Math 161D
Calculus I
Fall, 2007

Course information

Course syllabus
Course calendar
Homework assignments
Goals for Week 1: Tuesday | Wednesday | Thursday
Information about: Exam 1 | Exam 2 | Exam 3 | Exam 4
Algebra: Codes to messages from grader | Top Algebra Errors Made by Calculus Students
Professor Scofield's homepage
Drop-in calculus help is available on M-Th evenings, 7-9 pm in NH 251

Reading 1: “17th Century mathematics and mathematical notation”

Precalculus:
Functions and graphs:
A simple graphing utility
Polar functions
Parametric curves: site 2 | in 3D
Transformations that shift a graph vertically or horizontally
How a parameter may be used to morph one graph into another
Function composition
Cycloids: applet 1 | another one from Maths online
A spirograph applet that can be manipulated to produce popular polar curves
Limits:
Numerical investigation of a certain type of limit.
Some examples showing why numerical evaluation of limits can be untrustworthy.
Illustrating the (ε-δ) definition of limit
Practice: Given ε (specified value), find δ algebraically. Solutions provided.
Practice: Given ε (left unspecified), find δ. Solutions provided.
Drill on finding horizontal and vertical asymptotes. Solutions provided.
The limit of sin(x)/x as x -> 0
The number e: site 1 | site 2
Derivatives:
The tangent line as the limit of secant lines: site 1 | site 2
Drill on finding derivatives from the definition of derivative.
Applets on the relationship between a function and its derivative: site 1 | site 2
Differentiability implies continuity, but the converse is not true.
Some important theorems
Newton's method: in the complex plane
Integration
Applet demonstrating Archimedes' use of polygons to get approximate area of unit circle
Riemann sums applet
Simpson's rule applet
Get correct antiderivatives using webMathematica's integrator
Volumes of solids
General volumes site 1 | site 2
Volumes of revolution site 1 | site 2
Supplemental
Why Calculus?
A context for calculus
Connected Calculus (from the Connected Curriculum Project)
A relatively-inexpensive book, How to Ace Calculus: the Streetwise Guide