Math 283 Honors Multivariate Calculus (Fall 2018)

Final Exam: Tuesday, Dec 11, 4:00-5:50pm in Wil 1-138 (our classroom)

Grades will be entered either late Thursday afternoon or Friday morning.

Email me at pernarow@math.montana.edu to request final exam scores and course % and grade.

You may pick up the exams from me when you return in January

 Instructor Mark Pernarowski Textbook Calculus: Early Transcendentals, 3rd ed.: J. Rogawski, C. Adams Section 01 Office Hours Schedule (Wil 2-236) Phone 994-5356 Classroom Wil 1-138  (MTRF 11am)

 Grading: The course % is determined by:   Midterm 1      M1           100    Midterm 2      M2           100   Final                F            100   Quizzes           Q           100  ________________________________                                        400          % = (M1+M2+F+HW)/4  The final is not comprehensive. Six quizzes each worth 20 points will be given. Your best 5 quiz scores determine Q above.Exam and quiz dates are indicatedbelow. Their content will be announced in class. All exams and quizzes are closedbook and no electronic devices are permitted. Syllabus: Material covered in text is from:Chapter 12: Vector Geometry  Chapter 13: Vector Valued Functions  Chapter 14: Differentiation in Several Variables  Chapter 15: Multiple Integration  Chapter 16: Line and Surface Integrals  Chapter 17: Fundamental Theorems of Vector Analysis  Homework: Suggested homework is listed below. Although the homework is not graded it is representative of the kinds of questions which will be on quizzes and exams. Some additional problem sets and/or handouts will be handed out in class and/or posted on this site below.

Schedule Anticipated schedule for lectures showing quizzes (orange), tests (red) and holidays (green).

 Sunday Monday Tuesday Wed Thursday Friday Saturday 26 27 (12.1/12.2) 28 (12.1/12.2) 29 30 (12.2/12.3) 31 (12.3) 1 2 3Labor Day 4(12.3/12.4) 5 6(12.4) 7    (Q1) (12.4) 8 9 10 (12.5) 11 (12.5) 12 13(12.5/12.6) 14(13.1) 15 16 17(13.1) 18(13.2) 19 20 (13.3) 21  (Q2)(13.3) 22 23 24 (13.4) 25 (13.5) 26 27Review 28Midterm 1 29 30 1 (14.1) 2 (14.2) 3 4 (14.3) 5 (14.3) 6 7 8 (14.4) 9(14.5) 10 11 (14.5) 12  (Q3) (14.6) 13 14 15(14.6) 16(14.7) 17 18(14.7) 19 (14.7) 20 21 22 (14.8) 23(14.8) 24 25 (15.1) 26  (Q4)(15.2) 27 28 29(15.2) 30(15.2) 31 1Review 2Midterm 2 3 4 5 (15.3) 6Election Day 7 8 (15.3)/(15.4) 9(15.4) 10 11 12Vetran's Day 13(15.4) 14 15 (15.4) 16  (Q5)(15.4) 17 18 19 (16.1) 20 (16.2) 21Thanksgiving 22 Thanksgiving 23Thanksgiving 24 25 26 (16.2) 27 (16.3) 28 29 (16.4/16.5) 30  (Q6)(16.4/16.5) 1 2 3 (17.1) 4 (17.2) 5 6 (17.3) 7Last Class 8 9 10 11 Final 4-5:50 12 13 14 15

#### Suggested Homework and Syllabus

 12.1 9,23,33,35,37,39,43,47,61 Vectors in the plane 12.2 5,9,11,19,25,29,31,35,37,43,47,51,52,53 Vectors and lines in R^3 12.3 1,11,13,15,19,21,23,25,35,39,43,,49,55,57,67 Dot Products, angles, orthogonal, projection 12.4 9,11,13,21,28,30,37,41,43,44,45 Cross Product 12.5 3,13,15,17,21-23,25,27,29,39,41,55,57,63,65,69 Planes in 3D 12.6 just read the section Survey of Quadratic Surfaces 12.7 Will be done in tandem with Volume integrals in Chapte 15 Cylindrical Spherical coordinates 13.1 1,2,7,10,12b,12c,17,19,25,33(use "s" for r_2(t)),39 Vector Valued Functions 13.2 3,5,7,9,13,17,20,23,29,31,39,47(integrate),51(integrate twice),57 Calculus of Vector Valued Functions 13.3 1,3,5,9,11,15,25,31 Arclength and Speed 13.4 1,5,7,11,13,37,39,41,43,53 Curvature 13.5 3,5,11,15,33,35,37,41 Motion in Space Chapter 12-13 Supplementary problems Midterm 1 14.1 1,5,7,29,31,33,39a, 39b Functions of several variables 14.2 7,8,9,13,15,17,18 (polar in chapter 11),29,34 Limits and Continuity 14.3 3,5,7,13,15,17,19,23,25,29,42,43,57,61,67,76 Partial Derivatives 14.4 1,5,11,13,19,21,23,25 Tangent Planes 14.5 5,7,9,11,15,17,19,21,23,25,29,31,37,39,41,44,45,61(hard) Gradient and Directional Derivatives 14.6 1,3,7,11,13,19,27,29 Chain Rule 14.7 1,3,7,9,11,13,16,19,35,37 (on boundary),47,48 Optimization in Several variables 14.8 1,2,5,7,8,11,17,19,21,23 Lagrange Multipliers Chapter 14 Supplementary problems Midterm 2 15.1 19,21,31,37 Double Integrals: Rectangles 15.2 3,9,11 (dy dx),17,21,25,27,31,45,49 Double Integrals: General Cartesian 15.3 3,9,11,17,21 (intersect planes),26,35 (dxdydz) Triple Integrals: Cartesian 15.4 1,3,5,7,9,11,13,15,19,23,25,27,29,31,38,39,42,43,45,47,51,53,55 Integrals: Polar, Cylindrical, Spherical coordinates 15.5 not covering Integrals: Applications 15.6 not covering Integrals: Change of Coordinates 2D 16.1 13-16, 23,24,27,29,39,41,43 Vector-Fields 16.2 1,3,5,7,9,11,19,21,23,27,28,29,45,53 Line Integrals 16.3 1,57,8,9,12,17,19 Conservative Vector Fields 16.4 4,5,15,17,21,23,25 (Use Eqn 9 on pg 938 for all) Parametrized Surfaces and Surface Integrals. (extra material) 16.5 2, 5,7,9,11,13 (Nhat=khat) Flux integrals (extra material) Chapter 15-16 Review questions and examples 17.1 not covering Green's Theorem 17.2 not covering Stokes Theorem 17.3 5,7,9,11,15 Divergence Theorem
 Supplemental Notes 12a here - most of 12.1-12.4 in text

#### Exam and Quiz Outlines

 Content Description Quiz 1 Sep. 7 Quiz is on 12.1-12.3 (text and in class) and you must know how to compute a cross pruduct. (25 min - no electronic devices). Quiz 2 Sep 21 12.4-12.5 Cross product applications and all manor of geometry problems: lines, planes intersections, orthogonal vectors and planes, angles between and distance between. Also for 13.2 must know tangent lines/vectors. No graphing of curves.(25 min - no electronic devices) 3 Oct 12 14.2-14.4 Limits, Partial derivatives, Tangent planes and Linear approximations, Gradients and Directional derivatives. For limits concentrate on a) if you're told a limit exists can you compute it b) if you're told it does not, show that it does not. Partial derivatives might be 1-2 very simple calculations. Section 14.5 has the most material. Know how to compute gradients, their geometric properties, rates of change, chain rule, tangent planes. Lastly, know the implicit differentiation questions done in class. 4 Oct 26 14.5-14.8 Gradients, Directional Derivatives, The chain rule for F(t)=f(x(t),y(t)) and F(s,t)=f(x(s,t),y(s,t)) only, critical points and the second derivative test, Lagrange multipliers. There will be no question on maximizing a function f(x,y) on a closed bounded region. Also, for Lagrange multipliers, you will only be asked to optimize a function of two variables: max of f(x,y) subject to g(x,y) and not: max of f(x,y,z) ..... 5 Nov 16 15.1-15.4 (but not spherical coordinates in 15.4). Specifically double integrals in cartesian coordinates, interchanging limits of integration, double integrals in polar coordinates, triple integrals in cartesian (15.3) and cylindrical (15.4) coordinates. 6 Nov 30 15.4 (Spherical coordinates only), Knowing div(F), curl(F) and grad(V) in 16.1, 16.2 eqn 4 and 16.2 eqn 8, and conservative vector fields and line integral properties in 16.3, especially Theorem 1 and how to find potential functions. Midterm 1 Sep 28 12.1-12.5, 13.2-13.5       Review Sheet (50min, No electronic devices or notes/formula sheet)  recommended HW questions (above) and the Review Sheet especially are accurate representations of the kind of Midterm questions  50 minutes. No electronic devices, notes/formula sheet There will be no question on curvature There will be a question on tangential and normal acceleration There will be a question on arclength Midterm 2 Nov 2 a) 14.1-14.8 inclusive.    Review Sheet  (mostly corrected) b) 15-20% of the exam may be on Lagrange multipliers/ constrained optimization for problems of 2 or 3 variables (and one constraint), i.e f=f(x,y) or f=f(x,y,z), etc. c) There will be no problems involving maximing f(x,y) on a region like (7) in the Review Sheet above. Final Dec 11 4:00-5:50pm Location: Wil 1-138 (our classroom) Will cover all the material cover in Chapters 15-16 (above) and 17.3 (Divergence Theorem)  A review sheet is  Chapter 15-16 Review questions and examples   You have 1hr 50min but I'm trying to write a 75min exam. There will be 10 questions you'll be required to evaluate about half the integrals. The rest you will only be required to "set up" the integrals There will be: one double integral one reversing the order of integration on a double integral a triple integral in cartesian, cylindrical and spherical coordinates two line integrals (one conservative, one not) a surface integral a flux integral a Divergence Theorem question