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Math118x

MATH 118x Fundamental Principles of Calculus


Syllabus

Schedule

Solutions

Fun


Syllabus [pdf]

Instructor

Office
KAP 470A
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

Previous Final Exams: The Math Center


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" ;)