Text: Swokowski, Earl. Calculus. Classic edition, Brooks/Cole Publishing Co.,
1991. Course Description: This course is intended for computer science, ...
MATH 11 CALCULUS III Course Syllabus Fall Session, 2013 Instructor: Brian Rodas Class Room and Time: MC 10 M-Th 12:45pm-1:50pm Office Room: MC 38 Office Phone: (310)434-8673 Office Hours: M 11am-12pm, TTh 2:30pm-3:30pm, W 2:30pm-3:30pm(Math Study Room MC 84B) and by appointment E-mail: rodas
[email protected] Class Website: http://homepage.smc.edu/rodas brian Text: Swokowski, Earl. Calculus. Classic edition, Brooks/Cole Publishing Co.,1991. Course Description: This course is intended for computer science, engineering, mathematics and natural science majors. Topics in this third course include vectors and analytic geometry in two and three dimensions, vector functions with applications, partial derivatives, extrema, Lagrange Multipliers, multiple integrals with applications, vector fields, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. The prerequisite is MATH 8 with a grade of C or better. Format of Course: The first 10 minutes of each class will be devoted to addressing students’ questions regarding homework or material from the previous section. The remainder of the class will be spent presenting new material. Homework: Homework will be assigned daily but not collected. The problems assigned are practice problems in understanding the material covered for the day. It has been known that a genuine understanding and completion of the homework results in quality performance. Supplemental homework may also given during class. Quizzes: Quizzes will be given periodically. They will be approximately 10-15 minutes long. It has been my nature to give quiz problems identical to the homework. Therefore it would be in your best interest to do the homework. Each quiz is worth ten points. The lowest quiz score will be dropped. Exams: There will be four exams and a final. Each exam is worth 100 points. The lowest exam will be scaled out of 50 points. So if your test scores are 100, 90, 80, and 70, then your test average is (100+90+80+35)/350. The final is worth 200 points and is cumulative. You must show all necessary work to receive full credit. Calculators: Although the use of calculators are not permitted for exams or quizzes, they can be useful for doing tedious calculations and graphing. I encourage you to check your answers on the calculator when doing your homework but do not become dependent on the calculator. Grading: Top three exams Lowest exam Quizzes Final exam Total
300 50 50 200 600
points points points points points
The expectation is that a letter grade will be given using the following scale for the semester average: 90-100%(A), 80-89%(B), 70-79%(C), 60-69%(D), 0-59%(F). Academic Conduct: You are expected to abide by Santa Monica College’s code of academic conduct on all exams, quizzes and homework. Copying homework solutions or quiz or test answers from someone is considered cheating as is altering a quiz or examination after it has been graded or giving answers to someone during an exam or quiz. If caught cheating or using an electronic device during an exam, the parties involved will receive a zero on the exam and an academic dishonesty report will be filed. Note that cell phones are to be turned off for the duration of each class. Since attendance is essential for normal progress in class, a student is expected to be in class regularly and on time. Missing classes puts you in danger of being dropped. There are no makeup assignments, quizzes or exams. Late assignments will not be accepted. No excuses. IT IS THE STUDENT’S RESPONSIBILITY TO BE AWARE OF WITHDRAWAL DATES AND TO TAKE THE APPROPRIATE NECESSARY STEPS. Refer to your Corsair Connect account for specific dates. If a student does not withdraw and stops coming to class, the student will receive a failing grade. Entry Skills for Math 11: Prior to enrolling in Math 8 students should be able to: A. Apply concepts of limits, continuity and differentiability in two dimensions. B. Differentiate and integrate exponential and logarithmic functions. C. Differentiate and integrate transcendental functions and inverses. D. Perform integral by parts. E. Perform integration using trigonometric substitution. F. Perform integration with powers of trigonometric functions. G. Resolve indeterminate forms using L’Hopital’s Rule. H. Set up Taylor Series representations of transcental functions. I. Use polar and parametric coordinates for plane curves. J. Find center of mass/centroid. Exit skills for MATH 11: Upon successful completion of this course, the student will be able to: A. Perform the basic algebra of vectors including dot and cross products. B. Write the equations of lines and planes in three dimensions, both in non-vector and vector forms. C. Sketch planes, cylinders and quadric surfaces. D. Distinguish between scalar-valued and vector-valued functions. E. Differentiate and integrate vector-valued funtions. F. Represent curvilinear motion in vector form both algebraically and geometrically. G. Find the derivatives of scalar-valued and vector valued functions of two or more independent variables. H. Find extrema of functions of two of more independent variables both by the Second Derivative Test and by Lagrange Multipliers. I. Evaluate double and triple integrals. J. Use multiple integrals to solve various applied problems. K. Use rectangular, cylindrical and spherical coordinates for graphing and the evaluation of multiple integrals. L. Set up and evaluate line integrals and surface integrals and apply them to physical applications. M. Apply Green’s Theorem, Divergence Theorem and Stoke’s Theorem. N. Apply the concepts of the gradient, divergence and curl.
SCHEDULE OF LECTURES, HOMEWORK & EXAMS Date 8/26 8/27 8/28 8/29 9/2 9/3 9/4 9/5 9/9 9/10 9/11 9/12 9/16
Section 14.1 14.2 14.3 14.4
15.1 15.2
Material Vectors in Two Dimensions Vectors in Three Dimensions The Dot Product The Vector Product Holiday(No class) Lines and Planes Lines and Planes Surfaces Surfaces Review EXAM 1 on Ch.14 Vector-Valued Functions Limits, Derivatives and Integrals
9/17 9/18 9/19 9/23 9/24 9/25 9/26 9/30 10/1
15.3 15.4 15.4 15.5 16.1 16.1 16.2 16.2 16.3
Motion Curvature Curvature Tangential & Normal Components of Acceleration Functions of Several Variables Functions of Several Variables Limits and Continuity Limits and Continuity Partial Derivatives
10/2 10/3 10/7 10/8 10/9 10/10 10/14 10/15 10/16 10/17 10/21 10/22 10/23 10/24
16.4 16.4
Increments and Differentials Increments and Differentials Review EXAM 2 on Ch.15, Sections 16.1-16.4 Chain Rules Directional Derivatives Directional Derivatives Tangent Planes and Normal Lines Extrema of Functions Extrema of Functions Lagrange Multipliers Lagrange Multipliers Double Integrals Double Integrals Area and Volume Double Integrals in Polar Coordinates Surface Area Review EXAM 3 on Sections 16.4-16.9, 17.1-17.4 Triple Integrals Triple Integrals Moments and Center of Mass Cylindrical Coordinates
10/28 10/29 10/30 10/31 11/4 11/5 11/6 11/7
14.5 14.5 14.6 14.6
16.5 16.6 16.6 16.7 16.8 16.8 16.9 16.9 17.1 17.1 17.2 17.3 17.4
17.5 17.5 17.6 17.7
Homework 1-21odd,25-35odd,41-53odd 3,5,7,11-19odd,23-31odd,35,37,41 1-33odd,39-49odd 1-7odd,11-19odd,25,29,33 1-15odd,19-23odd,27-39odd 41-51odd,57,65 1-7odd,21,39,41 23,25-29(a only),31-37odd,43,45
1,5-9odd,13,15,21,23 1-7odd,11,15-21odd,25-31odd, 35-39odd,49 1,3,5,9,13,17-25odd 1,5-11odd,23,29,31 13-21odd,25,37,45 1,4,9,11,13 1-13odd 15,19-23odd,37,39,45 1-15odd,21,23 25-31odd,35,37,45 1-7odd,17-21odd,25,27, 35,39-43odd,47,49,51a 1,7-13odd,17 3,5,19,23,26,31,33,41
1-7odd,11-19odd,23-25,27 7-15odd 1-5odd,21-27odd 3-21odd,27,27 5,9,13,17 21,25,31 1,3,9-13odd,17 1-11odd,13,17-33odd,39 43-49odd 13-17,19-23odd,31 1,5-9odd,13-17odd,23-27odd 1,7-13odd
1,17 3,7,13,15,23-27odd,31 1,3,9,11,17-25odd 1-21odd,25-31odd
Date 11/11 11/12 11/13 11/14 11/18 11/19 11/20 11/21 11/25 11/26 11/27 11/28 12/2 12/3 12/4 12/5 12/9 12/10
Section 17.8 18.1 18.1 18.2 18.2 18.3 18.3
18.4 18.5 18.5 18.6 18.7 18.7
Material Holiday (No class) Spherical Coordinates Vector Fields Vector Fields Line Integrals Line Integrals Independence of Path Independence of Path Review EXAM 4 on Sections 17.5-17.8 & 18.1-18.3 Green’s Theorem Surface Integrals Thanksgiving (No class) Surface Integrals The Divergence Theorem Stoke’s Theorem Stoke’s Theorem REVIEW for final FINAL EXAM 12pm-3pm
The instructor does reserve the right to add or modify the syllabus.
Homework 1-15odd,21-25odd,31,33 1,3,7,11,13 15-23odd,27,33 1,13 3-9odd,17,19 1,3,7-19odd,23-27odd 1,3,7-19odd,23-27odd
1-5odd,11,13,20,21,23 1-7odd 11-17odd,20 1-7odd,11,17,19 1-9odd,13 1-9odd,13
Addendum to the MATH 11 Fall 2013 Syllabus Course Content: Percentage of Term 17% 12% 30% 20% 21%
Topic Vectors and Surfaces Vector-Valued Functions and Curves Functions of Several Variables Multiple Integrals Vector Calculus
Student Learning Outcomes: 1.
Given vector-valued or real-valued functions involving two or more independent variables, students will identify and use appropriate techniques to analyze the fundamental properties of those functions. Included would be partial and directional derivatives, gradients, differentials, and integrals over lines, surfaces and solid regions
2. Students will be able to setup and solve physical applications problems related to all aspects of motion along a curve. Included would be the arc length parametrization of a curve and the use of tangent, velocity, normal and binormal vectors, curvature, and the tangential and normal components of acceleration and their relationship to the osculating plane containing the circle of best fit at a point on the curve
3. Students will be able to apply Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem with the concepts of divergence and curl and flux. Students will solve problems related to vector fields including magnetic fields, flow fields, and conservative vector fields
