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.