MTH-140 Calculus I: Chapter 3 Lectures
Alexander Alvarez
Dept. of Mathematics, Ryerson University
Winter 2012
February 25, 2012
Ryerson University
MTH 140, Winter 2012
Dierentiation rules
Dierentiation of a constant function f (x ) = C
pause
C C
f (x + h)
MTH-140 Calculus I: Chapter 2 Lectures
Alexander Alvarez
Dept. of Mathematics, Ryerson University
Winter 2012
January 29, 2012
Ryerson University
MTH 140, Winter 2012
Introduction
The tangent problem
Ryerson University
MTH 140, Winter 2012
Introduction
Th
MTH-140 Calculus I: Chapter 1 Lectures
Alexander Alvarez
Dept. of Mathematics, Ryerson University
Winter 2012
January 22, 2012
Ryerson University
MTH 140, Winter 2012
Lecture 1: Introduction to functions
The content for this lecture is in sections 1.1 and
Ryerson University
MTH 140, Winter 2012
Lecture 20: Optimization Problems
The content for this lecture is in section 4.7
Ryerson University
MTH 140, Winter 2012
Optimization Problems
In these optimization problems we try to solve a real world problem
of n
Ryerson University
MTH 140, Winter 2012
Lecture 19: Curve Sketching
The content for this lecture is in sections 4.5
Ryerson University
MTH 140, Winter 2012
Guidelines to sketch a curve y = f (x )
Domain
Intercepts
Symmetry
Asymptotes
Interval of increase
Ryerson University
MTH 140, Winter 2012
Lecture 18: Maximum and Minimum Values. Derivatives
and shape of a graph.
The content for this lecture is in sections 4.1 and 4.3.
Ryerson University
MTH 140, Fall 2012
Denition: Absolute Maximum and Minimum
Let c b
Ryerson University
MTH 140, Winter 2012
Lecture 17: The substitution rule
The content for this lecture is in section 5.5
Ryerson University
MTH 140, Winter 2012
Chain rule
(F (g (x ) = F (g (x ) g (x ) =
Ryerson University
F (g (x )g (x )dx = F (g (x )+C
Ryerson University
MTH 140, Winter 2012
Lecture 16: Fundamental Theorem of Calculus. Indenite
integrals. Net change theorem.
The content for this lecture is in sections 5.3 and 5.4
Ryerson University
MTH 140, Winter 2012
Dierential
Calculus
F .T .C .
Ryer
Ryerson University
MTH 140, Winter 2012
Lecture 15: The denite Integral
The content for this lecture is in section 5.2
Ryerson University
MTH 140, Winter 2012
Denite Integral
If f is a function dened for [a, b ] we divide the interval [a, b ] into
n subin
Ryerson University
MTH 140, Winter 2012
Lecture 14: Antiderivatives. Areas.
The content for this lecture is in sections 4.9 and 5.1
Ryerson University
MTH 140, Winter 2012
Antiderivatives
A function F is called an antiderivative of f on an interval I if
F
1
MTH 140 Test 1
MIDTERM TEST #1
Calculus I MTH 140
Last Name (Print): Maximus
Signature:
First Name: Max
Student Number: 999999999
.
Date: Feb. 3, 2012, 4:10 pm
Section (circle one)
Instructions:
Dr. Ord :
1234
Dr. Ha :
Duration: 1.5 hour
567 8
Dr. Alvar