Differential Calculus with Physical Applications year
MA 180y

Fall 2014
2.1: The Tangent and Velocity Problem
The Velocity Problem
1. Example. Suppose a car accelerates from a complete stop. After 10 seconds, it has
traveled 200 metres. On average, how fast was the car traveling?
2. Denition. We dene the average velocity of a
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
Physical Applications of Derivatives
With the widespread use of calculus in all areas of science, especially physics, for which Isaac Newton
invented it to begin with, it would be a shame to omit a discussion of applications of differential calculus to
ph
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
2.5: Continuity
lim f (x) discusses the behavior of f (x) near x = a, but not at x = a.
xa
f (a) discusses the value of f (x) at x = a, but ignores any nearby behavior.
The notion of continuity discusses both behaviors at once.
1. Denition. Let f (x) b
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
SOME PHYSICAL APPLICATIONS OF VECTOR CALCULUS
1. Fundamental Theorems of Vector Calculus
Let us rst recall the fundamental theorems of vector calculus. They will be
used many times in what follows.
Theorem 1.1. Let be an oriented curve in R3 with initial
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
May 26, 2014' Math 180 Midterm 1 Page 2 of 6
(10 points) 1. Answer the following multiple choice questions. Check your answer very carefully. Your answer will be
marked right or wrong (work will not be considered for this problem).
(2 points) (3.) Find
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
(5 points)
(1 points)
(1 points)
(1 points)
(1 points)
(1 points)
Jun 9, 2014
Math 180 Midterm 2
Page 2 of 6
1. Answer the following multiple choice questions. Check your answer very carefully. Your answer will be
marked right or wrong (work will
Differential Calculus with Physical Applications year
MA 180y

Fall 2014
Some Notes on Taylor Polynomials and Taylor
Series
Mark MacLean
October 30, 2007
UBCs courses MATH 100/180 and MATH 101 introduce students to the
ideas of Taylor polynomials and Taylor series in a fairly limited way. In these
notes, we present these ideas