MAT 131 Problem Sets | MAT 131 Schedule | MAT 131 Exams |

# Course Information

### Course Announcements

Announcements about the course will be posted here. Please check the site regularly for announcements (which will also be given in lecture and/or in recitation).- There is now a PDF version of the information on this webpage in the "Syllabus" portion of the Blackboard page for the lecture. You can also find a copy of the PDF file here.
- Prof. Julia Viro has produced videos of lessons accompanying MAT 131 Calculus I. Students are encouraged to use these videos to supplement the lectures and recitations as needed.

### Course Description

The description in the undergraduate bulletin: The differential calculus and integral calculus, emphasizing conceptual understanding, computations and applications, for students who have the necessary background from 12th-year high school mathematics. Differentiation of elementary algebraic, trigonometric, exponential, and logarithmic functions; graphing; modeling and maximization; the Riemann integral; and the fundamental theorem. May not be taken for credit in addition to MAT 125 or 141 or AMS 151.### Prerequisites

In order to take MAT 131, you must have either- passed MAT 123 with a B or higher, or
- received a score of 5 or better on the mathematics placement examination.

See the document first year mathematics at Stony Brook for more information about the math placement exam and other calculus courses.

### Textbook

*Calculus (an OpenStax resource)*, by Gilbert Strang, Edwin Herman, et al., freely available at the CNX website. We will also be using WebAssign for online homework assignments this semester. There is a link to the free ebook from within WebAssign.

### Lectures

Primary instruction will occur in lectures, with practice and reinforcement provided in a smaller classroom setting during recitations.### PLEASE DO THE ASSIGNED READING FROM THE SYLLABUS BEFORE LECTURE.

Lecture | Time | Room | Instructor |

LEC 1 | TuTh 9:45-11:05am | Frey Hall 102 | Jason Starr |

LEC 2 | TuTh 6:30-7:50pm | Frey Hall 100 | Radu Laza |

### Recitations

Please regularly attend recitation. Most of the one-on-one interaction so crucial in this course will happen in recitation.Recitation | Time | Room | Instructor |

R01 | TuTh 1:15-2:10pm | Library N4000 | Roberto Albesiano |

R02 | TuTh 8:00-8:55am | EarthSpaceSci 183 | Roberto Albesiano |

R03 | MW 10:30-11:25am | EarthSpaceSci 069 | Danfei Wang |

R04 | MW 4:25-5:20pm | Physics P130 | Danfei Wang |

R05 | MF 1:00-1:55pm | Staller Ctr 3218 | Luke Kiernan |

R06 | MW 9:15-10:10am | Frey Hall 328 | Yunpeng Niu |

R07 | WF 11:45am-12:40pm | Chemistry 128 | Jacob Laxer |

R08 | MF 10:30-11:25am | Physics P113 | Luke Kiernan |

R20 | TuTh 1:15-2:10pm | LgtEngrLab 154 | Myeongjae Lee |

R21 | TuTh 8:00-8:55am | EarthSpaceSci 181 | Myeongjae Lee |

R22 | MF 10:30-11:25am | Physics P112 | Yunpeng Niu |

R23 | MW 4:25-5:20pm | EarthSpaceSci 069 | Shamuel Auyeung |

R24 | MF 1:00-1:55pm | Library N4072 | Jiasheng Teh |

R25 | MW 9:15-10:10am | StallerCtr 3220 | Shamuel Auyeung |

R26 | WF 11:45am-12:40pm | Chemistry 128 | Jacob Laxer |

R27 | MF 10:30-11:25pm | Physics P113 | Luke Kiernan |

### Grading System

The relative significance of exams and problem sets in determining final grades is as follows.20% | |

20% | |

45% | |

15% |

### Handbacks

Graded problem sets and exams will be handed back in recitation. If you cannot attend the recitation in which a problem set or exam is handed back, it is your responsibility to attend your recitation instructor's office hours and get your graded work.**FAILURE TO RETRIEVE GRADED WORK IS NOT GROUNDS FOR A MAKE-UP, A REGRADE, OR CHANGE OF A FAIL TO AN INCOMPLETE.**

You are responsible for collecting any graded work by the end of the semester. After the end of the semester, the recitation instructor is no longer responsible for returning your graded work. If you have a question about the grade you received on a problem set or exam, you must contact the recitation instructor (not the grader or the lecturer).

## Course Learning Objectives

The course learning objectives include the following. Each of these is an important learning objective for*all*mathematics courses. Each is amplified with specific examples.

**Acclimate to New Mathematics.**Gain familiarity with a new mathematical idea (be it a definition, a result, an algorithm, etc.) through examples, through basic results that involve that idea, and through deeper results that reflect the significance of the idea.**Example.**The derivative is an example of a limit: the limit of the difference quotient.**Apply and Model.**Understand how an abstract notion or result can lead to an algorithm or computation arising in a context different from the original notion or result. Understand the necessary hypotheses and limitations of that model.**Example.**The result that a local max / min of a differentiable function on an open interval is a critical point leads to the algorithm for solving optimization problems.**Specialize.**Pass from general theorems, definitions, and methods to specific examples. Be able to compute with those examples.**Example.**The general formula for the Riemann integral as a limit of Riemann sums specializes to computable limits for the Riemann integral of a polynomial function.**Generalize.**Understand examples of ideas, constructions and arguments originally developed in one context yet that extend to another context.**Example.**The formula for the derivative of a general inverse function, which extends the power law to fractional exponents, also allows us to compute derivatives of logarithm functions and inverse trigonometric functions.**Prove.**For a conjectured result, often expected from examples, heuristics and other indirect evidence, understand when an argument is a complete proof.**Example.**The power law tells us a quick formula for the derivative of a polynomial function, but the complete proof of the power law using the limit of a difference quotient requires the Binomial Theorem.

## Course Outcomes / Key Skills

The course outcomes / key skills include the following.- Definition, basic properties and graphs of elementary functions: powers, exponentials, logarithms, and trigonometric.
- The definition, basic properties and graphs of even and odd functions.
- The definition and meaning of increasing and decreasing for functions and graphs.
- Reflection, translation and scaling of graphs and the corresponding transformation of the functions.
- Definition, basic properties, and graphs of inverse functions. Computation of an inverse function.
- Definition, basic laws, and techniques for computing limits, one-sided limits, limits using the squeeze theorem, limits equal to infinity, and limits at infinity.
- Identifying all discontinuity points (both the location and type), the domain of a function, and all vertical and horizontal asymptotes. Application of these notions to curve-sketching.
- The statement of the Intermediate Value Theorem and its use in finding zeroes of functions.
- The definition of the derivative as the limit of a difference quotient, and methods for computing derivatives directly from the definition.
- Using the derivative to compute the equations of tangent lines.
- Using the rules of differentiation: the sum rule, the product rule, the power rule and the derivatives of exponentials.
- Given the values of the limits of sin(x)/x and of 1-cos(x) as x tends to zero, find the formulas for the derivatives of the functions sin(x) and cos(x) from the definition as a limit of a difference quotient.
- Finding derivatives of other trigonometric functions such as tan(x), cot(x), sec(x) and csc(x) using the derivatives for sin(x) and cos(x) and the rules for differentiation.
- Finding derivatives using the chain rule.
- Finding the tangent slope to a parametric curve at a specified point.
- Finding derivatives using implicit differentiation, including derivatives of inverse functions.
- Finding derivatives using logarithmic differentiation.
- Finding the linear approximation to the value of a function, using a known nearby value and derivative or using differentials.
- Understanding differential notation and the geometric interpretation of differentials. Using differentials to approximate values of functions.
- Solving related rates problems.
- Absolute maxima and minima; local maxima and minima; inflection points. Know how to find the absolute maximum and absolute minimum value of a differentiable function on a closed, bounded interval. Know how to find local maxima and minima and inflection points of functions, and use this to help graph the function.
- LHopitals rule. Recognize indeterminate forms. Simplify limits leading to indeterminate forms using lHopitals rule. Know how to transform other indeterminate forms into one of these two types.
- Optimization problems. Given a word problem attempting to maximize or minimize some quantity given a collection of constraints, turn this into a calculus problem for finding an absolute maximum or absolute minimum. Solve this calculus problem.
- Know how to set up a Riemann sum associated to a given integrand and a given interval. Be able to evaluate the limit of Riemann sums to compute the Riemann integral in the case of some simple integrands.
- Antiderivatives. Recognize the most common antiderivatives: those arising as the derivatives of polynomial functions, trigonometric functions, exponential functions, logarithmic functions and inverse trigonometric functions.
- Know the statement of the Fundamental Theorem of Calculus. Understand how to use this to evaluate definite integrals when you can find a simple form for the antiderivative. Understand how the fundamental theorem always gives an antiderivative of a continuous function, where the antiderivative is defined in terms of the Riemann integral/definite integral.
- Given a limit of sums, recognize when this is a limit of Riemann sums. Be able to use the fundamental theorem of calculus to evaluate this limit of Riemann sums.
- Simplify antiderivatives using direct substitution.
- Evaluate definite integrals using substitution and the Fundamental Theorem of Calculus.

### Academic Resources

There are a number of organizations on campus offering tutoring and other academic resources in various locations. The mathematics department offers drop-in tutoring in the Math Learning Center. You are strongly encouraged to talk to a tutor in the MLC if you have an issue and are unable to attend your lecturer's or recitation instructor's office hours (or if you have previously arranged to meet them in the MLC).Please be aware that tutors in the MLC deal with students on a first-come, first-served basis. Thus it may be preferrable to speak with your lecturer or instructor in their office hours. (Even if you find them in the MLC, they may be obliged to speak to other students before speaking with you.)

### Disability Support Services

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact the Student Accessibility Support Center, Stony Brook Union Suite 107, (631) 632-6748, or at sasc@stonybrook.edu. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and the Student Accessibility Support Center. For procedures and information go to the following website: https://ehs.stonybrook.edu//programs/fire-safety/emergency-evacuation/evacuation-guide-disabilities and search Fire Safety and Evacuation and Disabilities.### Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty is required to report any suspected instances of academic dishonesty to the Academic Judiciary. Faculty in the Health Sciences Center (School of Health Technology & Management, Nursing, Social Welfare, Dental Medicine) and School of Medicine are required to follow their school-specific procedures. For more comprehensive information on academic integrity, including categories of academic dishonesty please refer to the academic judiciary website at http://www.stonybrook.edu/commcms/academic_integrity/index.html### Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Student Conduct and Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Until/unless the latest COVID guidance is explicitly amended by SBU, during Fall 2021 "disruptive behavior" will include refusal to wear a mask during classes.Jason Starr

4-108 Math Tower

Department of Mathematics

Stony Brook University

Stony Brook, NY 11794-3651

Phone: 631-632-8270

Fax: 631-632-7631

Jason Starr