Fall Term, 2009-2010
MTH 168-P1: Calculus and Analytic Geometry I
MTH 129-05: Calculus for Business
MTH 430: Real Analysis
Office Hours:
M W F 11:00 - 11:40, T Th TBA,
and by Appointment.
MTH 168: ANALYTIC GEOMETRY AND CALCULUS I.
T.A. : Nasrin Sultana
Office(SC 319) hours: T Th 10:30 - 11:30, W
11:40 - 12:40
Text: Calculus James Stewart 6th Edition
Catalogue Description: Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to science and engineering. Prerequisite: MTH 116 or equivalent.
I. Course Goal: This is the first course in the three course calculus sequence, MTH 168, MTH 169, MTH 218; it is intended for mathematics, mathematics in secondary education, physical science and engineering majors. This course is an introduction to the concepts of single variable calculus. It is designed to help the student develop knowledge in the areas of differential and integral calculus of functions of a single variable, including polynomial, trigonometric, exponential, logarithmic and other transcendental functions, and to help the student develop analytic, computational, and problem solving skills.
II. Course Objectives:
Objective 1. The student will demonstrate, in writing, knowledge of factual content in traditional subject areas of analytic geometry, limits, differentiation and its applications, and integration of a function of one variable.
Strategy 1. The instructor will demonstrate to the student the development of traditional problem solving algorithms in single variable calculus, and require the student to develop analogous algorithms.
Strategy 2. The instructor will demonstrate the application of traditional problem solving algorithms to the student and require the student to successfully employ traditional problem solving algorithms.
Objective 2. The student will further develop skills related to problem solving and critical thinking.
Strategy. The instructor will require that the student successfully pose or model a problem correctly, select appropriate problem solving algorithms to solve a well posed problem, and present results to peers or teachers in written or verbal form.
Objective 3. The student will further develop skills related to problem solving and technology.
Strategy. The instructor will require that the student write code successfully to implement a problem solving algorithm on a personal computer or calculator.
Objective 4. The student will further appreciate (attitude) mathematics, the language of science.
Strategy I. The instructor will communicate in precise and logically correct terms, and require the student to communicate in precise and logically correct terns.
Strategy 2. The instructor will develop and employ efficient problem solving algorithms.
Objective 5. The student will further appreciate (attitude) the impact of the computer in the usage and teaching of mathematics.
Strategy .The instructor will require that the student employ computer graphics to better understand and further explore the relationship between geometry and analysis in single variable calculus.
Objective 6. The student will further appreciate (value) applications of mathematics to solve real world problems.
Strategy. The instructor will stress where theory is meaningful in applications.
llI. Course Topics:
Limit of a function at a point and at infinity, infinite limits.
Continuity of a function at a point and on an interval, one-sided limits.
The definition of the derivative as a limit.
The derivative and the tangent line problem, basic differentiation rules, rates of change.
The product rule, quotient rule and chain rule, higher-order derivatives and implicit differentiation.
Related rates, extrema on an interval, curve sketching along with the relationship between the sign of the first derivative and increasing and decreasing functions, and concavity and the second derivative, optimization.
Rolle’s theorem and the mean value theorem for derivatives.
Newton’s method for estimating the roots of a function.
Differentials and approximations.
Antiderivatives and indefinite integration.
Area, Riemann sums and the definite integral as a limit.
The Fundamental Theorem of Calculus.
Integration by substitution.
Numerical integration.
Study of the natural and general exponential and logarithmic functions, including definitions, differentiation and integration, and applications.
Definition of inverse trigonometric functions and their derivatives.
Introduction to hyperbolic functions.
IV. Instructional Procedures: The objectives are accomplished through lectures, problem sessions, computer laboratories and private consultation.
V. Student Evaluation Criteria:
The student's written communication is evaluated in three ways. These are: monthly examinations covering major sections or chapters, a one time cumulative final examination and a set of homework problems to be solved employing MAPLE, a computer software. Problems range from theoretical to applied word problems.
Course Content: (Calculus by Stewart 5th Edition)
Chapter 2 - Limits and Rates of Change (2.2-2.5).
Chapter 3 - Derivatives (3.1-3.6,3.8-3.9).
Chapter 4 - Applications of Differentiation: (4.1-4.9).
Chapter 5 - Integrals: (5.1-5.5).
Chapter 7 - Inverse Functions: exponential, logarithmic, and inverse trigonometric
functions (7.1, 7.2*-7.4*, 7.5-7.7).
Format: Lectures on Mondays, Wednesdays, and Fridays; problem
sessions on Tuesdays and Thursdays. MAPLE, a computer algebra system,
will be used in the course.
Tests and Final Exam: There will be four tests and a comprehensive final. All tests including the final are in-class, and closed-book. All tests weigh equally (15% each). The tests will be given on Tuesdays or Thursdays. Tentative dates for the tests are: Tue Sept 15, Tue Oct 6, Tue Nov 3, Th Dec 3.
Important: No make-up will be given for missing tests unless you have very strong reason. If you must ask for a make-up you need to contact me before the test is given. In any case, a make-up test will be more difficult than the original test.
Final Exam:
TBA
Calculator Policy: Students are allowed to use scientific calculators with numerical packages in the tests and in the final exam. Calculators with symbolic packages (such as TI-89 or TI-92) are not allowed in the tests and in the Final.
Grading Scheme: Grade will be based on
Four Tests (60%)
HW with MAPLE assignments (15%)
Final (comprehensive)(25%)
Here is the list of Practice Homework problems. These problems are for your practice only; they will not be collected for grade. Your T.A. will be conducting problem sessions on Tuesdays and Thursdays, and she will be helping me grade the tests.
Practice Homework Problems:
Section
2.2: 4 - 10, 12, 13, 15, 21, 25
2.3: 1,2,4,7,9,10,11,13,15,17,21,25,37,45,47,49,61
2.4: 15 - 20 (all)
2.5: 3, 4, 5, 7, 9, 10, 15, 16, 18, 19, 20, 41, 47, 63
3.2: 1,3,5,7,11,17-21,26,33-36,49.
3.3: 1 - 41 (all), 49, 50.
3.4: 1 - 20 (all), 39, 40.
3.5: 1 - 53 (odd), 88.
Test 1 (Tue Sept 15) Sec 2.2-2.5, Sec3.2 - 3.5
3.6: 5-20 (all), 25, 26
3.8: Examples 1 -4, Ex. 1-9, 11, 13, 17, 23.
3.9: 1-5, 11-22, 31 - 33.
4.1: 3-6, 15-27 (odd), 29-41 (odd), 45-55(odd).
4.2: 1-5, 11-15, 29
4.3: 9-13,15,16,18,20-24,29,31,32,35,39
Test 2 (Tue Oct 6) Secs 3.6, 3.8-3.9, 4.1 - 4.3
4.4: Review Examples 3-7. Ex. 9-29(odd), 33,35,40,43,45,
51-54(all).
4.7: Examples 1,2,3,5. Ex. 1-9 (odd),
13,17,19, 23,26.
4.9: 1 - 39 (odd), 51 - 56 (all).
5.1 and 5.2: Materials covered in class
and exercise problems assigned there
5.3: 7-35 (odd), 37, 38, 47 - 50 (all).
5.4: 5,9,11,12,13,15,16,19,23,25,28,33,35,42
5.5: 1-6, 7-33(odd), 32, 35-47(odd).
Test 3 (Tue Nov 3) Secs 4.4 - 5.5
7.1: 1-19, 23-25
7.2* 1-12, 15-35(odd),63-72(all).
7.3*: 1-11(odd),17,18,19,27-32,33-51
(odd),75-84,92.
7.4*: 11,12,21,22,23,25-43,45-51.
7.6: 1(a) -3(a), 5-7, 22-35, 38, 59 - 70.
7.7: 30,31,32,33,35,38,57-61(all).
The information provided here is subject to change, modification, or revision.
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MTH 129: Calculus for Business
Text: Applied Mathematics for the Managerial, Life, and Social
Sciences (4th Edition)
Author:
S. T. Tan
Math 129 Calculus for Business
Departmental Syllabus
Text: Applied Mathematics for the Managerial, Life, and Social Sciences, S.T. Tan, 4th edition. 9780495015819
Course Description: A study of the basic fundamentals of differential and integral calculus and their applications to graphing and optimization problems related to business and economics. Multivariable calculus and partial derivatives are used in optimization problems.
Prerequisite: Math 128 or sufficient preparatory mathematics
Syllabus for Math 129 Calculus for Business
I. Limits and Continuity
-evaluate limits of functions as x approaches c and as x approaches infinity
-use the definition of continuity in studying functions
II. Differentiation
-evaluate elementary derivatives using the definition of the derivative
-use the basic rules in finding the derivative of functions
-use of the product and quotient rule
-find higher order derivatives
-use of the chain rule in the differentiation of composite functions
-differentiate logarithmic and exponential functions
-evaluate marginal functions with applications in business and economics
III. Applications of the Derivative
-use the derivative to determine critical points and the direction of the function
-use the second derivative to determine the concavity
-use the first and second derivative to determine the maximum, minimum and points of inflection
-use the derivatives to do curve sketching
-find relative and absolute extrema in problems relative to business and
economics
IV. Antiderivatives
-know the basic rules of integration for algebraic and exponential functions
-solve applied problems using integration
-integrate using u and du substitution
-know the Fundamental Theorem of Calculus and how to apply it
-evaluate definite integrals relative to business, economics, and social sciences
-use integration to find the average value of a function
-use integration to find areas below or between curves
-use integration to find consumer and producer surplus and other problems related to business and economics
V. Multivariable Calculus
-evaluate multivariable functions
-compute first and second partial derivatives
-find critical points and identify as maximum, minimum, or saddle points
-optimize multivariable problems related to business and economics
Course Content:
Chapter 9 - All Sections
Chapter 10 - All Sections
Chapter 11 - All Sections
Chapter 12 - All Sections
Format: Lecture 4:30 - 5:15
Quiz or Problem Session 5:20 - 5:45
Grading Scheme:
Four Tests: 400 points (100 points for each test)
Four Quizzes: 100 points (25 points for each quiz)
A Comprehensive Final: 200 points
Tentative Dates for Tests and Quizzes:
Tests: Sept 14, Oct 7, Nov 9, Dec 2
Quizzes: Sept 2, Sept 28, Oct 21, Nov 23
Final Exam:
Dec 14 4:30 - 6:20
Important: No make-up will be given for missing quizzes.
For tests, a make-up can be given if you have very strong reason. If you must ask for a make-up you need to contact me before the test is given. In any case, a make-up test will be more difficult than the original test.
Calculator Policy: Students are allowed to use scientific calculators with numerical packages in the tests and in the final exam. Calculators with symbolic packages (such as TI-89 or TI-92) are not allowed in the tests, quizzes, and in the Final.
Here is the list of Practice Homework problems. These problems are for your practice only; they will not be collected for grade.
Practice Homework Problems:
Sec 9.1: 1-8(all), 9-61(odd), 73-79(odd)
Sec 9.2: 1-19(all), 23,25,29,37, 39-43(all), 45,47,49,53,57, 77-80(all)
Sec 9.3: 9 - 27 (odd), 34, 35, 36.
Sec 9.4: 1-23 (odd), 24, 25, 27, 29, 35, 36, 41 - 44 (all)
Sec 9.5: 1-27 (odd), 35, 36, 39, 41
Test 1 (Monday, Sept 14) Sec 9.1 - Sec 9.5
Sec 9.6: 1 - 47 (odd)
Sec 9.7: 1-67 (odd)
Sec 9.8: Self - Check Problem, 13 - 17
Sec 10.1: Self - Check Problem, 1-8, 11-23 (odd), 35, 39 - 45, 51 - 65
(odd), 76
Test 2 (Wed., Oct 7) Sec 9.6 - 9.8, 10.1
Sec 10.2: Self - Check Problems, 1 - 13, 17 - 19,
23,25,27,31,39,47,49,51,57,61,63,65,69,71,85,89,95.
Sec 10.4: Self-Check Problems, 1-8 (all), 9-21(odd), 33, 35, 39, 44, 45,
49
Sec 10.5: Self-Check Problems. Examples. Ex. 1 - 5, 7, 17, 18,
20, 27.
Sec 11.1: Self-Check Problems, Examples., Ex. 9-49 (odd), 51-58
(all), 63, 68,68,69,71
Test 3 (Wed Nov 4) Sec 10.2, 10.4, 10.5, 11.1
Sec 11.2; Self Check Problems, Examples, Ex 1-11(odd), 17, 19, 23, 27,
29, 35, 37, 39, 45, 55, 57, 59.
The information provided here is subject to change, modification, or revision.
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Summer 2009
MTH 169/149
Text: Calculus by James Stewart - 6th Edition.
Tests and Final Exam:
There will be four tests. All tests are in-class, and
closed-book. Tentative dates for the tests are: May 20 (Wed), May 29
(Fri), June 9 (Tue), and June 19.
Grading Scheme: Grade will be based on
Three Tests (360 points; 120 points for each test)
Test 4 (140 points)
Course Content:
Chapter 6: 6.1 - 6.3
Chapter 7: 7.8
Chapter 8: 8.1 - 8.4, 8.7, 8.8
Chapter 9: 9.1 - 9.2
Chapter11: 11.1-11.5
Chapter12: 12.1 - 12.6, 12.8 - 12.10
Homework: These homework problems are for your practice only; they will not be collected or graded.
Sec 6.1 : Examples 1,2,5,6
Ex. 1 - 8, 11, 13, 17, 21, 23.
Sec 6.2: Examples 1 - 8,
Ex. 1, 3, 5, 7, 9, 11, 15.
Sec 6.3: Examples 1 - 4,
Ex. 3 - 5, 9 - 12, 15, 17, 21.
Sec 7.8: All Examples.
Ex. 5, 6, 9, 11, 15, 16, 17, 21, 37, 39, 47, 49, 53, 55, 59.
Sec 8.1: All Examples.
Ex. 1 - 7, 9, 10, 11, 15, 22, 23
Sec 8.2: Notes given in class
Test 1 (May 20, Wed) Covers Sections 6.1 - 6.3, 7.8, 8.1 - 8.2
Sec 8.3: Examples 1, 3, 4, 5, 6.
Ex. 1 - 7, 9, 11, 12, 13.
Sec 8.4: All Examples.
Ex. 1-6, 7, 9, 11, 15, 19, 39, 41, 49, 50
Sec 8.7: Materials covered in class
Sec 8.8: All Examples.
Ex. 1, 2, 5, 6, 7, 9, 11, 13, 14, 21, 25, 27, 31, 49, 50.
Sec 9.1: Examples 1, 3
Ex. 1, 3, 5, 7, 12
Sec 9.2: Examples 1, 2
Ex. 1, 3, 5, 7
Test 2 Covers 8.3 - 9.2
Sec 11.1: Examples 1, 2, 3, 7
Ex. 1, 5, 7, 11, 15, 16
Sec 11.2: Examples 1, 2, 3, 4, 6
Ex.1,3,5,7,11,13,37,39,41,57,60,61.
Sec 11.3: Examples 1 - 9 (all)
Ex. 1-15(all), 22, 29, 31-33(all), 35-39(all), 57-59(all), 63.
Sec 11.4: All Examples.
EX. 1,3,5-10(all), 13,17,19,23,24,29,30,45,46,48
Sec 11.5: All Examples.
Ex. 1-6, 11-15, 19-23, 25-30.
Sec 12.1:Examples 1-6.
Ex. 17 - 30
(all), 36, 37, 39, 41, 43
Test 3 Covers 11.1 - 12.1
Sec 12.2: All Examples
Ex.
1-3, 9-33(odd), 41-43
Sec 12.3: All Examples.
Ex. 3-7 (all), 9-13 (all), 15, 16, 17-23 (odd).
Sec 12.4: All Examples,
Ex. 1-4
(all), 17-21 (all), 25, 27, 28
Sec 12.5: All Examples,
Ex. 2, 3, 5,
7, 9, 11-19 (all), 27, 28, 29, 30
Sec 12.6: All Examples,
Ex.
2,3,4,5,8,9,10,11,17,18,21,22,23,25
Sec 12.8: Examples 1,2,4,5
Ex.
1,2,3,4,5,7,9,15,17,19
Sec 12.9: Examples 1,2,3,5,6,7,8
Ex. 3-7
(all), 11,13(a),14(a) (b),15
Sec 12.10: Examples 1,2,4-7
Ex. 5-10,
13-18
Test 4 Covers 12.1 - 12.10
The information provided here is subject to change, modification, or revision.
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Summer 2009
MTH 551: Methods of Math Phys
Text: Methods of Applied Mathematics -
Francis Hildebrand
Dover Publications, Inc.
Course Content:
Chapter One: 1.1 - 1.19, 1.25, 1.26,
1.28, 1.29
Chapter Three: 3.1 - 3.3, 3.6 - 3.9
Chapter Two: 2.1 - 2.7
Grading Scheme:
Two Tests (Mid-Term, Final):
50%
HW Problems:
50%
The information provided here is subject to change, modification, or revision.
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Winter Term 2008-2009
Office Hours: W 12:30 - 1:30, and by appointment
MTH 169-p2: Calculus and Analytic Geometry II
MTH 169-03: Calculus and Analytic Geometry II
MTH 310-01: Linear Algebra & Matrices
MTH 169
Text: Calculus by James Stewart - 6th Edition.
T.A. Qian
Li
Office: SC 319
Office Hours: M W 1:30 - 2:30, and T 3:00 -
4:30
Tests and Final Exam:
There will be four tests and a
comprehensive final. All tests including the final are in-class, and
closed-book. Tentative dates for the tests are: Jan 22 (Th), Feb 17
(T), Mar 17 (T), Apr 16 (Th).
Final Exam.:
MTH 169-p2: Apr 27
(Mon) 10:10 - 12:00
MTH 169-03: Apr 27
(Mon) 12:20 - 2:10
There will be a selected set of homework problems that will be collected and graded. You will work on these problems employing Maple software.
Grading Scheme: Grade will be based on
Four Tests (60%)
HW / MAPLE assignments (15%)
Final (comprehensive)(25%)
Course Content:
Chapter 6: 6.1 - 6.3
Chapter 7: 7.8
Chapter 8: 8.1 - 8.4, 8.7, 8.8
Chapter 9: 9.1 - 9.2
Chapter11: 11.1-11.5
Chapter12: 12.1 - 12.6, 12.8 - 12.10
Homework: These homework problems are for your practice only; they will not be collected or graded.
Sec 6.1 : Examples 1,2,5,6
Ex. 1 - 8, 11, 13, 17, 21, 23.
Sec 6.2: Examples 1 - 8,
Ex. 1, 3, 5, 7, 9, 11, 15.
Sec 6.3: Examples 1 - 4,
Ex. 3 - 5, 9 - 12, 15, 17, 21.
Sec 7.8: All Examples.
Ex. 5, 6, 9, 11, 15, 16, 17, 21, 37, 39, 47, 49, 53, 55, 59.
Sec 8.1: All Examples.
Ex. 1 - 7, 9, 10, 11, 15, 22, 23
Test 1: Sec 6.1 - 8.1
Sec 8.2: Notes given in class
Sec 8.3: Examples 1, 3, 4, 5, 6.
Ex. 1 - 7, 9, 11, 12, 13.
Sec 8.4: All Examples.
Ex. 1-6, 7, 9, 11, 15, 19, 39, 41, 49, 50
Sec 8.7: Materials covered in class
Sec 8.8: All Examples.
Ex. 1, 2, 5, 6, 7, 9, 11, 13, 14, 21, 25, 27, 31, 49, 50.
Sec 9.1: Examples 1, 3
Ex. 1, 3, 5, 7, 12
Sec 9.2: Examples 1, 2
Ex. 1, 3, 5, 7
Sec 11.1: Examples 1, 2, 3, 7
Ex. 1, 5, 7, 11, 15, 16
Sec 11.2: Examples 1, 2, 3, 4, 6
Ex.1,3,5,7,11,13,37,39,41,57,60,61.
Test 2: Sec 8.2 - 11.2
Sec 11.3: Examples 1 - 9 (all)
Ex. 1-15(all), 22, 29, 31-33(all), 35-39(all), 57-59(all), 63.
Sec 11.4: All Examples.
EX. 1,3,5-10(all), 13,17,19,23,24,29,30,45,46,48
Sec 11.5: All Examples.
Ex. 1-6, 11-15, 19-23, 25-30.
Sec 12.1:Examples 1-6.
Ex. 17 - 30
(all), 36, 37, 39, 41, 43
Sec 12.2: All Examples
Ex.
1-3, 9-33(odd), 41-43
Sec 12.3: All Examples.
Ex. 3-7 (all), 9-13 (all), 15, 16, 17-23 (odd).
Test 3: Sec 11.3 - 11.5, 12.1 - 12.3
Sec 12.4: All Examples,
Ex. 1-4
(all), 17-21 (all), 25, 27, 28
Sec 12.5: All Examples,
Ex. 2, 3, 5,
7, 9, 11-19 (all), 27, 28, 29, 30
Sec 12.6: All Examples,
Ex.
2,3,4,5,8,9,10,11,17,18,21,22,23,25
Sec 12.8: Examples 1,2,4,5
Ex.
1,2,3,4,5,7,9,15,17,19
Sec 12.9: Examples 1,2,3,5,6,7,8
Ex. 3-7
(all), 11,13,14,15,23,24, 27, 28
The information provided here is subject to change, modification, or revision.
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MTH 310-01: Linear Algebra & Matrices
Text: Linear Algebra and Its Applications (Third Edition) -- David C. Lay
Course Contents:
Chapter 1: 1.1 - 1.9
Chapter 2: 2.1 - 2.3, 2.8 - 2.9
Chapter 3: 3.1 - 3.3
Chapter 4: 4.1 - 4.6
Chapter 5: 5.1 - 5.3
Chapter 6: 6.1 - 6.4
Chapter 7: 7.1 - 7.2 (7.3, 7.4 if time permits)
Grading Scheme:
Two Tests (Mid-Term, Final):
50%
HW Problems and Projects:
50%
Final Exam:
Friday, May 1, 12:20 - 2:10.
The information provided here is subject to change, modification, or
revision.
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Fall Term, 2008-2009
MTH 218-02: Calculus and Analytic Geometry III
MTH 218-02: Calculus and Analytic Geometry III
MTH 330-01: Intermediate Analysis
Office Hours:
M W F 2:00-2:50, T Th
4 - 5
and by Appointment.
T.A. : Lu Le Peh
Office(SC 319) hours: M W : 11 - noon, 2 - 4
T Th: 2 - 4
F: 11 - 1
Text: Calculus James Stewart 6th Edition
Course Content: (Calculus by Stewart 6th Edition)
Chapter 13 - All sections.
Chapter 14 - Sections 1 - 3.
Chapter 15 - All sections.
Chapter 16 - All sections (from 16.5 density and mass only).
Chapter 17 - All sections.
Tests and Final Exam: There will be three tests and a comprehensive final. All tests including the final are in-class, and closed-book. All tests weigh equally (120 points each). Final will have 140 points. Tests will be given on Tuesdays or Thursdays. Tentative dates for the tests are: Tue Sept 9, Tue Oct 14, Th Nov 20.
Final Exam:
MTH 218-02 Sat. Dec 13
10:10 - 12:00
MTH 218-03 Mon Dec 15
2:30 - 4:20
Calculator Policy: Students are allowed to use scientific calculators with numerical packages in the tests and in the final exam. Calculators with symbolic packages are not allowed in the tests and in the Final.
Policy on Make-Up Tests: Let me know as soon as you know that you will not be able to take the scheduled test. Depending on the reasons, a make-up test can be given. Warning. A make-up test will be more difficult than the original scheduled test!
Here is the list of Practice Homework problems. These problems are for your practice only; they will not be collected for grade. Your T.A. will be conducting problem sessions on Tuesdays and Thursdays, and she will be helping me grade the tests.
Practice Homework Problems:
Section
13.1: 5 - 7, 11, 15, 16
13.2: 1, 3, 5, 6, 15, 17, 19, 23
13.3: 2, 5, 7, 9, 11, 13, 23, 27, 29, 31, 37, 39
13.4: 1 - 9 (odd), 19, 20, 33 - 37 (odd)
13.5: 2,3,7,9,11,13,15,19,20,23,24,25,27,31,49-53,55,57,69,71,72
13.6: Review all Examples. 3-5, 11,12,14-16,19, 29.31,33
Test 1 (Tue Sept 9) covers 13.1 - 13.6
14.1: 1,3,5,7,9,15,17
14.2: 9,11,13,15,23,25,33,35,37
14.3: 1,3,5,17,18,21-24
15.1: Find domains of the functions in 6 - 13 (all), and 17, 19.
15.2: 5, 6, 7, 9, 11, 13, 15, 29, 31, 33, 35, 37.
15.3: 15 - 35 (odd), 39,41,45,46,51,55,56,61
15.4: 1-4, 11-13,25-27, 31-32.
15.5: 1-5, 7, 9, 10,11, 17-19,21,23,25
15.6: 4-15, 21, 23, 25
15.7: 1, 2, 5, 7, 8,11,29,31, 39. Also,
review Examples 1,2,3,5,6,7.
15.8: Examples 1,2,3,4. Ex. 3, 4, 5, 6.
Test 2 (Tue Oct 14) covers Chapters 14 and 15
16.2: 1 - 21 (odd), 25, 26.
16.3: 1 - 13 (odd), 19, 20, 39, 43, 45, 49.
16.4: 7, 9, 11, 15, 19, 21, 29, 31.
16.5: Examples 1, 2, 3. Ex. 1, 3, 5, 7, 11, 13.
16.6: Examples 1, 2, 3. Ex. 1 - 9 (all), 11, 15, 17, 19.
16.7: Examples 1 - 4. Ex. 15, 17, 19, 21, 27
16.8: Examples 3, 4. Ex. 15, 17, 19, 21, 39
16.9: Examples 1, 2, 3. Ex. 1-4, 7, 10, 11, 13, 19, 21.
17.1: 1, 2, 3, 6, 11, 12, 13, 21, 22, 23.
17.2: 1 - 15 (odd), 19, 20, 21, 39, 41.
17.3: 3 - 7, 9, 12, 13, 15, 17, 19, 21
17.4: Examples 1 - 4, Ex. 1, 3, 5, 7, 9, 13
17.5: Examples 1, 2, 3, 4. Ex. 1, 3, 7, 12, 13, 15, 17 (for the last
three just determine whether or not the vector field is conservative)
Test 3 (Th Nov 20) covers sections 16.2 to 17.5 above.
The information provided here is subject to change, modification, or
revision.
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Fall Term, 2007-2008
MTH 168-01/P1: Calculus and Analytic Geometry I
MTH 168-05: Calculus and Analytic Geometry I
MTH 403/535: Boundary Value Problems/ Partial Differential Equations
Office Hours:
M W F 10:00 - 10:50, T Th 4:30 - 5:30,
and by Appointment.
MTH 168 ANALYTIC GEOMETRY AND CALCULUS I.
T.A. : Jinyang
Sun
Office(SC 319) hours: ??
Text: Calculus James Stewart 6th Edition
Catalogue Description: Introduction to the differential and integral calculus; differentiation and integration of algebraic and transcendental functions with applications to science and engineering. Prerequisite: MTH 116 or equivalent.
I. Course Goal: This is the first course in the three course calculus sequence, MTH 168, MTH 169, MTH 218; it is intended for mathematics, mathematics in secondary education, physical science and engineering majors. This course is an introduction to the concepts of single variable calculus. It is designed to help the student develop knowledge in the areas of differential and integral calculus of functions of a single variable, including polynomial, trigonometric, exponential, logarithmic and other transcendental functions, and to help the student develop analytic, computational, and problem solving skills.
II. Course Objectives:
Objective 1. The student will demonstrate, in writing, knowledge of factual content in traditional subject areas of analytic geometry, limits, differentiation and its applications, and integration of a function of one variable.
Strategy 1. The instructor will demonstrate to the student the development of traditional problem solving algorithms in single variable calculus, and require the student to develop analogous algorithms.
Strategy 2. The instructor will demonstrate the application of traditional problem solving algorithms to the student and require the student to successfully employ traditional problem solving algorithms.
Objective 2. The student will further develop skills related to problem solving and critical thinking.
Strategy. The instructor will require that the student successfully pose or model a problem correctly, select appropriate problem solving algorithms to solve a well posed problem, and present results to peers or teachers in written or verbal form.
Objective 3. The student will further develop skills related to problem solving and technology.
Strategy. The instructor will require that the student write code successfully to implement a problem solving algorithm on a personal computer or calculator.
Objective 4. The student will further appreciate (attitude) mathematics, the language of science.
Strategy I. The instructor will communicate in precise and logically correct terms, and require the student to communicate in precise and logically correct terns.
Strategy 2. The instructor will develop and employ efficient problem solving algorithms.
Objective 5. The student will further appreciate (attitude) the impact of the computer in the usage and teaching of mathematics.
Strategy .The instructor will require that the student employ computer graphics to better understand and further explore the relationship between geometry and analysis in single variable calculus.
Objective 6. The student will further appreciate (value) applications of mathematics to solve real world problems.
Strategy. The instructor will stress where theory is meaningful in applications.
llI. Course Topics:
Limit of a function at a point and at infinity, infinite limits.
Continuity of a function at a point and on an interval, one-sided limits.
The definition of the derivative as a limit.
The derivative and the tangent line problem, basic differentiation rules, rates of change.
The product rule, quotient rule and chain rule, higher-order derivatives and implicit differentiation.
Related rates, extrema on an interval, curve sketching along with the relationship between the sign of the first derivative and increasing and decreasing functions, and concavity and the second derivative, optimization.
Rolle’s theorem and the mean value theorem for derivatives.
Newton’s method for estimating the roots of a function.
Differentials and approximations.
Antiderivatives and indefinite integration.
Area, Riemann sums and the definite integral as a limit.
The Fundamental Theorem of Calculus.
Integration by substitution.
Numerical integration.
Study of the natural and general exponential and logarithmic functions, including definitions, differentiation and integration, and applications.
Definition of inverse trigonometric functions and their derivatives.
Introduction to hyperbolic functions.
IV. Instructional Procedures: The objectives are accomplished through lectures, group learning projects, problem sessions, computer laboratories and private consultation.
V. Student Evaluation Criteria:
The student's written communication is evaluated in three ways. These are: monthly examinations covering major sections or chapters, a one time cumulative final examination and a set of homework problems to be solved employing MAPLE, a computer software. Problems range from theoretical to applied word problems.
Course Content: (Calculus by Stewart 5th Edition)
Chapter 2 - Limits and Rates of Change (2.2-2.5).
Chapter 3 - Derivatives (3.1-3.6,3.8-3.9).
Chapter 4 - Applications of Differentiation: (4.1-4.9).
Chapter 5 - Integrals: (5.1-5.5).
Chapter 7 - Inverse Functions: exponential, logarithmic, and inverse trigonometric
functions (7.1, 7.2*-7.4*, 7.5-7.7).
Format: Lectures on Mondays, Wednesdays, and Fridays; problem
sessions on Tuesdays and Thursdays. MAPLE, a computer algebra system,
will be used in the course.
Tests and Final Exam: There will be four tests and a comprehensive final. All tests including the final are in-class, and closed-book. All tests weigh equally (15% each). The tests will be given Fridays or Thursdays. Tentative dates for the tests are: Fri Sept 7, Th Sept 27, Th Oct 25, Th Nov 29.
Final Exam:
Section 01/P1: Mon Dec 10 from 2:30 to
4:20,
Section 05:
Tue Dec 11 from 10:10 to 12:00.
Calculator Policy: Students are allowed to use scientific calculators with numerical packages in the tests and in the final exam. Calculators with symbolic packages are not allowed in the tests and in the Final.
Grading Scheme: Grade will be based on
Four Tests (60%)
HW with MAPLE assignments (15%)
Final (comprehensive)(25%)
Here is the list of Practice Homework problems. These problems are for your practice only; they will not be collected for grade. Your T.A. will be conducting problem sessions on Tuesdays and Thursdays, and she will be helping me grade the tests.
Practice Homework Problems:
Section
2.2: 4 - 10, 12, 13, 15, 21, 25
2.3: 1,2,4,7,9,10,11,13,15,17,21,25,37,45,47,49,61
2.4: 15 - 20 (all)
2.5: 3, 4, 5, 7, 9, 10, 15, 16, 18, 19, 20, 41, 47, 63
3.2: 1,3,5,7,11,17-21,26,33-36,49.
Test 1: (Sept 7) 2.2 - 2.5, 3.2
3.3: 1 - 41 (all), 49, 50.
3.4: 1 - 20 (all), 39, 40.
3.5: 1 - 53 (odd), 88.
3.6: 5-20 (all), 25, 26
3.8: Examples 1 -4, Ex. 1-9, 11, 13, 17, 23.
3.9: 1-5, 11-22, 31 - 33.
Test 2: (Sept 27) 3.2 - 3.6, 3.8 - 3.9
4.1: 3-6, 15-27 (odd), 29-41 (odd), 45-55(odd).
4.2:
4.3: 9-13,15,16,18,20-24,29,31,32,35,39
4.4: Review Examples 3-7. Ex. 9-29(odd), 33,35,40,43,45,
51-54(all).
4.7: Examples 1,2,5,6. Ex. 1-7,
9,11,21,31,35,53,54.
4.9: 1 - 49 (odd), 51 - 56 (all).
Test 3 (Oct. 25) 4.1, 4.2, 4.3, 4.4, 4.7, 4.9
5.1 and 5.2: Materials covered in class
and exercise problems assigned there
5.3: 7-35 (odd), 37, 38, 47 - 50 (all).
5.4: 5,9,11,12,13,15,16,19,23,25,28,33,35,42
5.5: 1-6, 7-33(odd), 32, 35-47(odd).
7.1: 1-8, 23-25
7.2* 1-12, 15-35(odd),63-72(all).
7.3*: 1-11(odd),17,18,19,27-32,33-51
(odd),75-84,92.
7.4*: 11,12,21,22,23,25-43,45-51.
Test 4 (Nov 29) 5.1 - 5.5, 7.1, 7.2* - 7.4*
7.6: 1(a) -3(a), 5-7, 22-35, 38, 59 - 70.
7.7: 30,31,32,33,35,38,57-61(all).
The information provided here is subject to change, modification, or revision.
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MTH 535/MTH 403: Partial Differential Equations and Boundary Value Problems
TEXT: Fourier Series and Boundary Value
Problems by James Brown and Ruel Churchill
Seventh Edition, McGraw Hill
COURSE CONTENT:
Chapter 1: Fourier Series
Chapter 2: Convergence of Fourier Series
Chapter 3: Partial Differential Equations of
Physics
Chapter 4: The Fourier Method
Chapter 5: Boundary Value Problems
Chapter 6: Fourier Integral and Applications
Chapter 7: Orthonormal Sets
Chapter 8: Sturm-Liouville Problems and Applications
GRADE: Based on
Two in-class tests 60%
A set of homework problems 40%
The information provided here is subject to change, modification, or revision.
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Fall Term, 2006-2007
MTH 168-01/P1: Calculus and Analytic Geometry I
MTH 168-03: Calculus and Analytic Geometry I
MTH 403/535: Boundary Value Problems/ Partial Differential Equations
MTH 535/MTH 403: Partial Differential Equations and Boundary Value Problems
TEXT: Fourier Series and Boundary Value
Problems by James Brown and Ruel Churchill
Sixth Edition, McGraw Hill
COURSE CONTENT:
Chapter 1: Partial Differential Equations of
Physics
Chapter 2: The Fourier Method
Chapter 3: Orthonormal
Sets and Fourier Series
Chapter 4: Convergence of Fourier Series
Chapter 5: Boundary Value Problems
Chapter 6: Sturm-Liouville Problems and Applications
Chapter 7: Fourier Integral and Applications
First-Order Linear and Quasi-Linear Partial Differential Equations (notes will be provided for this topic).
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Summer 2006
MTH 169-61 & MTH 149-61: Analytic Geometry & Calculus II
MTH 219-Z1: Applied Differential Equations
MTH 535-Z1 & MTH 403-Z1: Partial Differential Equations and Boundary Value
Problems
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MTH 343: Math for Electrical and Computer Engineers
Course Topics:
Linear Algebra and Matrices
Mathematical Transforms (both discrete and continuous)
Complex Variables
Grading Scheme:
Homework
(30%)
Two
Tests
(40%; 20% each)
MATLAB Projects (30%)
The information provided here is subject to change, modification, or revision.
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Fall Term 2005
MTH 137-01: Calculus I with Review
MTH 137-P1: Calculus I with Review
MTH 138-01: Calculus I with Review
MTH 403-01 :Boundary Value Problems
MTH 535-N1:Partial Differential Equations
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Winter Term 2004-2005
MTH 116-01: Precalculus Mathematics
MTH 343-01: Mathematics for Computer and Electrical Engineers
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Fall Term, 2004-2005
MTH 168-07: Calculus and Analytic Geometry I
MTH 343: Mathematics for Computer & Electrical Engineers
MTH 403/535: Boundary Value Problems/ Partial Differential Equations
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MTH 531: Advanced Differential Equations
TEXT: A First Course in the Qualitative Theory
of Differential Equations - James Liu
Prentice
Hall
COURSE CONTENT:
Chapter 1: A Brief Description
(Sections 1,2,3)
Chapter 2: Existence and Uniqueness (Sections 1,2)
Chapter 3: Linear Differential Equations
(Sections 1,2,3)
Chapter 4: Autonomous Differential Equations (Sections
1,2,3,4)
Chapter 5: Stability. Part I (Sections 1,2,3,5)
Homework:
Problem Set 1
TBA
Problem Set 2
TBA
Problem Set 3
TBA
Problem Set 4
TBA
Problem Set 5
TBA
Problem Set 6
TBA
The information provided here is subject to change, modification, or revision.
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MTH 490: (MTH 343) Mathematics for Electrical & Computer Engineers
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MTH 302: Linear Algebra and Matrices.
Text: Linear Algebra and Its Applications (Second Edition) - David C. Lay
Course Content: Chapter 1 (1.1-1.7, 1.9)
Chapter 2 (2.1-2.3, 2.8)
Chapter 3 (3.1, 3.2)
Chapter 4 ( 4.1-4.6, 4.8)
Chapter 5 (5.1-5.3, 5.6)
Chapter 6 (6.1-6.5)
Chapter 7 (7.1-7.2, 7.4)
More information and details of the course will be given in class.
The information provided here is subject to change, modification, or
revision.
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SYLLABUS for MTH 430: Real Analysis.
Text: Methods of Real Analysis - Richard R. Goldberg
Course Content:
Chapter 1: Real-valued functions, Countability,
Least upper bounds.
Chapter 2: Sequences and Subsequences - limits, convergence and divergence,
bounded, monotone, lim sup and lim
inf, Cauchy sequences.
Chapter 3: Series of Real Numbers - convergence and divergence, tests for
convergence, class of square summable sequences.
Chapters 4 - 6: Metric Spaces - limits in metric spaces, functions on metric
spaces, open sets, closed sets, connected sets, complete and compact metric
spaces, continuous functions on compact metric spaces, uniform continuity.
Chapter 7: Riemann Integral - sets of measure zero, definition of Riemann
integral, existence of Riemann integral, and properties of Riemann integral.
Chapter 9: Sequences and series of functions - pointwise
vs uniform convergence of sequences of functions,
consequences of uniform convergence, convergence and uniform convergence of
series of functions.
Each test will have two parts; an in-class part and a take-home part. In addition to the practice problems, a set of selected problems will be assigned for grading each week. There can be discussion sessions on the homework problems and the students might be asked to come to the board and solve some of these problems.
Prerequisites: MTH 330, Intermediate Analysis, or equivalent
The information provided here is subject to change, modification, or revision.
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MTH 302: Linear Algebra and Matrices.
Text: Linear Algebra and Its Applications (Second Edition) - David C. Lay
Course Content: Chapter 1 (1.1-1.7, 1.9)
Chapter 2 (2.1-2.3, 2.8)
Chapter 3 (3.1, 3.2)
Chapter 4 ( 4.1-4.6, 4.8)
Chapter 5 (5.1-5.3, 5.6)
Chapter 6 (6.1-6.3, 6.5)
Chapter 7 (7.1-7.2)
Grading Scheme: Grade will be based on
The other information and details of the course will be given in the class.
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SYLLABUS for MTH 531
TEXT: The Qualitative Theory of Ordinary
Differential Equations - An Introduction.
Fred Brauer and John A. Nohel. Dover Publications, Inc., New york,1989.
COURSE CONTENT:
Chapter 1: Systems of Differential
Equations.
Systems of
first-order equations; existence, uniqueness, and continuity; Gronwall's inequality.
Chapter 2: Linear Systems.
Existence and uniqueness for linear systems;
linear homogenous and nonhomogenous systems; linear
systems with constant coefficients; similarity of matrices and Jordan canonical
form; asymptotic behavior of solutions of linear systems with constant
coefficients; autonomous systems.
Chapter 3: Existence Theory.
Existence theory
for the scalar case and for systems of first-order equations; uniqueness of
solutions; continuation of solution; dependence on initial data.
Chapter 4: Stability of Linear and Almost Linear
Systems.
Definition of
stability; linear and almost linear systems; conditional stability; stability
of periodic solutions.
Chapter 5: Lyapunov's
Method.
Lyapunov's
theorems; invarient sets and stability; asymptotic
stability; nonautonomous systems.
GRADE: Based on
Two in-class, Open-book tests 50%
A set of homework problems 35%
An independent or group project 15%
(details about the project will be discussed in class)
Homework:
Problem Set 1
Due: Sept 8, 1999
1) Exercises 1, 2, and 3 on page 11
2) Exercise 4 on page 12
3) Exercise 2 on page 18
4) Exercise 5 on page 20
Problem Set 2
Due: Sept 22, 1999
1) Exercise 8 (a), (b), (c)
on page 27
2) Exercise 10 on page 27
3) Exercise 14 (a), (b) on page 29
4) Exercise 3 on page 32
Problem Set 3
Due: Oct 4, 1999
1) Exercise 9, and 10 on page
42
2) Exercise 24 on page 49
3) Exercise 28 on page 50
4) Exercise 3 on page 53
Problem Set 4
Due: Oct 18, 1999
1) Exercise 6 and 7 on page 58
2) Exercise 11 (b), (c) on page 61
3) Exercise 17 on page
71
4) Exercise 24 and 25 on page 73
Problem Set 5
Due: Nov 3, 1999
1) Exercise 1 on page 81
2) Exercise 8 on page 93
3) Exercise 19 on page 95
4) Exercise 12 on page 106
Problem Set 6
Due: Nov 29, 1999
1) Exercise 3 on page 149
2) Exercise 12 on page 154
3) Exercise 17 on page 159
4) Consider the equation of Example 4 on page 225,
where uf(u)>0, u not = 0, f(u)>0, u not = 0,
Apply Lyapunov's direct method to prove that the zero
solution is stable.
Final Exam (open-book): Monday, December 13, in SH 106 from 4:30 - 6 pm.
The information provided here is subject to change, modification, or revision.
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TEXT: Numerical Analysis (Sixth Edition) - Richard L Burden and J. Douglas Faires.
COURSE CONTENT: Chapters 4, 5, 8, 11, 12. (Review of Calculus from Chapter I. Also, Read Sections 1.2 and 1.3 of Chapter I)
Chapter 4: Numerical Differentiation and
Integration
Chapter 5: Initial-Value Problems for Ordinary Differential Equations
Chapter 8: Approximation theory
Chapter 11: Boundary Value Problems for Ordinary Differential Equations
Chapter 12: Numerical Solutions to Partial Differential Equations
GRADE: Based on
Two in-class, Open-book tests 50%
A set of homework problems 35%
An independent or group project 15%
(details about the project will be discussed in class)
The information provided here is subject to change, modification, or revision.
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SYLLABUS for MTH 552
Text: Applied Mathematics - J. David Logan, Second Edition, John Wiley & Sons, Inc., 1997.
Course Content:
. Dimensional Analysis and Scaling: dimensional methods, pi theorem,
scaling (Chapter 1).
. Perturbation Methods: regular and singular perturbations, boundary
layer analysis, applications (Chapter 2).
. Stability and Bifurcation: stability and bifurcation of equilibrium
solutions for one-dimensional and two-dimensional problems, classification of
bifurcation points, applications (Chapter 7).
. Similarity Methods: invariant partial differential equations - self
similar solutions, similarity and dimensional analysis, the Lie plane (notes
will be given for this material)
Grade: based on two tests, a set of homework problems, and a term-project. The details about the project will be discussed in class.
Two tests (50%) (25% for each test)
Homework (35%)
Project (15%)
Prerequisites include a good command of calculus, especially several variables, and the rudiments of a postcalculus course in ordinary differential equations; familiarity with elementary matrix theory (eigenvalues and linear systems)
The information provided here is subject to change, modification, or revision.