|
|
120121 ESM1C -
Calculus and Matrix Algebra, Fall 2009
|
|
Lectures: Mondays 11:15 am - 12:30 pm, Wednesdays 2:15 pm -
3:30 pm.
Lecture Room: Lecture
Hall Research II.
Instructor: Onur Oktay
Office: Research I, Room
126
Office Hours: By appointment.
Email: 
Teaching Assistants and Tutorial sessions: Click to see participant lists, time and
place for tutorials.
Course Description: The course ESM1C - Calculus and Matrix
Algebra covers the standard topics of pre-calculus (numbers, units,
transformations, inequalities, elementary functions and their properties
and graphs), single variable calculus (sequences and series, limits and
continuity, derivatives and differential calculus, anti-derivatives and
Riemann integral, with selected applications) and a brief introduction to
matrix-vector calculus. Sufficient time is spent on the acquisition of
solid problem solving skills.
ESM1C is an entrance
Mathematics course for students in the School of Engineering and Science
from Life Sciences and Chemistry majors, students from SHSS, as well as
for students with a less rigorous high school preparation in Mathematics
(approval by adviser/major coordinator necessary). It serves as a
prerequisite for later ESM and more advanced Mathematics courses. It can
be complemented by the lab units 110111 NatSciLab Math Symbolic Software
or 110112 NatSciLab Math Numerical Software.
Primary Textbook: [S] "The Chemistry
Maths Book", by Erich Steiner. 2nd edition, Oxford University Press, 2008
(ISBN 9780199205356).
Recommended: [EP] "Calculus", by C.H.
Edwards, D.E. Penney. 6th edition, Prentice Hall, 2002 (ISBN 0130950068).
Course web page: http://www.math.umd.edu/~ooktay/ESM1C/index.html
Syllabus: Syllabus
Course format: ESM1C meets in large lectures, and in
25-student tutorial sessions. Each meeting lasts 75 minutes. Main
material is covered during the lectures. Tutorial sessions are devoted
to solving problems related to the material covered during the lectures.
Homework is assigned regularly and going to be posted
on this webpage (see schedule below). You are expected to do homework
assignments and check answers (answers of the textbook problems are in
the back of the textbook). Homework will be discussed during the
tutorials.
Tutorials: Attendance and
participation will be monitored. You have to come prepared to tutorials.
You are responsible for both the material covered during the lectures
and the announced homework assignments, in the preceding week. Tutorials
are interactive; you might be asked to solve problems on the board. You
may also ask your TAs questions you are stuck with, during the tutorial
sessions. Homework may be collected without prior announcement. Homework
is not graded, but you will receive/lose "participation credits" for
complete/incomplete homework. You are encouraged to work on the problem
sets in cooperation with others, but you must write up the solutions by
yourself.
Quizzes: 10 quizzes are
administered during class time on Mondays every week starting form week
2. They cover the material of the last two classes. Quizzes are composed
of 2-3 short problems, the allocated time to solve them is about 15
minutes.
Exams: A Midterm Exam and a Final
Exam will be administered. Details about the exams will be given in the
review sessions preceding the exams.
Calculators
are not allowed at exams and quizzes.
Grading: The final grade will be computed from four
components: Tutorials 20%, Quizzes 20%, Midterm Exam 20%, Final Exam
40% according to the table below.
| Cutoff score: |
95% |
90% |
85% |
80% |
75% |
70% |
65% |
60% |
55% |
50% |
45% |
40% |
| IUB Points: |
1.0 |
1.33 |
1.67 |
2.0 |
2.33 |
2.67 |
3.0 |
3.33 |
3.67 |
4.0 |
4.33 |
4.67 |
Attendance and absences: You are responsible for the material
covered in class, whether you attend or not. You are also responsible
for the announcements made during class; they may include changes in the
syllabus. Excused absences will be given only
with documentation (e.g., doctor's report). Any student with a
documentation should forward a copy to the Registrar's Office. The
Registrar's Office informs the student's instructors when s/he is
officially excused (i.e., excused by the registrar).
No
make-up quizzes or make-up midterm will be given. Excused
quizzes will not be used in computing the final grade. If you miss the
midterm (and you are officially excused by the registrar), then your
final exam counts %60 of your total grade. Any unexcused quizzes or
exams will be counted as a "0", including the final exam.
Useful resources: Math
Support Center | Visual Calculus
| Interactive Mathematics(www.intmath.com ) | WolframAlpha |
- Tentative Course Outline : We
will cover the Chapters 1-7 and 16-18 of [S]. If
time remains, we will cover parts of the Chapters 11, 19 and 20.
Additional notes will be posted here.
Problem and Sections numbers are from the
textbook. Homework problems, which are not from the
textbook, are suggested but not mandatory. Links under "Visual
aids and Summaries" column is not mandatory to read, but included here
for the students' convenience.
| Date |
Topic |
Reading
|
Visual aids and
Summaries |
Homework
|
| Sep 2 |
Introduction and overview. Numbers, operations, prime
factorization theorem, exponential quantities. |
1.1-1.6 |
|
p.29,#1-25, 32, 34-77 (all short
) |
| Sep 7 |
Complex Numbers. Algebraic functions, factoring algebraic
expressions. Simplifying fractional expressions. |
1.7, 2.1-2.3 |
|Quadratics|
Factorization 1,
2,
3,
4|
|
p.30 #78,79; p.58 #1-6, 9-22. |
| Sep 9 |
Inverse function and its graph. Polynomials. Graphs of linear
and quadratic polynomials. Rational Functions, polynomial
division. Partial fractions. |
2.4-2.8 |
|function
def'n.| vertical
line test| |inverse function 1,
2,
3|
Polynomials 1,
2|
Polynomial
division| Partial
fractions| |
p.59 #23-29, 31, 33-35, 38-41, 44, 47-50, 57-65 |
| Sep 14 - Sep 16 |
Trigonometric and inverse trigonometric functions, their
graphs and properties. Even and odd functions, periodic
functions and their graphs. Compound angle and half angle
identities, and their variations. |
3.1-3.4 |
|trig.
identities| Graph
of sin(x)| translation
property| even&odd functions 1,
2,
3|
|
p.89 #3-5, 9-11, 14-17, 19, 22-24 |
| Sep 21 - Sep 23 |
Polar coordinates. Exponential and logarithmic functions,
their graphs and properties. |
3.5-3.8 |
|Polar coord. 1,
2|
Graphs of exp
and log|
|
p.91 #27-30, 31, 37-40, 42 |
|
Sep 28 - Sep 30 |
Continuity and limit. Differentiation. Rate
of change, and mathematical definition of derivative.
Differentiating powers, exponential, logarithmic and trigonometric
functions. Product rule, quotient rule and chain rule. |
4.1-4.6 |
|Visualization - tangent 1 2 3 |
Numerical
experiment | Definition of derivative 1
2
3 4| Formula
sheet| |
p.122 #1,2; p.123 # 18-21, 23-27, 29-55; HW4a,
HW4b,
HW4c,
HW4d,
HWquiz |
| Oct 5 |
Derivative of the inverse function. Implicit differentiation.
Some applications in real life problems. |
4.7, 4.8, 4.11 |
|Deriv. inverse 1
2
3 |
Deriv.
inverse trig. functions | Implicit diff. 1 2|
Optimization 1
2
3
4 5| |
p.124 #60-71; 84, 85, 87, 88; HW4e1,
HW4e2,
HW4f1,
HW4f2 |
| Oct 7 |
Logarithmic Differentiation. Review. |
|
|
study_problems, HW4g |
| Oct 12 |
No Class (Reading
Day) |
|
|
|
| Oct 14 |
Higher order derivatives. Maximum, minimum and turning
(inflection) points. Sketching graphs of functions.
Horizontal, vertical and oblique asymptotes. |
4.9, 4.10 |
|Maxima/minima 1 2 3|
Graphing 1 2 3|
Graphing-summary| |
p.124 #74-83, HW4h,
HW4k,
HWquiz1,
HWquiz2 |
| Oct 19 |
Integration.
Antiderivative, indefinite integral. Linearity of integral
operation. Definite integral. Riemann sums, graphical
interpretation of the definite integral of a function. Improper
and infinite integrals. |
5.1-5.3 |
Formula
Sheet | Riemann Sums 1 2 3 4 5 6| Indefinite int. 1
2
3|
Definite
int.| Improper int. summary, tutor|
|
p.160 #1-14, 16-23; HW5d |
| Oct 21 |
Methods of Integration: Integrals of rational functions, and
method of partial fractions. |
6.7 |
tutor
|
p.189 #63-71; HW6a1, HW6a2 |
| Oct 26 - Oct 28 |
Methods of Integration: Change of variable. Trigonometric
substitution. Integration by parts. |
6.1-6.6 |
|Substitution summary |
Int. by parts summary,
tutors t1
t2
t3| |
p.187#11-30, 33-38, 40-51; HW6b1,
HW6b2,
HW6c,
HW6d1,
HW6d2 |
| Nov 2 |
Midterm Exam |
|
Millionaire
Calculus |
Sample midterm 1, Sample midterm 2 |
| Nov 4 |
Applications of the integral. Static properties of
matter: Center of mass, first moment and moment of inertia.
Dynamics: distance, velocity, acceleration. Force and Work. |
5.5-5.7; [Strang]
ch 8.5, 8.6 |
|distance, velocity, accelaration 1 2|
Center
of mass| |
p.161 #50-54. |
| Nov 9 - Nov 11 |
Sequences and series. Sequences defined
by a general term and/or a recurrence relation.
Arithmetic, geometric and alternating sequences. Limits of
sequences. Series and partial sums. Convergence tests: comparison
test, ratio test, root test, integral test. McLaurin and Taylor
series. |
7.1-7.6 |
|geometric
series| telescoping series 1
2|alternating
series summary|integral
test 1
2
3,summary s1 s2 |comparison
test summary|
ratio test summary|
Taylor series 1
2
3
4| |
p.221 #6,10,11,14-16, 37-39, 44, 46-51, 54-57, 59, 62,
63, 65, 68-70; HW7b1,
HW7c1,
HW7c2,
HW7c3 |
| Nov 16 - Nov18 |
Vectors and vector algebra. Scalar product,
cross product. Vector valued functions, and their derivatives.
Applications to some simple real-life problems that are formulated
with vectors, and vector valued functions. |
16.1 -16.6 |
|
p.472 #6-12, 14-24, 31-39. |
| Nov 23 - Nov 25 |
Matrices and linear transformations. Matrix
algebra. Inverse matrix. Orthogonal matrices. |
18.1-18.8 |
|
|
| Nov 30 - Dec 2 |
Determinants. Minors and cofactors. Determinants of
triangular matrices. Properties of determinants. |
17.1-17.6 |
|
|
| Dec 7 |
|
|
|
| |