Lecture Time: 12:00pm – 1:50pm (TR) Location: Knudson Hall 309

Recitation Time: 12:00pm – 12:50pm (F) Location: Engineering & Computer Science 300

Instructor: Mei Yin

Office and Office Hours: Zoom, 3:30pm – 5:00pm (TR), or by appointment

TA: Mark Doeller

Office and Office Hours:

Calculus, which is covered at DU with the courses MATH 1951, 1952, 1953 and 2080, is the study of inﬁnitesimal change. Whereas MATH 1951 is focused on the derivative, MATH 1952 is focused on integrals. Both of these concepts are defined in terms of a limit, which is a central idea that underlies all of Calculus. It turns out that these two special limits, the integral and the derivative, are closely related, and in particular the integral is tied to the idea of an antiderivative. This will force us to learn to 'undo' the derivative rules which we learned in 1951. Integrals have several important applications. The most fundamental is that an integral gives the area under the graph of a positive function on an interval. Beyond measuring area under the curve, we can use the integrals to compute many other important quantities such as the volume or surface areas of an object, the average value of a continuous function, the amount of work done by a force (as in physics) or the probability of a certain random event.

By the end of the course, you should be able to:

· Be able to approximate the area under a curve using a Riemann sum or other techniques (Trapezoid Rule, Simpson's Rule). For certain functions, be able to determine whether your estimate is an overestimate/underestimate.

· Give the definition of a Riemann integral as a limit, identify a limit of Riemann sums as a definite integral, and compute a Riemann integral by the definition.

· Find the indeﬁnite or definite integral of a basic function via antiderivatives.

· Find the exact area under a curve or between curves, by computing the deﬁnite integral of a function on an interval.

· Apply the fundamental techniques of integration in order to ﬁnd the indeﬁnite integral of more complicated functions: substitution, integration by parts, trigonometric substitution.

· Be able to compute volumes of solids generated by rotating functions using integration.

· Find the average value of a continuous function over an interval via integration.

· Compute the surface areas of basic objects by integration.

· Be able to apply the concept of integration to problems in physics, and economics.

Your grades will be a weighted average of the following components.

Component |
Points |
Percentage |

WebAssign Homework |
45 |
12% |

Written Assignments |
45 |
6% |

Quizzes |
60 |
12% |

Midterm 1 |
100 |
20% |

Midterm 2 |
100 |
20% |

Final Exam |
150 |
30% |

Total |
500 |
100% |

Note that the final exam will be comprehensive (covering the entire quarter).

·

·

Point
Range |
Percentage |
Grade |

465-500 |
93-100% |
A |

450-464 |
90-92.9% |
A- |

435-449 |
87-89.9% |
B+ |

415-434 |
83-86.9% |
B |

400-414 |
80-82.9% |
B- |

385-399 |
77-79.9% |
C+ |

365-384 |
73-76.9% |
C |

350-364 |
70-72.9% |
C- |

335-349 |
67-69.9% |
D+ |

315-334 |
63-66.9% |
D |

300-314 |
60-62.9% |
D- |

0-299 |
0-59.9% |
F |

Week |
Sections Covered |

Jan 3 – Jan 7 |
4.9 – Antiderivatives 5.1 – Areas and Distances |

Jan 10 – Jan 14 |
5.2 – The Definite Integral 5.3 – The Fundamental Theorem of Calculus |

Jan 17 – Jan 21 |
5.4 – Indefinite Integrals and the Net Change Theorem 5.5 – The Substitution Rule |

Jan 24 – Jan 28 |
6.1 – Areas between Curves 6.2 – Volume MIDTERM 1 |

Jan 31 – Feb 4 |
6.3 – Volumes by Cylindrical Shells 6.4 – Work |

Feb 7 – Feb 11 |
6.5 – Average Value of a Function 7.1 – Integration by Parts |

Feb 14 – Feb 18 |
7.2 – Trigonometric Integrals 7.3 – Trigonometric Substitution |

Feb 21 – Feb 25 |
7.4 – Integration of Rational Functions by Partial Fractions 7.5 – Strategy for Integration MIDTERM 2 |

Feb 28 – Mar 4 |
7.7 – Approximate Integration 8.1 – Arc Length |

Mar 7 – Mar 11 |
8.2 – Area of a Surface of Revolution Review |

Mar 18 |
FINAL EXAM |

Students are encouraged to come to office hours or go to the Math Center. A great deal of learning mathematics comes outside of the classroom and your professor enjoys having students come to office hours to talk about the material.

The Math Center

If you have a disability/medical issue protected under the Americans with Disabilities Act (ADA) and Section 504 of the Rehabilitation Act and need to request accommodations, please visit the Disability Services Program website at http://www.du.edu/disability/dsp. You may also call (303) 871-2372, or visit in person on the 4th floor of Ruffatto Hall; 1999 E. Evans Ave., Denver, CO.

In this class, we will work together to develop a learning community that is inclusive and respectful. Our diversity may be reflected by differences in race, culture, age, religion, sexual orientation, socioeconomic background, and myriad other social identities and life experiences. The goal of inclusiveness, in a diverse community, encourages and appreciates expressions of different ideas, opinions, and beliefs, so that conversations and interactions that could potentially be divisive turn instead into opportunities for intellectual and personal enrichment.

A dedication to inclusiveness requires respecting what others say, their right to say it, and the thoughtful consideration of others' communication. Both speaking up and listening are valuable tools for furthering thoughtful, enlightening dialogue. Respecting one another's individual differences is critical in transforming a collection of diverse individuals into an inclusive, collaborative and excellent learning community. Our core commitment shapes our core expectation for behavior inside and outside of the classroom.

All work submitted in this course must be your own. You are encouraged to work together on homework, but make sure that working together does not turn into copying another student's answer. For consequences of violating the Academic Misconduct policy, refer to the University of Denver website on the Honor Code (

As you go through this course, it is common for questions to arise about how you will use these concepts in a potential career. Feel free to ask faculty members about their career paths and research areas, and also know the University of Denver offers a number of resources to help you on your career development journey. Career & Professional Development can help you explore your interests, develop your job and internship search skills, and connect you with individuals in the field of your choice. Learn more, schedule an appointment, and see upcoming events at du.edu/career.