Math 251 Fall 2017

Instructor: Robert Lipshitz

Basic course information

Time: MTWF 2:00–2:50 p.m.
Place: 306 Deady.
Textbook: Calculus: Concepts and Contexts by James Stewart, 4th edition.
Office hours: Monday 3:00-4:00, Wednesday 12:00-1:00, Friday 12:45 - 1:45. Subject to change.
Final exam: Per the university Final Exam Schedule
Midterm exams: October 23 and November 10. Subject to change if necessary.
There is also WebWork homework and a Canvas webpage for tracking grades.


Math 112 (with a C- or better) or satisfactory placement exam score.

Description and goals

Calculus, the quantitative study of change, is is one of the basic mathematical tools in physical and social sciences and mathematics. Math 251-253 is an introduction to calculus, aimed primarily at students in mathematics and the physical sciences. This quarter focuses on differential calculus---defining and computing the rate of change of a quantity, and how the rate of change is useful. (Math 252 focuses on integral calculus---going from the rate of change to the original quantity.)

Specific “learning outcomes” include:

  • Understanding the intuition behind limits and continuity and being able to compute limits and test for continuity in simple situations.
  • Understanding the meaning of the derivative and being able to compute the derivatives of elementary functions. ("Elementary functions" is a technical term.)
  • Be able to relate features of graphs to first and second derivatives.
  • Be able to use derivatives to solve optimiation, related rates, and other modelling problems.

A course is more than its “learning outcomes”: the goal is understanding, not the ability to perform specific manipulations.



Written homework 20%
Online homework 10%
Midterm 1 20%
Midterm 2 20%
Final 30%



The course will have both written and online homework. Written homework is due at the beginning of class on Mondays, except as noted. Online homework, via WebWorks, is due before class on Mondays, except as noted. (Due dates may change.) There will be written and online homework assignments due during “dead week”. Well-prepared students should expect to spend 8-12 hours per week (2 to 3 hours per hour of class) outside of class on homework and review.

You may use any resources you like on the homework, but all resources except the textbook must be cited on your assignment. This includes help from your classmates, friends, or Google. Failure to cite sources constitutes plagiarism, a serious form of academic dishonesty, and will be punished and reported.

You may work together on homework assignments, but you must write up the final version of your answers by yourself. Working on the final write-ups together constitutes cheating.

Late homeworks will not be accepted, but the lowest written homework score and lowest online homework score will be dropped. Due to limited resources, only part of the homework will be graded carefully.

The WebWork homework site, for online homework: .
Written homework assignments are posted below.


All exams will be given in class, and there will typically not be makeup exams. If you know in advance that you will miss an exam, contact me immediately to make arrangements. If you miss an exam because of an emergency (medical, family, ...) you will be expected to provide documentation of that emergency.

All exams are closed-note, closed-book, and without electronic assistance (including calculators and cell phones). Using any notes or electronic device or communicating with anyone except me during an exam constitutes cheating.

Students with disabilities

I, and the University of Oregon in general, are committed to an inclusive learning environment. If you have a disability which may impact your performance on exams, please contact the Accessible Education Center to discuss appropriate accommodations. If there are other disability-related barriers to your participation in the course, please either discuss them with me directly or consult with the Accessible Education Center.

Written homework

Again, all written homework is due at the beginning of class on the due date. Recall that WebWork homework is also assigned.


This schedule is tentative, and may change during the quarter.

Week Date Topic Sections
1 9/25 Introduction to the class. Motivation for limits. §2.1
  9/26 Intuition for limits, working with limits. §2.2, 2.3
  9/27 Continuity. §2.4
  9/29 Review
2 10/2 Limits involving infinity. Homework 1 due.

This is the last day to drop the class without a W.
  10/3 Precise definition of continuity and limits. Applications to error analysis. Appendix D
  10/4 Derivative at a point §2.6
  10/6 Review.  
3 10/9 Derivative as a function. Homework 2 due. §2.7
  10/10 Derivatives and graphs. §2.8
  10/11 Derivatives of sums, polynomials and exponential functions. §3.1
  10/13 Review.  
4 10/16 Product and quotient rules. Homework 3 due. §3.2
  10/17 Derivatives of trig functions. §3.3
  10/18 Chain rule. §3.4
  10/20 Review.  
5 10/23 Midterm 1. Homework 4 due.  
  10/24 Implicit differentiation. §3.5,
  10/25 Derivative of logarithm. §3.7
  10/27 Review.  
6 10/30 Derivatives of inverse trig functions. Homework 5 due. §3.6
  10/31 Rates of change and linear approximation. §3.8, 3.9
  11/1 Related rates. §4.1
  11/3 Review.  
7 11/6 Finding maxima and minima. Homework 6 due. §4.2
  11/7 More maxima and minima. §4.2
  11/8 Review  
  11/10 Midterm 2

The last day to withdraw from the class or change grading option is 11/12.
8 11/13 Mean value theorem. Homework 7 due. §4.3
  11/14 Derivatives and graphs, redux. §4.3
  11/15 Optimization problems. §4.6
  11/17 Review.  
9 11/20 L'Hospital's Rule. Homework 8 due. §4.5
  11/21 More optimization. §4.6
  11/22 Review.  
  11/24 Thanksgiving holiday (no class).  
10 11/27 Newton's method. Homework 9 due. §4.7
  11/28 More Newton's method. §4.7
  11/29 Review.  
  12/1 Review. (Last day of classes.)  



Handouts will be posted here, in case you lost the physical copy.

WebWork Advice

Mathematics is best done (and practiced) with pencil and paper. Avoid solving WebWorks problems at your computer: it leads to guessing, which doesn't help you learn. Instead, write down or print out the WebWorks problems and then step away from your computer. Solve them with pencil and paper (and eraser), keeping track of the steps involved. Once you have the solution, type it in and have WebWorks check your answer. If WebWorks tells you your answer is wrong, step away from your computer again and check your work. Try to find the mistake. If you can't find the mistake, try office hours, a classmate, or the math library.

General Advice

Reading mathematics. You are expected to read the sections in the textbook before coming to class. It's usually only a few pages, so read it carefully. Note down the questions you have; I would expect you to have at least one per page. Read the section again after class. See which questions you now understand. Think about the remaining questions off and on for a day. See which you now understand. Ask someone (e.g., me) about the questions you still have left.

Getting help. If you're having trouble, get help immediately. Everyone who works seriously on mathematics struggles, but if you don't get help promptly you will soon be completely lost. The first places to look for help are my office hours. You can also try the drop-in help at the Math Library. The Teaching and Learning Center also facilitates individual and small-group tutoring.

Teaching to learn. The best way to learn mathematics is to explain it to someone. You'll find that, particularly in office hours, I'll try to get you to explain the ideas. You should also try explaining the material to each other. The person doing the explaining will generally learn more than the explainee. Another thing to try is writing explanations to yourself, in plain English or as close as you can manage, of what's going on in the course. File them somewhere, and then look back at them a few days later, to see if your understanding has changed.