MATH
118x Fundamental Principles of Calculus
Syllabus
[pdf]
Instructor |
|
Office |
|
Email |
kzuev@usc.edu (please
include “118” in the subject line) |
Office
Hours |
MWF
1:30-3:30 pm or by appointment |
Section |
39435 |
39443 |
Lectures |
MWF
11:00-11:50 in THH 116 |
MWF
12:00-12:50 in ZHS 352 |
Discussions |
Tue,
Thu in GFS 202 |
Tue,
Thu in KAP 141 |
Teaching Assistant |
Spencer
Gerhardt, sgerhard@usc.edu |
Zhengkan
Wang, zhengkaw@usc.edu |
Coure
Description
The
main goal of this course is to give an introduction to the fundamental
principles, methods, and concepts of Calculus: Functions, Graphs,
Limits, Derivatives, Integrals, and Calculus of several variables.
|
Prerequisites
MATH
117 Introduction to Mathematics for Business and Economics |
Textbooks
1.
Required: L.D. Hoffman and G.L. Bradley, Calculus for Business,
Economics, and the Social and Life Sciences, Brief 11th ed.,
McGraw-Hill, New York, 2013.
2. Recommended: Student’s Solution Manual |
Course
Plan
The
following is a tentative outline of the material to be covered
this term.
Sections |
Topic |
Lectures |
§
1.1 – 1.6 |
Functions,
Graphs, and Limits |
1-5 |
§
2.1 – 2.6 |
Differentiation:
Basic Techniques |
6-11 |
§ 3.1,
3.2, 3.4, 3.5 |
Additional
Applications of the Derivative |
12-19 |
§ 4.1
– 4.4 |
Exponential
and Logarithmic Functions |
20-23 |
§ 5.1
– 5.4 |
Integration |
24-29 |
§ 6.1 |
Integration
(by Parts) |
30-31 |
§ 7.1
– 7.3, 7.6 |
Calculus
of Several Variables |
32-40 |
|
Grading
Quizzes |
15% |
Midterm I |
25% |
Midterm II |
25% |
Final |
35% |
|
Homework
Suggested
homework problems will be posted here
after each lecture. These problems will be assigned but not
collected.
|
Quizzes
A
quiz will be given each week on Tuesday, except for the first
week of class, and for the two weeks when midterms are held.
The quiz problems will be similar to homework problems assigned
in the previous week. For example, the quiz problems on Sept
4 will be similar to homework problems assigned on Aug 27, 29,
and 31. The two lowest quiz grades will be dropped in the final
grade calculations. All quizzes will be closed-book and no calculators
are allowed or needed. |
Midterm
Exams
There
will be two midterm exams: Wednesday, October 10 (exam 1) and
Monday, November 5 (exam 2). The time and place will be announced
later. Both exams will be closed-book. No calculators are allowed
or needed. |
Final
Exam
The
final exam is comprehensive and will be held at the time specified
in the
University Schedule of Classes: Wednesday, December 19,
2-4pm, location to be announced. The final exam will be closed-book
and no calculators are allowed or needed. |
Important
Dates
Homework |
Weekly
on Mondays, Wednesdays, and Fridays |
Quizzes |
Sep
4, 11, 18, 25, Oct 2, 16, 23, 30, Nov 13, 20, 29, Dec
4 |
Midterm
I |
Wednesday,
October 10 |
Midterm
II |
Monday,
November 5 |
Final |
Wednesday,
December 19, 2-4pm, THH 101 |
Expectations
Official
announcements, homework assignments, quizzes and midterms
solutions will be posted on the course website. You
are expected to check the course website on a regular
basis. You are encouraged to read the appropriate sections
of the textbook in advance and discuss the homework
assignments with other students. |
Behavior
Behavior
that persistently or grossly interferes with classroom
activities is considered disruptive behavior and may
be subject to disciplinary action. Such behavior inhibits
other students’ ability to learn and an instructor’s
ability to teach. A student responsible for disruptive
behavior may be required to leave class pending discussion
and resolution of the problem and may be reported to
the Office
of Student Judicial Affairs for disciplinary action.
In particular, the use of cell phones during class or
conversation is disruptive behavior. |
Academic Integrity
All
students are responsible for maintaining standards of
academic integrity. In particular, collaboration, use
of notes, or any electronic devices during quizzes,
midterms or the final are strictly prohibited. |
Useful
Links
|
Schedule
Date |
Lecture |
Topic |
Homework |
August
27 |
1 |
Intro;
Calculus: A Big Picture; Functions |
Sec.1.1:
#7,17,23 |
August
29 |
2 |
Operations
with Functions; Graphs; Intercepts |
Sec.1.1:
#25
Sec.1.2: #21,31 |
August
31 |
3 |
Basic
Types of Functions; Linear Functions |
Sec.1.3:
#17,23,33 |
September
3 |
N/A |
Labor
Day |
N/A |
September
5 |
4 |
Limits:
Definition and Properties; Limits of Polynomials and Rational
Functions |
Sec.1.5:
#11,19,25 |
September
7 |
5 |
Limits
at infinity; Infinite limits; One-sided limits; Continuous functions |
Sec.1.5:
#33
Sec.1.6: #15,37 |
September
10 |
6 |
The
Derivative: Definition; Geometric meaning; Differentiability
and Continuity |
Sec.2.1:
#5,21,35 |
September
12 |
7 |
Techniques
of Differentiation I; Relative Rate of Change; Rectilinear Motion |
Sec.2.2:
#17,33,49 |
September
14 |
8 |
Techniques
of Differentiation II; Higher-oder derivatives |
Sec.2.3:
#13,27(29),47 |
September
17 |
9 |
Techniques
of Differentiation III: The Chain Rule |
Sec.2.4:
#17,35,41(45) |
September
19 |
10 |
Approximation
by increments; Differentials |
Sec.
2.5: #7,15(17),21(25) |
September
21 |
11 |
Implicit
Differentiation |
Sec.
2.6: #5,19,29 |
September
24 |
12 |
Increasign
and Decreasing Functions |
Sec.
3.1: #5-8,15,21 |
September
26 |
13 |
Relative
Extrema; Critical Numbers; The First Derivative Test for Relative
Extrema |
Sec.
3.1: #23,41,47 |
September
28 |
14 |
Concavity;
Second derivative procedure for determining intervals of concavity |
Sec.
3.2: #3,11,23 |
October
1 |
15 |
Inflection
points; The Second Derivative Test for Relative Extrema |
Sec.
3.2: #29,39,47 |
October
3 |
16 |
Graph
Sketching: A General Procedure and Examples |
Sec.
3.3: #23,29,31 |
October
5 |
17 |
Optimization
I: Procedure for finding the Absolute Extrema on a Closed Interval |
Sec.
3.4: #5,7,9 |
October
8 |
18 |
Optimization
II: Finding the Absolute Extrema on different intervals |
Sec.
3.4: #11,13,15 |
October
10 |
N/A |
Midterm
1 |
N/A |
October
12 |
19 |
Applied
Optimization |
Sec.
3.5: #1,9(15),13(7) |
October
15 |
20 |
Exponential
functions; Logarithmic functions |
Sec.
4.1: #27
Sec. 4.2: #23,39 |
October
17 |
21 |
Differentiation
of Exponential functions |
Sec.
4.3: #35,41,49 |
October
19 |
22 |
Differentiation
of Logarithmic functions; Logarithmic differentiation |
Sec.
4.3: #19,45,51,61,63 |
October
22 |
23 |
Exponential
Models: Exponential Growth and Decay, Learning Curves, Logistic
Curves |
Sec.
4.4: #25(31),39(23),67(27) |
October
24 |
24 |
Antidifferentiation:
The Indefinite Integral |
Sec.
5.1: #7,19,27 |
October
26 |
25 |
Integration
by Substitution |
Sec.
5.2: #11,13,23,27,29 |
October
29 |
26 |
The
Definite Integral |
Review
Lectures 17-25 |
October
31 |
27 |
The
Fundamental Theorem of Calculus |
Sec.
5.3: #41(27),49(37),55(43) |
November
2 |
28 |
Area
Between Curves |
Sec.
5.4: #3,7,13 |
November
5 |
N/A |
Midterm
2 |
N/A |
November
7 |
29 |
Average
Value of a Function |
Sec.
5.4: #19,21,23 |
November
9 |
30 |
Integration
by Parts |
Sec.
6.1: #1,5,11,23,25 |
November
12 |
31 |
Definite
Integration by Parts; Table Integrals |
Sec.
6.1: #15,19,29,31,33 |
November
14 |
32 |
Functions
of Several Variables |
Sec.
7.1: #15,21,31 |
November
16 |
33 |
Partial
Derivatives-I: Definition and Computation |
Sec.
7.2: #13,25,31 |
November
19 |
34 |
Partial
Derivatives-II: The Chain Rule |
Sec.
7.2: #37(67),75(43),85(81) |
November
21 |
N/A |
Thanksgiving |
N/A |
November
23 |
N/A |
Thanksgiving |
N/A |
November
26 |
35 |
Optimizing
functions of two variables-I: Relatime Extrema and Critical
Points |
Sec.
7.3: #3,7,21 |
November
28 |
36 |
Optimizing
functions of two variables-II: The Second Partials Test |
Sec.
7.3: #1,9,13 |
November
30 |
37 |
Double
Integrals over Rectangular Regions I |
Sec.
7.6: #3,5,9 |
December
3 |
38 |
Double
Integrals over Rectangular Regions II |
Sec.
7.6: #7,15,73 |
December
5 |
39 |
Review
I |
N/A |
December
7 |
40 |
Review
II |
N/A |
December
19 |
N/A |
Final
Exam |
N/A |
Solutions
Sep
4: Quiz 1 [pdf], average score = 8.59/10
Sep
11: Quiz 2 [pdf], average score = 6.76/10
Sept
18: Quiz 3 [pdf], average score = 7.15/10
Sept
25: Quiz 4 [pdf], average score = 6.61/10
Oct
2: Quiz 5 [pdf], average score = 6.20/10
Oct
10: Midterm 1 [pdf], average score =
70/100
Oct
16: Quiz 6 [pdf], average score = 7.87/10
Oct
23: Quiz 7 [pdf], average score = 5.96/10
Oct
30: Quiz 8 [pdf], average score = 5.42/10
Nov
5: Midterm 2 [pdf], average score = 71.3/100
Nov
13: Quiz 9 [pdf], average score = 7/10
Nov
20: Quiz 10 [pdf], average score = 4.65/10
Nov
29: Quiz 11 [pdf], average score = 6.21/10
Dec
4: Quiz 12 [pdf], average score = 1.25/10
Fun
25
divided by 5 equals 14: "I am a pretty good mathematician"
;)
|