Math 242 Mathematics for Engineering and the Sciences III
SECTION: 005
QUARTER:
Spring 2003
INSTRUCTOR: Bernd Schröder
CLASSROOM: GTM 317
OFFICE NUMBER: GTM 316
OFFICE HOURS: MWF 9:30-11:30, TR 8:30-10:00, 12:00-12:30
PHONE: x-2422
E-MAIL: schroder@coes.LaTech.edu WEB: http://www.LaTech.edu/~schroder
PREREQUISITE: Math 241
COREQUISITES: PHYS 201 and ENGR 122
COURSE GOALS: The student will become proficient in integration of single variable functions. In addition the
student will master techniques for solving first and second order differential equations with constant coefficients and
initial conditions. This proficiency will be demonstrated by satisfactorily completing a series of exams and
homework assignments.
TEXTBOOKS: Calculus: Concepts and Contexts by James Stewart, Notes on Differential Equations and Statistics
by B. Schröder, and A Custom Companion to Calculus by Thomson Learning
COURSE OUTLINE AND OBJECTIVES: The details are attached. To be covered are Concepts Sections 4.9,
5.1-5.8, 6.1, 6.2, 6.5, and 7.2; Custom Companion Sections 10.1, 19A-C, and 20B; and Modules EXB, FIR, LDT
and LDλ in the Notes on Differential Equations and Statistics
ATTENDANCE REGULATIONS: Class attendance is regarded as an obligation as well as a privilege. Attendance
and class participation are mandatory. It is the student's responsibility to keep informed of any announcements,
syllabus adjustments or policy changes made during scheduled classes. Notify the instructor in advance if you must
miss class, arrive late for class, or leave early from class.
GRAPHING CALCULATOR: A graphing calculator that does at least as much as the TI-82 and access to
Mathcad will be required for the course, but TI-92 is not allowed. Graphing calculator is not allowed for all tests,
a regular scientific one is optional.
EXAMINATIONS & Makeup Policy: There will three topical exams and a comprehensive final exam. If you
have to miss an exam, you must notify the instructor prior to the exam either in person or by phone. An unexcused
absence from an exam will result in a zero on that exam
Homework: For homework hand-in dates and assigned problems, please consult the included schedule of classes.
GRADE DETERMINATION POLICY: The grading scale will be: A = 90% - 100%; B = 80% - 89%; C = 70% 79%; D = 60% - 69%; F = 0% - 59%. The course grade will be calculated as follows:
Exams 1--3
Homework
Final
Total
60% (20% each)
. 10%
30%
100%
STUDENTS NEEDING SPECIAL ACCOMODATIONS & RETENTION OF GRADED MATERIALS:
Students needing testing or classroom accommodations based on a disability should discuss the need with the
instructor during the first week of class. In the event of a question regarding an exam grade or final grade, it will be
the responsibility of the student to retain and present graded materials which have been returned for student
possession.
Academic misconduct. In accordance with p.30 of the Louisiana Tech University bulletin, any form of plagiarism
is considered academic misconduct and will carry a minimum penalty of an “F” for the assignment in question. The
instructor reserves the right to enforce a more stringent penalty.
Math 242 – Mathematics for Engineering and the Sciences III – Course Outline
Day
Topic
Wed. 3-12-03 Stewart 4.9 and Companion 18 A-B: Antiderivatives
Fri. 3-14-03
Companion 19A-B: Area and Sums
Stewart 5.1: Areas and Distances
HW due
Mon. 3-17-03 Companion 19C: Riemann Sums and Interpretations;
Stewart 5.2: The Definite Integral
Wed. 3-19-03 Stewart 5.3: Evaluating Definite Integrals;
Companion 20B: Other Interpretations of the Definite
HW due
Integral
Fri. 3-21-03
Stewart 5.5: Substitution for Antiderivatives
Mon. 3-24-03
HW due
Wed. 3-26-03
Fri. 3-28-03
Mon. 3-31-03
HW due
Wed. 4-2-03
Fri. 4-4-03
HW due
Mon. 4-7-03
Wed. 4-9-03
HW due
Fri. 4-11-03
Mon. 4-14-03
Wed. 4-16-03
HW due
Wed. 4-23-03
Fri. 4-25-03
Mon. 4-28-03
HW due
Wed. 4-30-03
Fri. 5-2-03
HW due
Mon. 5-5-03
Wed. 5-7-03
HW due
Fri. 5-9-03
Mon. 5-12-03
HW due
Wed. 5-14-03
Fri. 5-16-03
Mon. 5-19-03
HW due
Wed. 5-21-03
Fri. 5-23-03
Stewart 5.6: Integration by Parts
Stewart 5.4: The Fundamental Theorem of Calculus
Exam 1: Stewart 4.9, 5.1-5.6
Which method do I use? (Review, p.438ff)
Homework
Stew 4.9 # 2-3, 5-7, 10, 12, 13, 16, 20, 21, 30,
35, 43, 45 Comp 18B Pg. 468 # 1-3
Comp 19A # 5,6; Comp 19B Pg. 483 # 5
Stew. 5.1 # 2,3, 18-20
Comp 19C Pg. 492 # 1-2;
Stew 5.2 # 5, 11, 17-18, 23, 24, 29-35, 39-43
Stew. 5.3 # 1, 4, 12, 15, 21-23, 31-32, 37, 41,
46, 49, 51-53;
Comp 20B Pg. 506 #3-4
Stew. 5.5 # 1, 2, 8, 10, 11, 14, 16, 19, 28, 32,
43, 45, 46 (trick question), 51-52, 55-56
Stew. 5.6 # 4, 5, 8- 13, 16-21, 26, 28, 34
Stew. 5.4 # 1, 3, 5, 6, 7-9, 11-16, 18, 19, 24
Stew. P.439 #11, 14, 17, 19, 20, 23, 26, 27, 31,
32, 34
Stewart 6.1: More about areas
Stew. 6.1 #2, 3, 5, 6, 10, 12, 14, 15, 19
Stewart 6.1: More about areas
Stew. 6.1 #20, 22, 25, 35
Stewart 6.2: Volumes
Stew. 6.2 #1, 2, 3, 8, 15
Stewart 6.2: Volumes
Stew. 6.2 #21, 22, 23, 30, 35, 48
Stewart 6.5: Applications to Physics and Engineering Stew. 6.5 #9, 10, 11, 13, 14
(Focus: Work)
Comp. Section 10.1: Systems of Linear Equations
Pg. 535 # 3-7, 19-21
Stewart 5.7: Additional Techniques of Integration
Stew. 5.7 # 17,18,19,21,23,24,25,27,28
(Focus: Partial Fractions)
Stewart 5.7: Additional Techniques of Integration
Stew. 5.7 # 1,3,5,7, 9,10,11
(Focus: Trigonometric Substitution)
Stewart 5.8: Integration Using Tables and CAS
Stew. 5.8 # 3, 10, 11, 13, 15, 23, 27, 32-34
Exam 2: Stewart 4.6, 6.1,6.2,6.5, cumulative on ch.
5, companion 10.1
EXB: Examples and Basics of Differential Equations
EXB # 1a,b,c,d,e, 3, 4
FIR.1: Separable ODEs
FIR.1 #1a,b,c,e,i,,2a,b,c,d
FIR.1: Separable ODEs(mixing problems)
FIR.1 #1g,j,#1h(rememberFTC),2e,f,g,h,i,j,5,6
LD  .1: Solving Homogeneous Linear Differential
LD  .1 # 1a,b,d,e,f,g,i,j,2a,b,c
Equation with Constant Coefficients
LD  .1: Solving Homogeneous Linear Differential
LD  .1 #1c,h,2d,e,f,h,j,3,4,5c,d,e,
Equation with Constant Coefficients(harmonic
EXB #5,7
oscillators)
LD  .2 #1,2
LDT.3: Linear Algebra Interlude
LDT.3 # 2,3c-e,h-j
LD  .3: Inhomogeneous Linear Differential Equations LD  .3 # 1a,b,c,d, 2
LD  .3: Inhomogeneous Linear Differential Equations LD  .3 #1e,f,g,h,i,j, 3, 4
Mixed review on DE’s and applications
Exam 3: Schröder EXB, FIR.1, LDT, LDλ
Stewart 7.2: Direction Fields
Stewart 7.2: Euler’s Method
Mixed review: Integration, DEs and their applications
FINAL EXAM
TBA
Stew. 7.2 # 1,2,3,4,5,6,7, 21,22, 23,24
TBA
Cumulative
Instructional Objectives for MATH 242
At the end of this course the student will be able to:
1. Solve indefinite integrals
a) By substitution,
b) Using integration by parts,
c) Using partial fractions,
d) Using an integral table.
2. When given an indefinite integral
a) Select the appropriate method(s) to solve the integral,
b) Solve the integral using the method(s) determined.
3. Explain the definition of the definite integral to a physicist or a geometer.
4. Approximate a definite integral using Riemann sums.
5. Solve definite integrals
a) With the fundamental theorem of calculus,
b) Using the definition of the definite integral,
c) Using data given on related definite integrals.
6. Solve systems of linear equations.
7. Compute areas under and between curves.
8. Compute volumes of geometric objects, in particular volumes of rotation.
9. Compute the work done in certain lifting tasks.
10. Classify differential equations as separable first order, homogeneous first order, Bernoulli,
linear homogeneous, linear inhomogeneous, Cauchy, or other.
11. Sketch the solution of an initial value problem when given the slope field of the differential
equation,
12. Solve the following types of differential equations and initial value problems involving these
equations
a) Separable first order,
b) Linear homogeneous equations with constant coefficients,
c) Linear inhomogeneous equations with constant coefficients and a variable
inhomogeneity.
13. Solve mixing problems.
14. Model a harmonic oscillator with a differential equation
a) Explain the physical interpretation of the coefficients in the differential equation,
b) Determine if the oscillator is overdamped, underdamped or critically damped,
c) Solve differential equations modeling the oscillator and calculate the total energy stored
in the oscillator at any time.