and can be used to evaluate both definite and indefinite integrals.
This week's lecture material corresponds to Problem Set 13. These lectures are posted online in our Dropbox folder.
Problem Set 12 is due today. Problem Set 13 is assigned and is due on Wednesday, December 9. See Problem Sets for more information.

November 30

Group B met online via Zoom.
Worked out practice problems related to Sections 5.2 and 5.3 of your text, and answered some questions related to Exam 3.
Problem Set 12 is due on Wednesday, December 2. See Problem Sets for more information.
Exam 3 will be given during class on Wednesday, December 2. The exam will cover the material from Chapters 3, 4 and 5, and a sheet of Practice Problems for Exam 3 was emailed to the class to help you prepare for the exam. See Announcements for more information.
A set of Solutions to the Practice Problems for Exam 3 was sent by email and is available here. Please let me know if you have any questions.

November 23 - 26

No class due to Thanksgiving Break.
Problem Set 12 is due on Wednesday, December 2. See Problem Sets for more information.
Exam 3 will be given during class on Wednesday, December 2. The exam will cover the material from Chapters 3, 4 and 5, and a sheet of Practice Problems for Exam 3 was emailed to the class to help you prepare for the exam. See Announcements for more information.

November 19

Group A met online via Zoom.
Worked out practice problems related to Sections 5.2 and 5.3 of your text.
Problem Set 12 is due on Wednesday, December 2. See Problem Sets for more information.
Exam 3 will be given during class on Wednesday, December 2. The exam will cover the material from Chapters 3, 4 and 5, and a sheet of Practice Problems for Exam 3 was emailed to the class to help you prepare for the exam. See Announcements for more information.

November 18

The class met over Zoom. We went over problems and answered questions from Sections 4.9 and 5.1.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 5.2 The Definite Integral: defines the definite integral of a function as a limit of Riemann sums; for a positive function, this represents the area under the curve; for a general function, this represents signed area: area above the x-axis is counted as positive and area below the x-axis is counted as negative; presents several examples of evaluating definite integrals using geometry and setting up limits of Riemann sums.
- Section 5.3 The Fundamental Theorem of Calculus: proves two version of the Fundamental Theorem of Calculus, which allows us to evaluate definite integrals using antiderivatives.
This week's lecture material corresponds to Problem Set 12. These lectures are posted online in our Dropbox folder.
Problem Set 11 is due today. Problem Set 12 is assigned and is due on Wednesday, December 2. See Problem Sets for more information.
Exam 3 will be given during class on Wednesday, December 2. The exam will cover the material from Chapters 3, 4 and 5, and a sheet of Practice Problems for Exam 3 was emailed to the class to help you prepare for the exam. See Announcements for more information.

November 16

Group B met online via Zoom.
Worked out practice problems related to Sections 4.9 and 5.1 of your text.
Problem Set 11 is due on Wednesday, November 18. See Problem Sets for more information.

November 12

Group A met online via Zoom.
Worked out practice problems related to Sections 4.9 and 5.1 of your text.
Problem Set 11 is due on Wednesday, November 18. See Problem Sets for more information.

November 11

The class met over Zoom. We went over problems and answered questions from Sections 4.2, 4.3 and 4.4.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 4.9 Antiderivatives: introduces the problem of finding the antiderivative of a function; proves that all antiderivatives of a given function differ by a constant, so the general family of antiderivatives includes all possible; works out several examples of using given function values to determine a specific value for the added constant; shows an application to velocity and acceleration.
- Section 5.1 Approximating Areas: introduces Riemann sums as a way of approximating the area under the curve of a positive function; reviews methods involving left endpoints, right endpoints and midpoints; introduces and uses sigma notation for sums of many terms.
This week's lecture material corresponds to Problem Set 11. These lectures are posted online in our Dropbox folder.
Problem Set 10 is due today. Problem Set 11 is assigned and is due on Wednesday, November 18. See Problem Sets for more information.

November 9

Group B met in person in NHS 410.
Worked out practice problems related to Sections 4.2 and 4.3 of your text.
Problem Set 10 is due on Wednesday, November 11. See Problem Sets for more information.

November 5

Group A met in person in NHS 410.
Worked out practice problems related to Sections 4.2 and 4.3 of your text.
Problem Set 10 is due on Wednesday, November 11. See Problem Sets for more information.

November 4

The class met over Zoom. We went over problems and answered questions from Sections 3.11 and 4.1.
Solutions to Exam 2 were emailed yesterday and graded papers were released on Blackboard. Please review your exams and let me know if you have any questions.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 4.2 The Mean Value Theorem: proves Rolle's Theorem and the Mean Value Theorem; these are the main theoretical results that connect average and instantaneous rates of change and lead to tests for finding local extreme values.
- Section 4.3 Tests for Local Extrema: formulates the first and second derivative tests for identifying critical values as local maxima or local minima; the first is based on where a function is increasing and decreasing while the second is based on the concavity of the function.
- Section 4.4 L'Hospital's Rule: formulated and proved a simple case of L'Hospital's Rule, which allows us to compute many types of limits of indeterminate type.
This week's lecture material corresponds to Problem Set 10. These lectures are posted online in our Dropbox folder.
Problem Set 9 is due today. Problem Set 10 is assigned and is due on Wednesday, November 11. See Problem Sets for more information.

November 2

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 3.11 and 4.1 of your text.
Problem Set 9 is due on Wednesday, November 4. See Problem Sets for more information.

October 29

Group A met via Zoom.
Worked out practice problems and answered questions related to Sections 3.11 and 4.1 of your text.
Problem Set 9 is due on Wednesday, November 4. See Problem Sets for more information.

October 28

Exam 2 was given during class.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 3.11 Hyperbolic Trigonometric Functions: introduces definitions of hyperbolic functions, some basic properties, identities and derivatives; defines inverse functions and their derivatives.
- Section 4.1 Maximum and Minimum Values: defines local and absolute extreme values; defines critical number and proves Fermat's Theorem relating critical number to local extrema; states Extreme Value Theorem and introduces Closed Interval Method for finding absolute extrema.
This week's lecture material corresponds to Problem Set 9. These lectures are posted online in our Dropbox folder.
Problem Set 8 is due today. Problem Set 9 is assigned and is due on Wednesday, November 4. See Problem Sets for more information.

October 26

Group B met via Zoom.
Worked out practice problems and answered questions related to Sections 3.9 and 3.10 of your text.
Problem Set 8 is due on Wednesday, October 28. See Problem Sets for more information.
Exam 2 will be given during class on Wednesday, October 28. The exam will cover the material from Chapter 3 and a sheet of Practice Problems for Exam 2 was emailed to the class to help you prepare for the exam. See Announcements for more information.

October 22

Group A met via Zoom.
Worked out practice problems and answered questions related to Sections 3.9 and 3.10 of your text.
Problem Set 8 is due on Wednesday, October 28. See Problem Sets for more information.
Exam 2 will be given during class on Wednesday, October 28. The exam will cover the material from Chapter 3 and a sheet of Practice Problems for Exam 2 was emailed to the class to help you prepare for the exam. See Announcements for more information.

October 21

I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 3.9: Related Rates: this topic is similar to implicit differentiation, except now two or more variables depend on a separate independent variable and we find rates of change with respect to this independent variable.
- Section 3.10: Linear Approximation: Uses the idea of the tangent line to approximate function values; introduces the linearization of a function and the differential of a function as two ways to view this approximation.
This week's lecture material corresponds to Problem Set 8. These lectures are posted online in our Dropbox folder.
Problem Set 7 is due today, Wednesday, October 21. Problem Set 8 is assigned and is due on Wednesday, October 28. See Problem Sets for more information.
Exam 2 will be given during class on Wednesday, October 28. The exam will cover the material from Chapter 3 and a sheet of Practice Problems for Exam 2 was emailed to the class to help you prepare for the exam. See Announcements for more information.

October 19

Group B met via Zoom.
Worked out practice problems and answered questions related to Sections 3.5 and 3.6 of your text.
Problem Set 7 is due on Wednesday, October 21. See Problem Sets for more information.

October 15

Group A met via Zoom.
Worked out practice problems and answered questions related to Sections 3.5 and 3.6 of your text.
Problem Set 7 is due on Wednesday, October 21. See Problem Sets for more information.

October 14

I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 3.5: Implicit Differentiation: introduces a technique whereby we can calculate the rate of change dy/dx in a given relation without first solving explicitly for y.
- Section 3.6: Derivatives of Logarithms and Inverse Functions: Using implicit differentiation and the chain rule, we are able to calculate the derivatives of many types of inverse functions, including the logarithm and inverse trigonometric functions; introduces logarithmic differentiation, which uses the properties of logarithms to simplify a function before taking the derivative; we prove the generalized power rule using the chain rule together with the derivatives of logs and exponentials; using the limit definition of e, we are able to rederive the derivative of ln(x) and e^x.
This week's lecture material corresponds to Problem Set 7. These lectures are posted online in our Dropbox folder.
Problem Set 6 is due today, Wednesday, October 14. Problem Set 7 is assigned and is due on Wednesday, October 21. See Problem Sets for more information.

October 12

Happy Columbus Day!
Group B met via Zoom, due to an increase in positive cover-19 test results. See Announcements for more information.
Worked out practice problems and answered questions related to Sections 3.3 and 3.4 of your text.
Problem Set 6 is due on Wednesday, October 14. See Problem Sets for more information.

October 8

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 3.3 and 3.4 of your text.
Problem Set 6 is due on Wednesday, October 14. See Problem Sets for more information.

October 7

I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 3.3: Derivatives of Trigonometric Functions: uses trigonometric identities and a geometric argument to find the derivative of sin(x) and cos(x); using these derivatives, we can find the derivatives of the other 4 trig functions; works through examples of finding derivatives of trig functions in combination with product and quotient rules.
- Section 3.4: The Chain Rule: derives a rule for taking the derivative of a composition of two functions if we know the derivatives of the two functions separately; provides several examples of using this rule in combination with other rules we have learned; using the chain rule, we are able to show that the derivative of b^x is b^xln(2) for any base b>0.
This week's lecture material corresponds to Problem Set 6. These lectures are posted online in our Dropbox folder.
Exam 1 was returned graded yesterday and solutions were sent by email. Please let me know if you have any questions.
Problem Set 5 is due today, Wednesday, October 7. Problem Set 6 is assigned and is due on Wednesday, October 14. See Problem Sets for more information.

October 5

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 3.1 and 3.2 of your text.
Problem Set 5 is due on Wednesday, October 7. See Problem Sets for more information.

October 1

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 3.1 and 3.2 of your text.
Problem Set 5 is due on Wednesday, October 7. See Problem Sets for more information.

September 30

Exam 1 was given by Zoom.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 3.1 Derivatives of Polynomial and Exponential Functions: this section derives rules for taking derivatives of power functions, sums and constant multiples of functions, and exponential functions; the main idea is to develop techniques for taking derivatives that allow us to compute quickly without having to return to the limit definition each time.
- Section 3.2 Product and Quotient Rules: proves rules for taking derivatives of products and quotients of functions whose derivatives we already know.
This week's lecture material corresponds to Problem Set 5. These lectures are posted online in our Dropbox folder.
Problem Set 4 is due today, Wednesday, September 30. Problem Set 5 is assigned and is due on Wednesday, October 7. See Problem Sets for more information.

September 28

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.7 and 2.8 of your text.
Problem Set 4 is due on Wednesday, September 30. See Problem Sets for more information.
Exam 1 will be given during class on Wednesday, September 30. The exam will cover the material from Chapter 2 and a sheet of Practice Problems for Exam 1 is available to help you prepare for the exam. See Announcements for more information.

September 24

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.7 and 2.8 of your text.
Problem Set 4 is due on Wednesday, September 30. See Problem Sets for more information.
Exam 1 will be given during class on Wednesday, September 30. The exam will cover the material from Chapter 2 and a sheet of Practice Problems for Exam 1 is available to help you prepare for the exam. See Announcements for more information.

September 23

The full class met over Zoom. We worked out practice problems and answered homework questions related to Sections 2.3, 2.5 and 2.6 of your text.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 2.7 The Derivative and Rates of Change: this section defines the derivative of a function f(x) as a limit, one of the two fundamental objects in Calculus; the derivative represents both the instantaneous rate of change of f with respect to x, as well as the slope of the tangent line to f.
- Section 2.8 The Derivative as a Function: views the derivative as a function and describes the connections between the properties of f and f '; explores the relations between continuity and differentiability.
This week's lecture material corresponds to Problem Set 4. These lectures are posted online in our Dropbox folder.
Problem Set 3 is due today, Wednesday, September 23. Problem Set 4 is assigned and is due on Wednesday, September 30. See Problem Sets for more information.
Exam 1 will be given during class on Wednesday, September 30. The exam will cover the material from Chapter 2 and a sheet of Practice Problems for Exam 1 was emailed to the class to help you prepare for the exam. See Announcements for more information.

September 21

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.3, 2.5 and 2.6 of your text.
Problem Set 3 is due on Wednesday, September 23. See Problem Sets for more information.

September 17

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.3, 2.5 and 2.6 of your text.
Problem Set 3 is due on Wednesday, September 23. See Problem Sets for more information.

September 16

The full class met over Zoom. We worked out practice problems and answered homework questions related to Sections 2.1, 2.2 and 2.4 of your text.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 2.3 Limit Laws: this section states important rules for computing limits algebraically; stated and applied the Squeeze Theorem to an example.
- Section 2.5 Continuity: defines continuity of a function at a point, as well as one-sided continuity; the limit laws allow us to construct more complex examples of continuous functions from ones we already know to be continuous; stated and applied the Intermediate Value Theorem to an example of finding roots.
- Section 2.6 Limits at Infinity: defines limits as x approaches positive or negative infinity; defines horizontal asymptotes; calculated a variety of limits at infinity algebraically.
This week's lecture material corresponds to Problem Set 3. These lectures are posted online in our Dropbox folder.
Problem Set 2 is due today, Wednesday, September 16. Problem Set 3 is assigned and is due on Wednesday, September 23. See Problem Sets for more information.

September 14

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.1 and 2.2 of your text.
Problem Set 2 is due on Wednesday, September 16. See Problem Sets for more information.

September 10

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 2.1 and 2.2 of your text.
Problem Set 2 is due on Wednesday, September 16. See Problem Sets for more information.

September 9

The full class met over Zoom. We worked out practice problems and answered homework questions related to Sections 1.1 to 1.5 of your text.
I have posted a new set of lectures for the coming week. These lectures cover the following sections.
- Section 2.1 Tangent Line and Velocity Problems: this section provides motivation for our definition of limit, and eventually for our definition of the derivative, from two classical problems: finding the slope of the tangent line to a graph, and defining instantaneous velocity.
- Section 2.2 The Limit of a Function: presents an intuitive formulation of the derivative and some numerical examples; defines one-sided limits and their relationship to the existence of a limit; discusses vertical asymptotes in the context of limits.
- Section 2.4 Precise Definition of Limit: gives a precise formulation of the existence of a limit by quantifying the errors involved.
This week's lecture material introduces one of the key concepts of Calculus: the limit. The material corresponds to Problem Set 2. These lectures are posted online in a Dropbox folder, which you can access at this link.
Problem Set 1 is due today, Wednesday, September 9. Problem Set 2 is assigned and is due on Wednesday, September 16. See Problem Sets for more information.

September 8

Group B met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 1.1 - 1.5 of your text.
Problem Set 1 is due on Wednesday, September 9. See Problem Sets for more information.

September 3

Group A met in person in NHS 410.
Worked out practice problems and answered questions related to Sections 1.1 - 1.3 of your text.
Create a WebAssign account today! Your first orientation assignment is due on Friday, September 4.
Problem Set 1 is due on Wednesday, September 9. See Problem Sets for more information.

September 2

Class meeting on Zoom:
- Reviewed course outline and policies on the Course Syllabus. This file and most others posted are pdf files.
- Introduced the main problems we will study in Calculus including the tangent line and area problems.
I have recorded lectures covering material from the following sections.
- Section 1.1 Representations of Functions: review of basic terminology for functions, domain, range, even and odd symmetry, increasing and decreasing.
- Section 1.2 Essential Functions: reviews basic properties of polynomials, rational and algebraic functions, trigonometric functions, exponential and logarithmic functions
- Section 1.3 New Functions from Old: compositions, including translations, dilations and reflections
- Section 1.4 Exponential Functions: recalls essential facts and properties of exponents
- Section 1.5 Inverse Functions and Logarithms: reviews properties of logarithms, and more general inverse functions, including inverse trigonometric functions
This is a review of material from Pre-Calculus, which you may use as a refresher for the functions we will be working with this semester. These lectures are posted online in a Dropbox folder, which you can access at this link.
Create a WebAssign account today! Your first orientation assignment is due on Friday, September 4. A Quick Start Guide to WebAssign is available to help you get started.
Problem Set 1 was assigned and is due on Wednesday, September 9. See Problem Sets for more information.