AMS 151.02 Applied Calculus I, Fall 2014
Instructor: Viacheslav Zhygulin (viacheslav.zhygulin@stonybrook.edu)
Office hours: Mondays 4pm - 5pm, Wednesdays 3pm 4pm or by appointment. Extra office
hours might be set before exams.
WebWork: http:/webwork2.ams.
AMS 151: Applied Calc
I
Lecture 7
Introduction to Continuity
Limits
Viacheslav Zhygulin
Revision:
Example: volume of a sphere of radius r is given by:
On the picture:
Odd and even
integer powers of x.
Revisiom:
Examples of graphs of the polynomials:
Revis
AMS 151: Applied Calc
I
Lecture 9
Continuity
Viacheslav Zhygulin
Revision - Limits
The concept of limit is the underpinning of calculus. Before we said that a function f is
continuous at x = c if the values of f(x) approach f(c) as x approaches c.
Revisio
AMS 151: Applied Calc
I
Lecture 6
Viacheslav Zhygulin
Power function:
Example: volume of a sphere of radius r is given by:
On the picture:
Odd and even
integer powers of x.
Polynomials - definition:
Examples of graphs of the polynomials:
Polynomials - exa
AMS 151: Applied Calc
I
Lecture 5
Viacheslav Zhygulin
Plan for today:
1. Congratulations! The first quiz is done.
2. Trigonometric functions:
-radians
-Sine and Cosine functions
-Tangent function
-Inverse Trigonometric functions
3. Exercises and examples
Solution Key
Pre-requisite Test: Applied Calculus I (Fall 2011, Section 2)
Loretta Au, instructor
Instructions. This is a closed-book exam to be completed in 40 minutes. No calculators are
3
allowed, so please leave your nal solutions as expressions, if n
Solution Key
Loretta Au
Homework 14: Applied Calculus I (Fall 2011, Section 2)
Sept. 29, 2011
Selected homework problems. Here are detailed solutions to homework problems that students appeared to have the most trouble with on WebWork.
HW1: problem 9
HW
Solution Key
Loretta Au
Quiz #1: Applied Calculus I (Fall 2011, Section 2)
Sept. 13, 2011
Instructions. This is a closed-book quiz worth 10 points, to be completed in 10 minutes. No
calculators are allowed; leave nal solutions as expressions, if necessary
Aug 24, 2011
Mathematics Placement Advice
for Zihao Wu (108256231)
Placement Level:
5
Course options: MAT 131, MAT 141, or AMS 151
Your choices for mathematics course are explained below. AMS 151 and MAT 141 are
intended for especially well-motivated stud
Solutions to Homework #9b
4.8(25 points)
1. The particle moves on straight lines from 0,1 1,0 0, 1 1,0 0,1 (1)
2. The particle moves on straight lines from 0,0 2,0 2,1 0,1 0,0
(1)
4. The particle moves on straight lines from 1,1 1,1 1, 1 1, 1 1,1 (1)
x 3c
Solutions to Homework #3
2.1(20 points)
1. v
s s(b) s(a) 400 135 265
km / hr (1)
t
ba
52
3
6. s (t ) et 1 s (2) e 2 1 s (4) e 4 1
(e 4 1) (e 2 1) e 4 1 e 2 1 e 4 e 2
v
m / sec (2)
42
2
2
8. a. v
v
s(t h) s(t )
s 3t 2
h
3(1 h) 2 3
h
plug in for values o
AMS 151
Assignment #2
Section 1.5 (29 points)
1. Sin(3/2) = 1 is negative.
Cos(3/2)= 0
Tan(3/2) is undefined.
9. Sin (1) is negative
Cos (1) is positive
Tan (1) is negative.
3
3
10. The period is 2/3, because when t varies from 0 to 2/3, the quantity 3t v
AMS 151
Assignment #4
(Total 79 points)
Section 2.4 (25 points)
1. (a) The statement f(200) = 1300 means that it costs $1300 to produce 200 gallons of the
chemical.
(b) The statement f(200) = 6 means that when the number of gallons produced is 200, costs
AMS 151: Applied Calc
I
Lecture 13
Midterm preparation
Viacheslav Zhygulin
Midterm Preparation:
1.
2.
3.
4.
5.
6.
Trigonometric functions, asymptotes
Polynomials
Exponential function
Proof problem
Limit
Derivative
You have to pick 5 of 6 problems to solve
AMS 151: Applied Calc
I
Lecture 7
Introduction to Continuity
Limits
Viacheslav Zhygulin
Revision:
Roughly speaking, a function is said to be continuous on an interval if its graph has no breaks,
jumps, or holes in that interval
Revision:
Exponential funct
AMS 151: Applied Calc
I
Lecture 22
Properties of Definite Integral
The Fundamental Theorem of Calculus
Viacheslav Zhygulin
Review:
Review:
Review:
Review:
The Definite
Integral
Review:
Review:
Review:
The Definite Integral:
The Definite Integral:
The Fund
AMS 151: Applied Calc
I
Lecture 24
Second Fundamental Theorem
Misc topics
Viacheslav Zhygulin
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Second Fundamental Theorem:
Second Fundamental Theorem:
Second Fundamental Theorem:
Second Fundam
AMS 151: Applied Calc
I
Lecture 4
Viacheslav Zhygulin
Plan for today:
1. Revision.
2. Concavity.
3. Practice exercises.
4. Questions on HWs, quiz #1
Next Lecture:
1. Quiz # 1 (10 minutes)
2. Trigonometric functions.
Revision:
A function is a rule that tak
AMS 151: Applied Calc
I
Lecture 25
Final Practice Exam
Viacheslav Zhygulin
Final:
Structure the same as for midterm exam. 6 problems:
1. Find limit of the function. May involve LHopitals rule, squeeze theorem.
2. Prove statement. May involve any theorems
AMS 151: Applied Calc
I
Lecture 26
Final Practice Exam
Viacheslav Zhygulin
Final:
Structure the same as for midterm exam. 6 problems:
1. Find limit of the function. May involve LHopitals rule, squeeze theorem.
2. Prove statement. May involve any theorems
AMS 151: Applied Calc
I
Lecture 20
Rate of change
LHopitals rule
Parametric equations
Viacheslav Zhygulin
How do we measure a distance
traveled:
How do we measure a distance
traveled:
How do we measure a distance
traveled:
How do we measure a distance
tra
AMS 151: Applied Calc
I
Lecture 19
Using the derivative: optimization
Viacheslav Zhygulin
CHAPTER 4
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Review:
Using first and second derivative:
Using first and second derivative:
Using first and secon
AMS 151: Applied Calc
I
Lecture 17
Theorems about differentiable functions
Using the derivative
Viacheslav Zhygulin
Theorems about differentiable
functions
Theorems about differentiable
functions
Theorems about differentiable
functions
Theorems about diff
AMS 151: Applied Calc
I
Lecture 16
Local linearization
Theorems about differentiable functions
Hyperbolic functions
Viacheslav Zhygulin
Revision:
Revision:
Revision:
Derivative of logarithm function proves
power rule:
Revision:
Revision:
Implicit function
AMS 151 Applied Calculus I
Sample Questions for Exam 1
In order to receive full credit, please show all work and justify your answers.
1. Answer the following questions:
(a) Find the linear function that passes through the points (-1,0) and (2,6).
(b) Fin
Answers to the Sample Questions for Exam 1
Applied Calculus I
1. (a) Using the points (-1, 0) and (2, 6), we have Slope = (6-0)/(2-(-1) = 2 Now we know that
y = 2x + b. Using the point (-1, 0), we have 0 = 2 + b, which yields b = 2. Thus, the linear
funct