Umd math 241

His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment.

View Test prep - FinalSpring2015soln from MATH 241 at University of Maryland. Math 241 Spring 2015 Final Exam Solutions 1. Find the equation of the plane containing the line x = y 1 = your finalDr. Justin Wyss-Gallifent. Principal Lecturer. 2236 Iribe. MATH115 Precalculus I haven't taught this course in maybe eight years but when I did, I typed up detailed notes. I can't vouch for the section numbers and I can't promise that MATH115 hasn't changed a bit, but I figured these notes might be useful to someone.Math 241 Exam 2 Fall 2018 Justin Wyss-Gallifent Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appro-priate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the problem. Please put problem 1 on answer sheet 1 1.Math 241, Spring 2014, Sections 03** Course Outline Time & Place MWF 2:00–2:50 ARM 0135 Instructor Dr. T. von Petersdorff, office MTH 4409, e-mail [email protected], office hours Tue 10–12 (or by appointment) Textbook Calculus w/ Concepts in Calculus (sixth edition) by Ellis and Gulick Syllabus (corresponding sections in the textbook are given in …MATH 241 - Mellet Calculus III Fall 2012 Review problems for the nal exam This is a selection of problems from exams given at the University of Maryland in the past few years. The exam may include material that is not on the review and the wording of questions may be somewhat di erent. Make sure that you do all suggested homework problems and ...Math 341 - Multivariable Calculus, Linear Algebra and Differential Equations II (Honors) ... Math 340. Topics. See the topics listed for Math 240, 241 and 246; and ...

The eight courses must include the following. At least one course from MATH 401, 403, 405. One course from AMSC 460, 466. MATH 410. A one-year sequence which develops a particular area of mathematics in depth, chosen from the following list: (i) MATH 410-411, (ii) MATH 403-404, (iii) Math 403-405, (iv) STAT 410-420.MATH 241, Spring 2014: Calculus III Vector field (F 1,F 2) with third curl component F 2x-F 1y shown by color: blue means clockwise, red means counterclockwise ... name@math means [email protected] Recommended Problems from the Textbook MATH 241 Resources. MATH241 Tutoring has started, see schedule.Completion of MATH 340 satisfies the requirement for MATH 241; completion of MATH 340-341 satisfies the requirement for MATH 240-241-246. 2. One course from MATH 246, 341, and 414. If MATH 414 is chosen it may count in requirement 3(g) below. ... Comments and questions to [email protected]: The Mathematics department is part ofHere's what I came up with from searching for class webpages: Contains samples and solutions for first four exams. One of Justin's Classes: Contains solutions for some exams and notes for others. Another of Justin's: Reply. Trying to find previous finals from MATH241 that have the correct answers to them as well.Apr 21, 2023 ... Chenzi Jin. 55 views · 8 months ago ...more. UMD Mathematics ... Math Professor Fixes Projector Screen (April Fools Prank) ... JR Tutorials•241K ...

MATH 241 Sections 03** Final Exam Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan and upload.A $27.2M Gift to the Math Department by the Brin Family. The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students.MATH 241 Calculus III Spring 2023 Groupwork 4: Sections 13.1-13.4 You should work on and discuss this worksheet with members of your group. Your TA will assist as needed. Turn in your solutions either on this sheet or a separate sheet of paper. Be sure to include your name! 1.For the surface f(x;y) = x2 y, sketch in one graph the level curves ...Or is it doable. MATH246 is differential equations. MATH241 is Calc 3. You don't need Calc 3 in order to take differential equations so you should be fine. However, they do recommend taking 241 first. In my experience, you should be able to teach yourself whatever you need to be successful even if you take them together.Math 241 Spring 2018 Final Exam • Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the first answer sheet. • Follow the instructions as to which problem goes on which answer sheet. You may use the

Fnaf vhs scream.

Dr. Justin Wyss-Gallifent. Principal Lecturer. 2236 Iribe. MATH115 Precalculus I haven't taught this course in maybe eight years but when I did, I typed up detailed notes. I can't vouch for the section numbers and I can't promise that MATH115 hasn't changed a bit, but I figured these notes might be useful to someone. MATH 241 Sections 03** Final Spring 2021 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan ...Mr. Aaron Skinner ([email protected]) Goals of the Course: The goal of MATH 241 is to learn multivariable calculus. The culmination of the course is chapter 15 which deals with the integral theorems which are essential for the derivation of the fundamental equations of classical physics (the heat equation, Maxwell's equations, the equations ... MATH 241 Sections 03** Final Spring 2021 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan ...

Math 241 Fall 2021 Final Exam Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the rst answer sheet. Follow the instructions as to which problem goes on which answer sheet. You may use the Math 241, Spring 2014, Sections 03** Course Outline Time & Place MWF 2:00–2:50 ARM 0135 Instructor Dr. T. von Petersdorff, office MTH 4409, e-mail [email protected], office hours Tue 10–12 (or by appointment) Textbook Calculus w/ Concepts in Calculus (sixth edition) by Ellis and Gulick Syllabus (corresponding sections in the textbook are given in …If you have a touchscreen Windows 10 device like a Surface, OneNote can now recognize handwritten math equations and will even help you figure out the solutions. If you have a touc...MATH 241 Sections 03** Exam 3 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan and upload ...His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment.Math 241 Exam 4 Spring 2019 Justin Wyss-Gallifent Directions: Do not simplify unless indicated. No calculators are permitted. Show all work as appropriate for the methods taught in this course. Partial credit will be given for any work, words or ideas which are relevant to the problem. Please put problem 1 on answer sheet 1 1.MATH 241 { CALCULUS III MATLAB PROJECT #1 { DUE OCTOBER 4 Instructions. This project is to be done using MATLAB. Use the diary command to save your work. Edit the saved le to include your name, problem numbers, and the answers to any questions asked in the problems. You should also hand in your printed output. Note Brief Summary Lecture Notes. Section 11.1; Section 11.2; Section 11.3; Section 11.4; Section 11.5; Section 11.6; Section 12.1; Section 12.2; Section 12.3; Section 12.4 MATH 241, Spring 2014: Calculus III Vector field (F 1,F 2) with third curl component F 2x-F 1y shown by color: blue means clockwise, red means counterclockwise ... name@math means [email protected] Recommended Problems from the Textbook MATH 241 Resources. MATH241 Tutoring has started, see schedule.MATH 241 { CALCULUS III MATLAB PROJECT #1 { DUE OCTOBER 4 Instructions. This project is to be done using MATLAB. Use the diary command to save your work. Edit the saved le to include your name, problem numbers, and the answers to any questions asked in the problems. You should also hand in your printed output. NoteMath 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ...

name@math means [email protected] Recommended Problems from the Textbook MATH 241 Resources. MATH241 Tutoring has started, see schedule. MATH241 Matlab Tutoring has started, see schedule. Previous exams for practicing: MATH 241, MATH 241H; How to Prepare Matlab Assignments. You have to write an m-file for each problem.

University of Maryland MATH 241 Expand/collapse global location MATH 241 Last updated; Save as PDF Page ID 33215 ... MATH 241 Last updated; Save as PDF Page ID 33215Spring Tutoring Schedule (We will be hiring more Math Majors as Math Hourly Tutors.) If you need tutoring you can also visit The Math Success Program (ESJ1224) offers FREE drop-in math coaching and collaborative small group math coaching for UMD students enrolled in many math and math-related courses. Start Date: Monday, February 5, 2024 … The Mathematics Department offers drop-in tutoring in Room 0301 of the Math Building. Note the many hours on the Drop-In Tutoring Schedule at which Math 241 TAs are available this semester Usually, it is better for you to make use of the many free opportunities for help, rather than pay someone not currently affiliated with the course ... MATH 241 Sections Exam 1 Spring 2021 (JWG) Exam Submission: 1. From the moment you download this exam you have three hours to take the exam and submit to Gradescope. This includes the entire upload and tag pro-cedure so do not wait until the last minute. 2. Tag your problems! Please! 3. You may print the exam, write on it, scan and upload. 4. 4176 Campus Drive - William E. Kirwan Hall College Park, MD 20742-4015 P: 301.405.5047 | F: 301.314.0827. Give to the Math DepartmentIf you have a touchscreen Windows 10 device like a Surface, OneNote can now recognize handwritten math equations and will even help you figure out the solutions. If you have a touc...An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.It gets hard around exam 3 time. First two exams should be a piece of cake, so make sure you do well on those. You can get an A for sure, you just need to study and be on top of your work often. I think one extremely beneficial habit is to stay absolutely on top of the homework, especially when it gets hard.Optimization. Critical points (a mupad notebook) and PDF version. Week of October 24 - October 28. 7. Lagrange Multipliers. Week of October 31 - November 4. 8. Double Integrals. Week of November 7 - November 11.MATH 241 Sections 03** Exam 3 Spring 2021 Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan ...

Early voting site crossword.

Is lacy aaron schmidt still in jail.

0132, 0142 TA: Thomas McCullough: [email protected] Office hours: Thu 1:00-3:00 in MTH 2119 Tutoring: There is official math department tutoring in MTH 0301 for MATH 241 during stated hours on the departmental tutoring schedule.MATH 241, Sec. 03xx: CALCULUS III (An Introduction to Multivariable Calculus) Department of Mathematics, UMCP Fall 2017 Handout 1: SYLLABUS AND POLICIES Date: Monday, 08/28/17Fall 2012 - Math 241 Calculus III Instructor: Antoine Mellet . Office: Math Building 3314. Classes: MWF 11:00am-11:50am (ARM 0126) ... This course is the third semester in the standard calculus sequence for students majoring in mathematics, engineering, and the physical sciences. The prerequisite is MATH 141 or 141H at UMCP or equivalent ...4176 Campus Drive - William E. Kirwan Hall College Park, MD 20742-4015 P: 301.405.5047 | F: 301.314.0827. Give to the Math DepartmentTrue to what your math teacher told you, math can help you everyday life. When it comes to everyday purchases, most of us skip the math. If we didn’t, we might not buy so many luxu...Math 241: Practice Problems for Exam 1 1. ConsiderthepointsP = (1;1;2),Q = (2;1;1),R = (1;2;1) (a) FindthesymmetricequationsofthelinethroughthepointsP andQ. Math 241 Fall 2021 Final Exam Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the rst answer sheet. Follow the instructions as to which problem goes on which answer sheet. You may use the MATH 241 Sections 03** Final Exam Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan and upload.Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ... ….

Virtually all engineering undergraduates at UMCP move through the freshman-sophomore level of the mathematics major -- MATH 140, 141, 241, 246, 240 (often with a comparable linear algebra course, such as MATH 461, in place of 240).The Math Success Program (ESJ1224) offers FREE drop-in math coaching and collaborative small group math coaching for UMD students enrolled in many math and math-related courses. University Libraries. (ONLINE) offers Statistical Consulting, they explain concepts - they do not tutor on homework. Currently specialize in SAS, SPSS, R, and provide ...Mr. Aaron Skinner ([email protected]) Goals of the Course: The goal of MATH 241 is to learn multivariable calculus. The culmination of the course is chapter 15 which deals with the integral theorems which are essential for the derivation of the fundamental equations of classical physics (the heat equation, Maxwell's equations, the equations ... MATH 241, Sec. 03xx: CALCULUS III (An Introduction to Multivariable Calculus) Department of Mathematics, UMCP Fall 2017 Handout 1: SYLLABUS AND POLICIES Date: Monday, 08/28/17 The OECD released its global education assessment index, known as PISA, on Tuesday, Dec. 3, and commentators predictably jumped on how countries compare in math, reading, and scien...It was a confident, high-powered investment firm with credit lines at top financial institutions. It made big bets using borrowed money to buy assets and generate higher returns. B...Math 241 Spring 2015 Final Exam. Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the first answer sheet. Follow the instructions as to which problem goes on which answer sheet. You may use the back of the answer sheets but if you do so, please write “See ...horizontal vectors in this guide because that’s how we think of them in Math 241, except with i, j and k. As a horizontal vector (like I’ll do) we use spaces or commas to separate values. u=[2,3,7] u = 2 3 7 We can put variables inside vectors too for VVFs and then take derivatives and stu like that: a=[t^2,1/t,2*t] diff(a) int(a,1,3) a ...4. The following integrals can be calculated using a theorem followed by an easy calculation. For each, state the theorem and evaluate. (a) Let Cbe parameterized by r(t) = t2 ^{+ tcost|^for 0 t ˇ. Umd math 241, Math 241, Spring 2014, Sections 03** Course Outline Time & Place MWF 2:00–2:50 ARM 0135 Instructor Dr. T. von Petersdorff, office MTH 4409, e-mail [email protected], office hours Tue 10–12 (or by appointment) Textbook Calculus w/ Concepts in Calculus (sixth edition) by Ellis and Gulick Syllabus (corresponding sections in the textbook are …, Whether you’re a teacher in a school district, a parent of preschool or homeschooled children or just someone who loves to learn, you know the secret to learning anything — particu..., Math 241 Fall 2018 Final Exam • Be sure your name, section number and problem number are on each answer sheet and that you have copied and signed the honor pledge on the first answer sheet. • Follow the instructions as to which problem goes on which answer sheet. You may use the , His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment., name@math means [email protected] Recommended Problems from the Textbook MATH 241 Resources. MATH241 Tutoring has started, see schedule. MATH241 Matlab Tutoring has started, see schedule. Previous exams for practicing: MATH 241, MATH 241H; How to Prepare Matlab Assignments. You have to write an m-file for each problem. , MATH 241 is the third semester of the calculus sequence for Mathematics, Physical Sciences, and Engineering majors. It deals with functions of several variables, and is more geometric in spirit than the earlier courses in this sequence. ... Department of Mathematics University of Maryland, MATH 241 Sections 03** Final Exam Exam Submission: 1.Submit this exam to Gradescope. 2.Tag your problems! 3.You may print the exam, write on it, scan and upload. 4.Or you may just write on it on a tablet and upload. 5.Or you are welcome to write the answers on a separate piece of paper if other options don’t appeal to you, then scan and upload., View MATH241_ALL-Sections_Fall2021_Final-Exam.pdf.pdf from MATH 241 at University of Maryland. AI Homework Help. Expert Help. Study Resources. Log in Join. MATH241 ALL-Sections Fall2021 Final-Exam.pdf.pdf - Doc Preview. Pages 2. Total views 9. University of Maryland. MATH. MATH 241. BrigadierCrab970., MATH 241, Sec. 03xx: CALCULUS III (An Introduction to Multivariable Calculus) Department of Mathematics, UMCP Fall 2017 Handout 1: SYLLABUS AND POLICIES Date: Monday, 08/28/17, Math 241, Spring 2014, Sections 03** Course Outline Time & Place MWF 2:00–2:50 ARM 0135 Instructor Dr. T. von Petersdorff, office MTH 4409, e-mail [email protected], office hours Tue 10–12 (or by appointment) Textbook Calculus w/ Concepts in Calculus (sixth edition) by Ellis and Gulick Syllabus (corresponding sections in the textbook are given in …, MATH 241: CALCULUS III (An Introduction to Multivariable Calculus)--Section 03xx Fall 2017 Instructor: Dionisios Margetis LARGE LECTURES: MWF, 11:00am -- 11:50am; Room: ARM 0126 Instructor's office hours: Mon & Wed, 12:00pm -- 12:50pm (after lecture); or by appointment. Regular office hours will start on Wed Sept. 6, Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ... , MATH 241: CALCULUS III (An Introduction to Multivariable Calculus)--Section 03xx Fall 2017 Instructor: Dionisios Margetis LARGE LECTURES: MWF, 11:00am -- 11:50am; Room: ARM 0126 Instructor's office hours: Mon & Wed, 12:00pm -- 12:50pm (after lecture); or by appointment. Regular office hours will start on Wed Sept. 6, Math 241 No MetaData for Search Engine Optimization. Math 241 No RRRR Department of Mathematical Sciences. University of Delaware. 501 Ewing Hall. Newark, DE 19716, USA. Phone: 302-831-2653. [email protected]. Site Map ©2024 University of Delaware. Comments. Legal Notices ..., Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ..., For me last semester, quizzes were every Thursday, and had one problem from the homework and 1–2 other problems. The exception was if we just had an exam, in which case the quiz was sometimes on Tuesday depending on when the exam was and the quiz was just solving a problem from the exam (which the TA walks through before). 1. Reply., The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and …, MATH 241: CALCULUS III (An Introduction to Multivariable Calculus)--Section 03xx Fall 2017 Instructor: Dionisios Margetis LARGE LECTURES: MWF, 11:00am -- 11:50am; Room: ARM 0126 Instructor's office hours: Mon & Wed, 12:00pm -- 12:50pm (after lecture); or by appointment. Regular office hours will start on Wed Sept. 6, 4176 Campus Drive - William E. Kirwan Hall College Park, MD 20742-4015 P: 301.405.5047 | F: 301.314.0827. Give to the Math Department, Answers should be neat and tidy and complete. 1. Let Lbe the line with symmetric equation: x 1 2 = z 3 ; y = 2 Let Pbe the plane with equation: 2x+ y 3z = 1 (a) Find the point at which Lmeets P. [10 pts] (b) At this point, what is the cosine of the angle between Land the normal vector for P? [15 pts] (c) If you went to the point on the line ..., The lecturer in these sections of MATH 241 is Professor Jonathan Rosenberg . His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment., Justin: jow@math. Description: Math 241 is the most advanced of the three basic calculus courses. We shall cover such topics as vectors, vector-valued functions, multiple integrals, line and surface integrals as well as the important fundamental calculus theorems. Book: The book is Calculus, Ellis & Gulick, 6th Edition (ISBN 0-759-31379-2)., The lecturer in these sections of MATH 241 is Professor Jonathan Rosenberg . His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment., It gets hard around exam 3 time. First two exams should be a piece of cake, so make sure you do well on those. You can get an A for sure, you just need to study and be on top of your work often. I think one extremely beneficial habit is to stay absolutely on top of the homework, especially when it gets hard., An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss., Math 241 Σxam 3 Spring 2018 Solution R ustin ∇∇yss-Gallifent 1. (a) Reparametrize the following integral as vertically simple and then evaluate. [15 pts] This is the only integral you need to evaluate. Z 4 0 Z √ y 1 2y xdxdy Solution: Picture omitted. We have: Z 4 0 Z √ y 1 2y xdxdy = Z 2 0 Z 2x x2 xdydx = Z 2 0 xy x x2 dx = Z 2 0 x(2x ..., Mathematics Department Site. MATH241. Calculus III. Syllabus Repository (3) Credits: 4. : Prerequisite: Minimum grade of C- in MATH141. Credit only granted for: MATH241 or …, Math 140, Math 141 and permission of the department. Incoming students can request permission to register for Math 340 by sending an e-mail to . Topics. The topics listed for Math 240, 241 and 246 are covered in Math 340-341, in greater depth. In addition there is supplementary material from differential geometry, Fourier series and calculus of ..., The lecturer in these sections of MATH 241 is Professor Jonathan Rosenberg . His office is in room 2114 of the Mathematics Building, and his university phone extension is 55166. (Calling from outside the university, call 301-405-5166.) He will generally hold office hours Mondays and Wednesdays 10:00-11:00, or by appointment., MATH 241, Spring 2014: Calculus III Vector field (F 1,F 2) with third curl component F 2x-F 1y shown by color: blue means clockwise, red means counterclockwise ... name@math means [email protected] Recommended Problems from the Textbook MATH 241 Resources. MATH241 Tutoring has started, see schedule., math 241 -- calculus iii An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss., Math 241 No MetaData for Search Engine Optimization. Math 241 No RRRR Department of Mathematical Sciences. University of Delaware. 501 Ewing Hall. Newark, DE 19716, USA. Phone: 302-831-2653. [email protected]. Site Map ©2024 University of Delaware. Comments. Legal Notices ..., math 241 -- calculus iii An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.