MATH 1030

Elementary Functions

Course Information and Policies
Daily Course Schedule

Here are the slides and notes from Costanzo's classes. If your instructor is not Costanzo, then your class notes might be slightly different. 

If you click on the date, then you will be able to download the blank slides that I (Costanzo) use in class. The annotated slides from class can be downloaded by clicking the handwritten notes corresponding to your section. I am also including a short description of the day's topic(s). By the way, there are almost always "extra" slides that I did not cover in class. I usually copy-and-paste them in the next day's lesson. So, if you happen to be absent (which you should not be), you can refer to the handwritten notes to see where I stopped.

  • August 21, 2024
    • Syllabus
    • Introduction to polynomials
    • Problem Set 0
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we went through the class syllabus for the first half of class, and then we officially started MATH 1030 with a review of basic information concerning polynomials. The major learning objectives here are the ability to add, subtract, and multiply polynomials. Note that the multiplication of polynomials requires the distributive laws, which we mentioned briefly in class. You should begin working on Problem Set 0. I urge you to have the software "generate" a few more examples on problems that you find difficult. We shall work a few more examples next class for warm-up problems. Then, we move into factoring polynomials, a classic topic!
  • August 23, 2024
    • factoring polynomials
      • greatest common factor
      • difference of two squares
      • sum & difference of cubes
    • Problem Set 1
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: The warm-up problems from today offered some more practice with adding, subtracting, and multiplying polynomials. After completing Problem Set 0, you should be comfortable with these skills. We started our discussion of factoring polynomials today. In particular, we discussed GCF factoring and we introduced a few patterns (difference of two squares, sum and difference of cubes). You should be able to start Problem Set 1. On Monday, we will demonstrate how to factor a trinomial and we will also learn to factor by grouping.  
  • August 26, 2024
    • factoring (continued)
      • factoring trinomials
      • grouping
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We finished off our discussion of factoring today. We have now seen examples of all of the following patterns/techniques: GCF factoring, difference of two squares, sum/difference of cubes, factoring trinomials, and grouping. We also saw an example where we had to make a change of variables. (We will see this technique again later too!) You are ready for Problem Set 1 now. Pay close attention to examples that require a variety of factoring techniques. Quiz 1 takes place on Wednesday. We shall move on to review exponents and radicals next.
  • August 28, 2024
    • Introduction to exponents
    • QUIZ #1
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Our warm-up problems today offered a bit more practice with factoring. Then, we moved on to introduce formally the topic of exponents---although MATH 1030 definitely assumes that you have worked with exponents previously. We covered the exponent rules and we did a few examples. We took our first quiz during the last part of class. We will continue our discussion of exponents on Friday, and we will also introduce radicals. It is a good idea to take a look at Problem Set 2 on exponents. 
  • August 30, 2024
    • exponents continued
    • Problem Set 2
    • intro to radicals
    • Problem Set 3
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we finished off our discussion of exponents. Then, we introduced the concept of radicals. You should be able to simplify radical expressions involving numbers and variables. We also took a very brief look at rationalization techniques (in other words, techniques to remove radicals from the numerator or the denominator). We will see a few more examples on Wednesday. It would be best if you started working on Problem Set 3 and working on Exercise 8 and Exercise 9 from the "Exam 1 Written" document.
  • September 2, 2024 (Labor Day, No class)
  • September 4, 2024
    • rationalization techniques (continued)
    • intro to rational expressions
    • Problem Set 4
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Our warm-up problems today featured a little more practice with rationalization techniques. Then, we moved to rational expressions. The primary learning objectives are simplifying, adding, subtracting, multiplying, and dividing rational expressions. You should be able to start Problem Set 4. On Friday, we will discuss complex fractions, and we may finally introduce the concept of a function. We also have our second quiz on Friday.
  • September 6, 2024
    • operations on rational expressions (continued)
    • complex fractions
    • QUIZ #2
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We finished our discussion of operations on rational expressions today and then worked on simplifying complex fractions. We will demonstrate how to simplify a complex fraction a few more times on Monday. Also on Monday, we will (finally) introduce the notion of a function! We took Quiz 2 during the last 15 minutes of class.
  • September 9, 2024
    • complex fractions continued
    • Problem Set 5
    • introduction to functions
    • domains of functions
    • Problem Set 6
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We finished our discussion of complex fractions today; the ability to simplify such expressions will be a valuable skill through this course (and MATH 1060). Problem Set 5 concerns absolute value and absolute value equations and is considered outside reading. (Note: by "outside reading," I mean that I will not discuss these problems in class. You can be indoors while working on this material, although doing mathematics outdoors can be exhilarating.) We introduced the concept of function. We also started practicing computing domains of functions. You should be able to start Problem Set 6.
  • September 11, 2024
    • the domain of a function (continued)
    • difference quotients
    • Problem Set 7
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we did a few more examples that involved determining the domain of a function. Then, we moved on to computing the difference quotient of a function. MATH 1030 students should be comfortable computing (and simplifying) difference quotients for linear, quadratic, rational, and root functions. Note that computing and simplifying a difference quotient for rational functions and root functions involve essential algebraic techniques discussed earlier this semester.
  • September 13, 2024
    • difference quotients (continued)
    • average rate of change
    • composition of functions
    • Problem Set 8
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We computed and simplified a few more difference quotients today. Number 3 from the Warm-up Problems is an excellent exercise, requiring a few of the fundamental algebraic skills we discussed earlier this semester. We quickly discussed the average rate of change of a function, and then we began our (much more in-depth) discussion of function composition. We did a few computations and determined the domain of a composition. We will return to our discussion of function composition on Monday. Function composition is the last topic on Exam 1. 
  • September 16, 2024
    • composition of functions (continued)
    • decomposition of functions
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We continued our discussion of function composition today. We computed both the formula and the domain of a composite function. Then, we moved on to the final topic for Exam 1: function decomposition. The ability to look at a function and write it as the composite of two functions is a necessary skill when applying the Chain Rule in Calculus.
  • September 18, 2024
    • review day during class (no new slides)
    • Exam 1 at night 
  • September 20, 2024 (No class, Friday after an exam)
  • September 23, 2024
    • linear functions
    • Problem Set 9
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We started Unit 2 today. For the following two units, we will study particular families of functions. To get the ball rolling, we started our discussion of linear functions today. We went through the corresponding terminology (like slope, y-intercept, etc.), and we also recalled an essential fact concerning parallel and perpendicular lines. Problem Set 9 is for homework.
  • September 25, 2024
    • piecewise-defined functions
    • polynomial functions
    • Problem Set 10
    • Problem Set 11
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Our warm-up problems today finished up our discussion of lines. The first warm-up problem from today is a particularly important type of problem. After our warm-up problems, we briefly discussed piecewise-defined functions. Finally, we started our discussion of polynomial functions. In particular, we found the zeros of a few polynomial functions and identified the multiplicity of these zeros.
  • September 27, 2024 (University closed due to weather)
  • September 30, 2024 (University closed due to weather)
  • October 2, 2024
    • zeros of polynomials (continued)
    • formal derivatives
    • QUIZ #3
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we finished our discussion of zeros of polynomials (and their multiplicities) for our warm-up problems. Then, we introduced the notion of "formal" derivatives of polynomial functions. (I explained the reason for covering this somewhat unusual topic in class.)  Then, we took Quiz 3. Remember that practice problems concerning "formal" derivatives are on my slides. More examples will be posted on the "Exam 2 written" PDF.
  • October 4, 2024
    • polynomial long division
    • Problem Set 12
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We compute a few more derivatives today for warm-up problems. You will learn a lot more about derivatives in MATH 1060. Then, we moved on to one of my favorite topics in the course: polynomial long division. These algebraic skills will show up a few times on the upcoming exam.
  • October 7, 2024
    • polynomial long division (continued)
    • Intro to rational functions
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Our warm-up problems today were intense, so I urge you to study their solutions carefully. The first warm-up problem featured an example of multivariate polynomial long division, and the second warm-up problem was an interesting application of polynomial long division. More examples similar to today's warm-up problems will be posted in the Exam 2 written exercise sheet. Then, we began our discussion of rational functions. I suggest looking at Problem Set 13 as soon as possible, as this homework is involved. 
  • October 9, 2024
    • rational functions continued
    • Problem Set 13
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we continued our investigation of rational functions. In particular, we introduced the concepts of vertical asymptotes and horizontal asymptotes. On Friday, we will discuss a third type of asymptote called a slant asymptote. Most of Problem Set 13 can be completed at this point, and so I urge you to work through as much of the homework as you can before Friday. 
  • October 11, 2024
    • slant asymptotes
    • intro to polynomial inequalites
    • Problem Set 14
    • QUIZ #4
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we discussed slant asymptotes, and this finishes our material concerning asymptotes. Then, we started our discussion of polynomial inequalites. We took Quiz #4 during the last 15 minutes of class.
  • October 14, 2024 (No class, Fall Break)
  • October 16, 2024
    • polynomial inequalities (continued)
    • rational inequalites
    • Problem Set 15
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We finished off our discussion of polynomial inequalites today, and we started working on rational inequalities. We used the "sign chart" method to solve both types of inequalities, but I will mention here that other methods exist. You should start working on Problem Set 15. We will solve a few more rational inequalities on Friday, and we will also start our discuss of inverse functions.
  • October 18, 2024
    • rational inequalities (continued)
    • one-to-one functions
    • inverse functions
    • Problem Set 16
    • QUIZ #5
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we finished our discussion of rational inequalities. Then, we moved on to inverse functions. We demonstrated a useful technique for computing inverse, and we also stated an important condition for determining whether two functions of inverses of each other.
  • October 21, 2024
  • October 23, 2024
    • review day during class (no new slides)
    • Exam 2 at night
  • October 25, 2024 (No class, Friday after an exam)
  • October 28, 2024
  • October 30, 2024
    • Intro to logarithms
    • Problem Set 18
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we finished up our discussion of exponential functions. Then, we introduced the notion of a logarithm. We started from first principles so that we can gain some intuition working with logs. But a key take-away here is that exponential functions and logarithmic functions are inverses of each other. We will discuss more properties of logarithms on Friday.
  • November 1, 2024
    • properties of logarithms
    • Problem Set 19
    • QUIZ #6
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we discussed the properties of logarithms. We also demonstrated a few useful techniques for computing inverses of exponentials and logarithms. We will discuss exponential equations on Monday, and then we start on unit of trigonometry.
  • November 4, 2024
    • exponential equations
    • intro to trig
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: We demonstrated a few useful techniques for solving exponential equations today. Then, we began our crash course on trigonometry. In particular, we defined a few basic terms to set the stage for the material to come!
  • November 6, 2024
    • Introduction to trig (continued)
    • Problem Set 20
    • QUIZ #7
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we demonstrated a few more problems involving logarithms, one of which required a nice change of variable. Then, we reviewed some basic trig terminology. We introduced the notion of coterminal angles and computed a few of them. Then, we took Quiz 7.
  • November 8, 2024
    • The trig functions as circular functions
    • Problem Set 21
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    •  Class synopsis: Our warm-up problems today featured a bit more practice with radian measure. Then, we introduced the six trig functions as circular functions. (We will define the trig functions again in terms of a right triangle later.) Finally, we introduced the very important Pythagorean Identity. We will continue working with the Pythagorean Identity on Monday.
  • November 11, 2024
    • Pythagorean identity continued
    • problems involving the Pythagorean identities
    • intro to right triangle trig
    • Problem Set 22
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we continued our discussion of the Pythagorean Identities. We solved a few problems that required an application of these identities (along with some other basic information about the trig functions). Then, we re-introduced the six trig functions; this time, we defined them in terms of a right triangle. We used these definitions to solve a few problems concerning lengths of sides of right triangles.
  • November 13, 2024
    • right triangle trig continued
    • Problem Set 23 and 24
    • intro to trig equations
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: For our warm-up problems today, we demonstrated a few more applications of right triangle trigonometry. Then, we started our discussion of trig equations. In particular, we covered 'plain' trig equations and 'twisted' trig equations.
  • November 15, 2024
  • November 18, 2024
  • November 20, 2024
    • review day during class (no new slides)
    • Exam 3 at night
  • November 22, 2024 (No class, Friday after an exam)
  • November 25, 2024
    • intro to the the inverse trig functions
    • Problem Set 26
    • Handwritten notes from Section 001
    • Handwritten notes from Section 005
    • Class synopsis: Today, we introduced the inverse trig functions. Recall that the sine, cosine, and tangent functions are not one-to-one. So, we had to make domain restrictions before defining these inverse functions properly. After going through the construction of arcsine and arccosine, we worked through some computations as a class.
  • November 27, 2024 (No class, Thanksgiving)
  • November 29, 2024 (No class, Thanksgiving)
  • December 2, 2024
  • December 4, 2024
  • December 6, 2024
    • review day during class (no new slides)
Exam Information
  • There are precisely four "high-stakes" assessments in MATH 1030; specifically, there are three 90-minute unit exams and one cumulative 150-minute final exam. These assessments are no joke and constitute the majority of your final grade. The final exam is mandatory; there are no exemptions. On the bright side, your final exam will replace your lowest exam score.
  • Here are the dates for these assessments. Please mark your calenders.
    • EXAM 1:  September 18, 2024   7:30 pm to 9:00 pm 
    • EXAM 2:  October 23, 2024  7:30 pm to 9:00 pm
    • EXAM 3:  November 20, 2024  7:30 pm to 9:00 pm
    • FINAL EXAM:  December 9, 2024 11:30 am to 2:00 pm
Additional Resources

Below are some archived versions of MATH 1030. You are encouraged to explore them. For the Fall 2024 semester, I have not made any drastic changes to the curriculum. However, I occasionally make some changes here and there based on student feedback. So, please be aware that your class might not be a replay of a previous semester. 

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ARCHIVED VERSIONS OF MATH 1030

*Summer 2024*

*Spring 2024*

*Fall 2023*

*Summer 2023*

  • MATH 1030 is offered as a part of Clemson's Summer Start program. Here are my class notes from Summer 2023. If you'd like copies of problem sets, quizzes, and/or exams, please email me!
    • June 28, 2023 (Introduction, operations on polynomials)
    • June 29, 2023 (Factoring polynomials: difference of two squares, sum/difference of cubes, trinomials)
    • June 30, 2023 (Exponents, Quiz #1)
    • July 3, 2023 (Intro. to radicals, properties of radicals)
    • July 5, 2023 (Operations on rational expressions, complex fractions, intro. to absolute value, Quiz #2)
    • July 6, 2023 (Intro. to functions, determining the domain of a function)
    • July 7, 2023 (Domains of functions continued, difference quotient, average rate of change, Quiz #3)
    • July 10, 2023 (Difference quotient continued, Intro. to function composition, the domain of a composite function, decomposing functions)
    • July 11, 2023 (Function composition continued, Intro to linear functions, slope-intercept form, parallel/perpendicular lines, piecewise function, Quiz #4)
    • July 12, 2023 (Exam 1)
    • July 13, 2023 (Zeros of polynomials, the Factor Theorem, polynomial long division)
    • July 14, 2023 (More fun with polynomial long division, intro to rational functions, all about asymptotes)
    • July 17, 2023 (Polynomial inequalities, rational inequalities, Quiz #5)
    • July 18, 2023 (More rational inequalities, one-to-one functions, inverse functions)
    • July 19, 2023 (More on inverse functions, intro to exponential functions, e^x, intro to logarithms, Quiz #6)
    • July 20, 2023 (Properties of logarithms, inverse functions of log and exponential functions, expanding & contracting logs, exponential equations)
    • July 21, 2023 (Inverses of exponential & logarithmic functions, prerequisites to trig: angles, coterminal angles, radians, Quiz #7)
    • July 24, 2023 (Exam 2)
    • July 25, 2023 (Reminders about radians, the trig functions as `circular functions', the Pythagorean Identities) 
    • July 26, 2023 (Basic right triangle trig: another approach to sine, cosine, tangent, secant, cosecant, cotangent, reference triangles, & reference angles, Quiz #8)
    • July 27, 2023 (Trigonometric equations)
    • July 28, 2023 (Varieties of trig equations: plain, twisted, mixed, & "hidden" polynomial trig equations, introduction to the inverse trig functions)
    • July 31, 2023 (The inverse trig functions continued: computations & techniques)
    • August 1, 2023 (Exam 3)
    • August 2, 2023 (Review Day for the Final Exam)

*Spring 2023*

  • You can click here to see MATH 1030 class notes from Spring 2023.

 

Course Coordinator: David G. Costanzo (dgcosta@clemson.edu)

 

Last Updated: 12/4/24 Comments to: dgcosta@clemson.edu