# Math 151H/151M, Fall 2004

## Course Materials

Schedule and Homework (Updated Daily)

## Exam 2 Information (Oct 31st)

Exam 2 is on Friday Nov 12th and will cover 3.1-3.10 and 4.1-4.3.

In additon to the required and recommended hwk problems I suggest the following review problems
Page 213 Concept Check: 2-7
Page 213 T/F: 1,3,5,8,9,10
Page 214 Ex: 1,2,4-7,10,11,13-48,51-66,69-72,75-79,83-86.
Page 308 Concept Check: 1-4
Page 308 T/F: 1-5
Page 309 Ex: 1-6,33-35

## Nov 22nd

Project 3 [pdf]
This project is due on FRIDAY December 10th. Note the change in due date!!

## Exam 3 Information (Nov 23rd)

Exam 3 is on Monday Dec 6th and will cover 4.4,4.5,4.7,4.9,4.10 and 5.1-5.3. See information on Final exam below for theoretical material from these scetions that may be examined on Midterm Exam 3.

In additon to the required and recommended hwk problems I suggest the following review problems
Page 308 Concept Check: 7,9,10
Page 308 T/F: 16,17
Page 309 Ex: 17-28,38-47,49-51,53-58,61,62
Page 368 Concept Check: 1-3
Page 368 T/F: 1-8
Page 369 Ex: 1-5,7-14,33-44,52,54,56

## Theory to Study for Final Exam (Nov 23rd)

The final exam will cover all the material covered on the first three exams as well as 5.4, 5.5, and 6.1

Just as there was on the Midterm Exams there will be some theoretical questions on the Final Exam. Here is a list of Definitions, Theorems and Proofs that I could ask about on the Final Exam. I may also ask you to use these theorems/definitions to solve problems that are the same as or very similar to problems that are on the required/recommended or review problems.

Precise definition of limit [Defn 2, p 93]
Definitions of left-hand and right-hand limit [Defns 3,4, p96]
Definition of infinite limit [Defn 6, p99]
Statements of limit laws 1-11 and Direct Subsitution Property [p82-85]
Statement of Theorem on left and right hand limits [Thm 1, p87]
Statement of Squeeze Theorem [Thm 3, p88]
Definition of continuity [Defns 1,2,3, p102-104]
Statement of Continuity Theorems 4-9 [p105-108]
Statement of Intermediate Value Theorem [p109]
Definition of Derivative and interpretation as slope and rate of change [p127-9]
Definition of a Differentiable function [p139]
Statement and PROOF of fact differentiable functions are continuous, and counterexample for converse [Thm 4, p140-1]
Definition of Vertical tangent line [p141]
Statements of all boxed differentation rules in 3.3 [p145ff]
PROOF of Power Rule for Differentiation (Case n is an integer)
PROOF of Product Rule for Differentiation
Statements of Derivative Theorems for Trig Functions [p172]
Proof that derivative of sin(x) is cos(x) given the limits [2] and [3] on page 170-1.
Statement of Chain Rule [p176]
Definitions of linear approximation and differentials, and pictures in Figs 1,6 on pages 205-208
Definitions of absolute and local max/min [p223-4]
Statement of Extreme Value Theorem [p225]
Statement and PROOF of Fermat's Theorem [p227]
Defn of crtical numbers and values [p227]
Statement of Closed Interval Method [p227]
Statements and PROOFS of Rolle's Thm and Mean Value Theorem
Defns of increasing/decreasing, concave up/down, inflections points
Statements of Inc/Dec Test, Concavity Test, 1st and 2nd Derivative tests
PROOF of Inc/Dec Test
Defns of limits at infinity and horizontal asymptotes [p251,257-9]
Defns of slant asymptotes
Statement and counterexamples for Newton's method
Defns of antiderivatives and Table 2 [p301]
Defn of Area as left/right-hand sum [p320]
Defn of definite integral [p326]
PROOF that right-hand sum is larger than left-hand sum for an increasing function
Statements of Properties 1-8 of definite integrals [p334-336]
Statements and PROOFS of FTC I and II
Statement of The Net Change Thm [p354]
Statement and PROOF of the Substitution Rule [p361,363]