SYLLABUS
MATHEMATICAL ANALYSIS-I
MAT 227 ID 2666 MAT 223 ID2925
Spring 2014
1. Lecturers:
Bakyt Urmambetov, Kandidat nauk in Physics and Mathematics, Professor,
[email protected];
Enver Atamanov, Kandidat nauk in Physics and Mathematics, Acting Professor,
[email protected]
Lubov Altynnikova, Kandidat nauk in Physics and Mathematics, Associated Professor,
[email protected]
2. Class meetings: 3 classes per week, 15 working weeks.
3. Office hours: according to the individual schedules of the instructors. Office: 332/1,
phone: 66-15-47.
4. Short course description:
This course will introduce to the basics of Mathematical Analysis, following topics will be
presented. Functions, limit of the functions and basics of differential calculus and its
applications. Derivative: First Derivative Test. Concavity: Second Derivative Test. Relative
Maxima and Relative Minima. Optimization Problems. Functions of two variables. Local
Extremum. Partial Derivatives. Conditional Extremum. Lagrange Multiplier method.
Indefinite and definite integrals.
Integration by substitution. Integration by Parts.
Applications of a Definite Integral. Basics of differential equations.
5. Prerequisites:
MAT 103 or MAT131.
6. Textbooks:
1. Mizrahi A. Sullivan M. Mathematics for business and social sciences.-John
Wiley&Sons.1988.
2. Lial M., Miller C. Finite Mathematics and Calculus with application.-Scott, Foresman
and Company. 1989.
3. Grossman S.I. Calculus of one variable. -Academic Press. Inc.1986.
4. Edwards C.H., Jr. David E. Penney “Calculus and analytic geometry.”
5. Larson R.E., Hosteller R.P. “Brief Calculus with applications”, -D.C. Heath and
Company. 1987.
6. Crass M. S. “Mathematics for Economists.” M. INFRA-M, 1998 .
7. Kremer N. Sh., “Mathematics for Economists”, M.: UNITI, 1998.
8. Crass M.S., Chuprynov B.P. “Bases of Mathematics with its Applications in
Economics”, M.: DELO, 2000
9. Kydyraliev S.K., Urmambetov S.M. “Collection of math and statistics tests. Bishkek,
AUK, 1999.
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7. Objectives:
• to develop abstract and logical (probative) thinking,
• understanding how to set and solve problems,
• acquiring as basic knowledge of mathematical analysis,
• appreciating the value of continued mathematical education for the major.
8. Expected outcomes.
After completing MAT 227 ( MAT 223) the student will be able to
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Formulate and apply the concept of a function to a contextual (real-world) situation.
Demonstrate understanding of the basic concepts of one-variable calculus; the limit of
 0
a function and indeterminate forms: , ,   , 0*  , asymptotes and the concept
 0
of continuity.
Demonstrate understanding of the meaning of derivatives and compute the derivative
of algebraic, exponential and logarithmic functions of one variable.
Use derivatives to solve problems involving rates of change, tangent lines, velocity
(speed), acceleration, optimization, related rates and elasticity of demand.
Investigate the graph of a function with the aid of its first and second derivatives:
asymptotes, continuity, tangency, monotonicity, concavity, extreme, inflection points,
etc.
Demonstrate understanding of the meanings of infinite and definite integrals,
fundamental theorems of calculus.
Evaluate integrals of polynomials, rational functions, exponential, logarithmic and
trigonometric functions.
Use rules of integration to evaluate indefinite and definite integrals.
Use integrals to solve applied problems.
Demonstrate understanding of functions of several variables and their graphs,
compute partial derivatives.
Use partial derivatives to solve optimization problems.
Use least square method.
9. Method of Evaluating Outcomes:
Grading
Tests are graded by a team of faculty from the Mathematics and Natural Sciences Department.
To ensure consistency each team member grades the same question(s) on each test. Students may
appeal the grading of a test question on a designated appeal day (time and room to be
announced). Students may discuss any problem with the faculty member who graded their work
and state the reason for the appeal. Only the grader determines whether any adjustment to the
grade should be made. Students should discuss the appeal with the course instructor who will
then make any necessary adjustment to the record and return the paper to the department office.
Grades will be based on a total of 100 points, coming from:
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Quiz 1
The lecturer sets day
and time
10 points
Midterm
Exam
March 9, 2014
25 points
Quiz 2
The lecturer sets day
and time
10 points
May 4, 2014
35 points
20 points
Final Exam
Home works
Every class
The total grade of the student is as follows:
0  F  40  D  45  C-  50  C 60  C+ 65 B- 70  B  80  B+  85 A-  90  A100.
Make-up Exams and Quizzes
 If the reason for missing the midterm exam is valid, the student’s final exam will be
worth up to 50 points. In this case extra tasks can be included in the final test.
 If the reason for missing the Final Exam is valid, the student can apply for the grade of
“I”.
 If a student misses both exams, he/she will not be attested for the course.
 If the reason for missing any exam or quiz is not valid, then the grade 0 will be given for
the missing exam or quiz.
Attendance Requirements
It is important to attend classes to master the materials in the course. Attendance affects
grades: students lose 1 point for any unexcused absence. Missing 10 or more classes for any
reasons will result in a grade of F in the course.
Academic Honesty
The Mathematics and Natural Sciences Department has zero tolerance policy for cheating.
Students who have questions or concerns about academic honesty should ask their professors or
refer to the University Catalog for more information.
Workbooks
Each student must maintain a math workbook with a clear record of completed homework.
Workbooks will be assessed from time to time. Students should bring their workbooks to
all classes as they are necessary for their class work. Workbooks must be submitted for
assessment immediately upon request of the instructor or full credit for homework may not
be earned. The workbook must contain calculations completed by the student. Photo-copies
of answers will not be accepted nor will answers that have been copied from the back of the
text book or transcribed from the solution manual. We highly recommend working jointly
with your fellow students on homework problems.
Calculators
Students will be advised whether calculators are needed for specific assignments. Graphic
calculators may not be used during quizzes and exams.
Cell phones
We ask students to turn off their cell phones during math classes. Use of cell phones is entirely
prohibited during the exams.
Syllabus change
Instructors reserve the right to change or modify this syllabus as needed; any changes will
be announced in class.
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10. Tentative Academic Calendar:
1-3 weeks
The idea of a limit. Algebraic techniques for evaluating limits. Continuous functions and its
properties, classification of discontinuities. [1]: p.453-475; [2]: p.40-90; [3]: p.55-92, p.
112-136; [4]: p.101-129; [5]: p. 49-75.
4 - 5 weeks
Derivative. Additional interpretations of the derivative. The product and quotient rules.
The Power Rule; The Chain Rule. Implicit Differentiation. Related Rates. Derivative and
Continuity. [1]: p.477-562; [2]: p.92-170; [3]: p.93-111, p. 137-191; [4]: p.131-220; [5]: p.
81-102.
6-7 weeks
First Derivative Test. Concavity; Second Derivative Test. Relative Maxima and Relative
Minima. Optimization Problems. [1]: p.564-624; [2]: p.172-240; [3]: p.192-264; [4]: p.222315; [5]: p.103-133.
Week 8. Preparation for the Midterm test.
Week 9 Spring break
10-11 weeks
Functions of two variables, Local Extremum. Extremum Conditions. Partial Derivatives.
[1]: p.661-681; [2]: p.748-784; [4]: p.553-602; [5]: p.230-300.
Problems on Conditional Extremum. Lagrange Multipliers. [1]: p.681-691; [2]: p.809-818;
[4]: p.604-613; [5]: p.310-315.
12-16 weeks
Indefinite Integral and its Properties. ”Table” Integrals. Integration by Substitution.
Integration by Parts. [1]: p.693-761; [3]: p.268-277; [4]: p.317-337; [5]: p.134-154.
Definite Integral and its Applications. Area under a Graph. Newton-Leibniz Formula.
Applications of a Definite Integral in Economics. [1]: p.721-761; [2]: p.242-358; [3]:
p.280-348; [4]: p.338-376, p. 428-491; [5]: p.155-203.
Preparation for the final exam.
Out-of class assignments:
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Least square method [1]: p.102-108
Exponential and log. functions [1]: p.626-659
L”Hopital’ Rule.
Dif. equations [1]: p.711-719, [2]: p.951-1000, [4]: p.518-551, [5]: p.388-427.
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