Math 242 Mathematics for Engineering and Science III



Math 242 Mathematics for Engineering & Science III

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PREREQUISITE: Math 241 COREQUISITES: PHYS 201 and ENGR 122

COURSE GOALS: The student will become proficient in integration and optimization 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. Schroder, 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 by Bernd Schroeder.

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

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 60% (20% each)

Homework . 10%

Final 30%

Total 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.

HONOR CODE: In accordance with the Academic Honor Code, students pledge the following: Being a student of higher standards, I pledge to embody the principles of academic integrity. For details refer to .

Math 242 – Engineering Mathematics III – Course Outline

Texts: Calculus: Concepts and Contexts, 2nd Edition, Stewart, Brooks/Cole.

Notes on Differential Equations and Statistics, ?-Edition, B. Schroder.

| |Topic |Homework |

| |4.9 and Companion 18 A-B Antiderivatives |Stew Pg. 334 # 2-3, 5-7, 9-13,16, 20, 35, 43, 45 Comp 18B Pg. 468 # 1-3 |

| |Companion 19A-B: Area and Sums |Comp 19A Pg. 477 # 4-6; Comp 19B Pg. 483 # 5 |

| |Stewart 5.1: Areas and Distances |Pg. 355 # 2, 18-20 |

| |Companion 19C: Riemann Sums and Their Interpretations; |Comp 19C Pg. 492 # 1-2; Stew Pg. 367 # 5, 11, 17-18, 23, 24, 29-35, 39-43 |

| |Stewart 5.2: The Definite Integral | |

| |Stewart 5.3: Evaluating Definite Integrals; |Stew Pg. 377 # 1, 4, 12, 15, 21-24, 29-32, 37, 41, 45, 46, 49, 51-53; Comp |

| |Companion 20B: Other Interpretations of the Definite Integral |20B Pg. 506 #3-4 |

| |Stewart 5.4: The Fundamental Theorem of Calculus |Pg. 386 # 1, 3, 5, 6, 7-9, 11-16, 18, 19, 24 |

| |Stewart 5.5: Substitution for Antiderivatives |Pg. 395 # 3-16, 19-32, 39-46, 51-52, 55-56 |

| |Setwart 5.6: Integration by Parts |Pg. 401 # 4, 5, 8- 13, 16-21, 26, 28, 34 |

| |Comp. Section 10.1: Matrices and Systems of Linear Equations |Pg. 535 # 3-7, 19-21 |

| |Stewart 5.7: Additional Techniques of Integration |Pg. 408 #1,3,5,7, 9,10,11, 17,19,21,23,25,27,28 |

| |Stewart 5.8: Integration Using Tables and Computer Algebra |Pg. 414 # 3, 10, 11, 13, 15, 23, 27, 32-34 |

| |Systems | |

| |Stewart 6.1: More about areas |Stew. 6.1 #2, 3, 5, 6, 10, 12, 14, 15, 19, 20, 22, 25, 35 |

| |Stewart 6.2: Volumes |Stew. 6.2 #1, 2, 3, 8, 15, 21, 22, 23, 30, 35, 48 |

| |Stewart 6.5: Applications to Physics and Engineering (Focus: Work)|Stew. 6.5 #9, 10, 11, 13, 14 |

| |EXB Examples and Basics of Differential Equations | # 1, 3, 4 |

| |FIR.1 Separable ODEs | # 1a-j,2a-d/2e-j |

| |LD[pic].1 Solving Homogeneous Linear Differential Equation with | # 1a-b,d-g,i-j,2a-c/ |

| |Constant Coefficients |1c,h,2d-j |

| |LDT.3 Linear Algebra Interlude | # 2,3c-e,h-j |

| |LD[pic].3 Inhomogeneous Linear Differential Equations | # 1a-d/1e-j,4 |

| |FIR.1 and LD[pic].1 Application problems | # 5-6, Pg. 76 # 3-4,6 |

| |Stewart 7.2: Direction Fields |Stew. 7.2 Pg. 519 # 1,2,3,4,5,6,7, 21,22, 23,24 |

| |Stewart 7.2: Euler’s Method | |

| |FIR.4: Further Types of Solvable DE’s |TBA |

Note: The parts from B. Schroeder’s notes are not up-to-date. Double check before posting.

Instructional Objectives for MATH 242

At the end of this course the student will be able to:

1. Solve systems of linear equations.

2. Solve indefinite integrals

a) By substitution,

b) Using integration by parts,

c) Using partial fractions,

d) Using an integral table.

3. When given an indefinite integral

a) Select the appropriate method(s) to solve the integral,

b) Solve the integral using the method(s) determined.

4. Explain the definition of the definite integral to a physicist or a geometer.

5. Approximate a definite integral using Riemann sums.

6. 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.

7. Calculate the area between two curves.

8. Calculate the area enclosed by a parametric curve.

9. Explain how some areas calculated with integrals can be negative.

10. Calculate the volume of a solid using single integrals.

11. Compute the work done in certain lifting tasks

12. Classify differential equations as separable first order, homogeneous first order, Bernoulli, linear homogeneous, linear inhomogeneous, Cauchy, or other.

13. Sketch the solution of an initial value problem when given the slope field of the differential equation,

14. 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.

15. Solve mixing problems.

16. 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.

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