01:640:300 - Introduction to Mathematical Reasoning
- Course Code: 01:640:300
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 3
- Counts toward math major/minor?: Yes
- Prerequisites: Math 250 or Calc III or special permission
General Information (Catalog Listing)
01:640:300 Introduction to Mathematical Reasoning (3)
Fundamental abstract concepts common to all branches of mathematics. Special emphasis placed on ability to understand and construct rigorous proofs. Prerequisite: 250 or 251 or 291 or permission of department.
This course is specifically intended to help Mathematics majors prepare for 640:311, 640:350, 640:351 and other proof-oriented courses.
It is required for any mathematics major who is not already experienced in doing mathematical proofs.
Students need to obtain a C or better in 640:300 in order to be eligible to take 640:311, 640:350, or 640:351.
If you are considering taking this course, please read this cautionary message.
Textbook
Textbook: For current textbook please refer to our Master Textbook List page
Schedule of Sections:
01:640:292 - Honors Calculus IV
- Course Code: 01:640:292
- Semester(s) Offered: Spring
- Credits: 4
- Counts toward math major/minor?: Yes
- Prerequisites: Math 291. Students who have taken Math 250 as well as Math 251 may also apply.
Description
01:640:291-292
Honors Calculus III,IV (4,4) Covers the same material as 01:640:251 and 252 in a more thorough and demanding fashion. Prerequisites: Permission of department. Prerequisites for 292: 01:640:291, or permission of the department.
Note: Students may not receive credit for more than one of the fourth-semester calculus courses 01:640:244, 252, or 292.
252 vs. 292
Math 252 is the fourth semester of calculus, following after multivariable calculus in the sequence Math 151, 152, 251. The subject is differential equations and after using one textbook for three terms, the fourth term has a different text.
Math 292 is a course in honors mathematics for students whose primary interest in the course is the mathematics it contains. Theorems may be proved in class and required on examinations.
The course makes use of linear algebra topics that are covered in Math 291 and Math 250.
Prerequisites
The “normal” prerequisites for Math 292 is Math 291. Students who have taken Math 250 as well as Math 251 (in an honors or a regular section) with outstanding results are welcome to apply during registration period. Applications for admission by special permission are available here.
Previous semesters
- Spring 2009. Prof. Wheeden
- Spring 2008. Sec. 01 Prof. R. Wheeden
- Spring 2007. Sec 01. Prof E. Teixeira
- Spring 2006. Prof. E. Teixeira
Schedule of Sections:
01:640:291 - Honors Calculus III
- Course Code: 01:640:291
- Semester(s) Offered: Fall
- Credits: 4
- Counts toward math major/minor?: Yes
- Prerequisites: Special permission only. Most students in Math 291 are incoming freshmen who scored a 5 on the AP Calculus BC exam.
Catalog Description
01:640:291. Honors Calculus III (4)
Covers the same material as 01:640:251 in a more thorough and demanding fashion.
251 vs. 251H vs. 291.
Math 251 continues the sequence begun with Math 151-152, usually with the same textbook and at the same level of rigor. The honors sections labeled 251H of Math 251 are (in general) intended for honors students in disciplines other than mathematics and are “more demanding versions of the same course.” By contrast, Math 291 is deliberately intended as a course in honors mathematics for students whose primary interest in the course is the mathematics it contains. The textbook may not be that used in other calculus courses, and the choice of course material is at the instructor's discretion to a greater extent than in other lower-division courses. Theorems may be proved in class and required on examinations, and “many variables” may mean n variables, not just 2 or 3.
Prerequisites
Most students who take Math 291 are incoming freshmen who scored a 5 on the AP Calculus BC exam. For more information, please contact the Head Advisor at <>.
Textbook
Textbook: For current textbook please refer to our Master Textbook List page
Schedule of Sections:
01:640:285 - Introduction to Interest Theory for Actuarial Science
- Course Code: 01:640:285
- Semester(s) Offered: Fall
- Credits: 3
- Counts toward math major/minor?: Actuarial track only
- Prerequisites: Calc III
General Information (Catalog Listing)
01:640:285 Introduction to Interest Theory for Actuarial Science (3)
Compound interest rate theory and application to valuation of financial instruments; measurement of interest; present value; equations of value and yield rates; amortization; annuities; bond valuation; duration; immunization.
Prerequisite: 01:640:251.
Textbook
Textbook: For current textbook please refer to our Master Textbook List page
Schedule of Sections
01:640:252 - Elementary Differential Equations
- Course Code: 01:640:252
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 3
- Counts toward math major/minor?: Yes
- Prerequisites: Math 250 and Calc III
General Resources
Textbook
Textbook: For current textbook please refer to our Master Textbook List page
Syllabus
A suggested syllabus is available. Dr. Sontag's section can find that syllabus and course material's in the course's Sakai website!
Supplements
Available supplements, in a uniform PDF format are collected here.
- N1 Introduction to first order equations, with an emphasis on modeling.
- RTB1 Euler's method, including error estimate and application to existence and uniqueness of solutions.
- N2 Some comments on bifurcations.
- N3 Some Remarks on Phase Planes.
- N4 Introduction to Matrix Exponentials.
- RTB2 An easily remembered formula for exponentials of matrices with complex eigenvalues.
- BW1 The method of variation of parameters for solving inhomogeneous systems.
Math 252 Syllabus for Third Edition of Blanchard, Devaney and Hall
Students in Section 2, Spring 06, should instead use the syllabus linked from that section's webpage
This syllabus is intended as a general outline of the course. It was originally written by E. Sontag for the first edition of the text and adapted to the second edition by R. Wheeden and to the third edition by E. Sontag (Jan 06). Individual instructors may alter its pace, assign different homework, and add or delete topics. Some variations will be described briefly in the notes following the syllabus. Note: The main difference between the 2nd and 3rd Editions is that old Section 1.8 is now "1.9", and a new section 1.8 has been inserted. In addition, many homework problems have been renumbered, and some new problems have been inserted.
Assignments usually refer to sections of the textbook. A designation such as N4 is a link to a supplementary note.
| # | Sections | Subjects | Assignments | Notes |
|---|---|---|---|---|
| 1 | N1 | Modeling | all ( answers) | |
| 2 | 1.1 | Modeling (continued) | 3, 5, 15, 17, 19, 21. | |
| 1.2 | Separation of Variables | 1, 3, 7, 13 | ||
| 3 | 1.2 | Separation of Vars (continued) | 25, 29, 31, 35. | |
| 4 | 1.3 | Slope Fields | all odd 1-13, 14, 15, 17. | a |
| 5 | 1.4 | Euler's Method | 1, 13, 15. | |
| 1.5 | Existence and Uniqueness | 1, 3, 5, 7, 10. | b | |
| 1.6 | Equilibria and Phase Line | 1, 3, 5, 7, 13, 15, 23, 25, 27, 31, 33, 37, 39, 43. | ||
| 6 | N2 | Bifurcations | (No exercises in N2) | |
| 1.7 | 1, 3, 5, 9, 11, 17. | |||
| 7 | 1.8 | Linear Differential Equations | all odd 1-13, 21, 23. | |
| 1.9 | Integrating Factors | all odd 1-11, 21, 23. | ||
| 8 | 2.1 | Modelling via Systems | 1, 2, 7, 8, 9, 17, 19, 21, 23, 25, 26, 27, 29. | c |
| 9 | 2.2 | Geometry of Systems | all odd 1-27. | a |
| 10 | 2.3 | Analytic Methods | all odd 1-11, 19. | d |
| 2.4 | Euler's Method | 1, 3, 5, 14, 15. | ||
| 11 | N3 | Phase Plane | all (answers) | e |
| 12 | exam 1 | Through 2.2 included | ||
| 13 | 3.1 | Linear Systems | all odd 1-9, 13, 17, 19, 21, 27, 29, 33, 35. | f |
| N4 | Matrix Exponentials | g | ||
| 14 | N4 | Matrix Exponentials (continued) | all (answers) | g |
| 15 | 3.2 | Straight-Line Solutions | all odd 1-19 | |
| 16 | 3.3 | Phase Plane: Real Eigenvalues | all odd 1-15. | |
| 17 | 3.4 | Phase plane: Complex Eigenvalues | all odd 1-15, 19, 21, 23. | |
| 18 | 3.5 | Repeated and Zero Eigenvalues | all odd 1-17. | |
| 19 | 3.7 | The Trace-Determinant Plane (emphasizing one-parameter families) |
parts "c" of: 3, 7, 11, 13. | h |
| 20 | 3.6 | Second-Order Linear | all odd 13-29; 36(a,b). | h,i |
| 21 | 3.8 | 3-Dim Linear | 4, 5, 6, 7. | |
| 22 | 4.1 | Forced Harmonic Oscillators | all odd 1-41. | |
| 4.2 | Sinusoidal Forcing | odd 1-13, 17, 27. | ||
| 23 | exam 2 | 2.3/3.7 (lectures 10/20) | ||
| 24 | 4.4 | Steady State | Special exercises. | j |
| 25 | 4.3 | Resonance | all odd 1-17, 21 | |
| 26 | 5.1 | Equilibria, Linearization | all odd 1-17, except 5. | h |
| 27 | 8.1 | Discrete Systems | all odd 1-9, 15, 19, 23, 27, 31. | |
| 28 | 8.2 | Fixed/Periodic points | 1, 7, 9, 13, 15. | k |
| 29 | final exam | all material covered during the semester | ||
Notes:
a. For numerical assignments, there is a package available in the CD ROM that comes with the book. A strongly suggested alternative is the Java Applet, JOde, which runs on any Java-enabled browser, including those at the University computer labs. Assignments using JOde will be posted to the Section 2, Spring 06 webpage
b. The existence and uniqueness theorem may be applied in abutting regions with continuity across the boundary to allow for piecewise continuous forcing functions. Projects exploring this have been used in the course.
c. Sections 2.1/2.2 are not really different, and should studied (and possibly lectured upon) simultaneously. Even 2.3 and 2.4 are not very different, actually.
d. The material on damped harmonic oscillator does not fit well with the topic of section 2.3, and may be deferred until the topic is considered in more detail in chapter 4.
e. Instead of the emphasis on exact trajectories in N3 and related supplements, instructors may introduce isoclines at this point to help guess phase plane portaits in simple cases like saddle points. The aim should be to complement the study of straight line solutions to appear in section 3.2 rather than to insert all of section 5.2 into the syllabus at this point.
f. Note to students: please make sure to review eigenvalues and eigenvectors from your linear algebra notes (which you kept from when you took the course!)
g. Some instructors may wish to skip the notes N4. The matrix exponential, while a useful topic (developed further in notes elaborating on the case of complex eigenvalues) , may be omitted. The time saved could be used to introduce variation of parameters.
h. Instructors may wish to introduce some or all of section 5.1 when discussing sections 3.6 and 3.7. Students should notice that phase planes for linear systems help predict those for nonlinear ones. Section 5.1 is an important part of the course; if it is not introduced in connection with sections 3.6 and 3.7, instructors should be sure to give adequate coverage later.
i. Problem 36(c) is worth looking at - the design of active automobile suspension systems is an area of much current research (at places like Ford, for example) - this question can be taken as an open ended one - be creative, and perhaps introduce nonlinear damping and nonlinear springs!
j. The exercises for 4.4 are to write the steady-state solution of the odd problems 1-9 of section 4.2 in the form A cos(wt+f).
k. Instructors emphasizing bifurcations should aim to allow more time for chapter 8 in order to include sections 8.3 and possibly also 8.4.
Schedule of Sections
Past Semester Pages
- Spring 2002
- Spring 2001 (Prof. Han's section)
- Spring 2000
01:640:251 - Multivariable Calculus
- Course Code: 01:640:251
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 4
- Counts toward math major/minor?: Yes
- Prerequisites: Calc II
General Information:
01:640:251 Multivariable Calculus (4 Credits)
This course covers multi-variable and vector calculus. Topics include analytic geometry of three dimensions, partial derivatives, optimization techniques, multiple integrals, vectors in Euclidean space, and vector analysis.
Prerequisite: Math 152
Textbook:
Thomas' CALCULUS Early Transcendentals, 15/e, by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 978-0137559756
MyMathLab access with etext: ISBN: 978-0137560103
MyMathLab access can be purchased directly from Pearson.
Standard Syllabus, and Homework
- Syllabus
- Lecture Topics
- Exam Protocols
- MyLab - Online Homework
- Grading Weights
- Practice exams and review materials
- There is a Canvas course site for each lecture group where all grades, exam reviews, syllabus, etc., are posted. You can access your Canvas course at https://canvas.rutgers.edu/.
Lecture Topics & textbook homework for Math 251
This is a very rapid plan of study. A great deal of energy and determination will be needed to keep up with it. Modifications may be necessary. Periodic assignments (matlab labs, workshops, etc.) may be due at times, and additional problems may be suggested.
The text is the 15th edition of Thomas' CALCULUS Early Transcendentals, by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 978-0137559756
Lecture Topics and Suggested Textbook Problems for 640:251
| Lecture | Topic(s) and text sections | Suggested Homework |
|---|---|---|
| 1 | 12.1 Three Dimensional Coordinate Systems 12.2 Vectors |
12.1/ #3,9,15,16,21,23,39,59 12.2/ #9,19,23,25,31,41,47 |
| 2 | 12.3 The Dot Product | 12.3/ #3,13,18,19,22 |
| 3 | 12.4 The Cross Product | 12.4/ #7,15,21,23,27,33,35,45 |
| 4 | 12.5 Lines and Planes in Space | 12.5/ #6,9,23,27,31,37,41, 47, 57 |
| 5 | 12.6 Cylinders and Quadric Surfaces | 12.6/ #1-12, 13, 15, 21, 25 |
| 6 | 13.1 Curves in Space and Their Tangents 13.2 Integrals of Vector-Valued Functions, Projectile Motion |
13.1/ #1,15,19,23, 31 13.2/ #3,5,8,11,15,19 |
| 7 |
13.3 Arc Length in Space 16.1 Line Integrals of Scalar Functions |
13.3/ #5,9,13 16.1/ #1-9,14,15,25,26,29,35,36 |
| 8 | 14.1 Functions of Several Variables | 14.1/ #6,9,15-18,27,31,41,58,59 |
| 9 | 14.2 Limits and Continuity in Higher Dimensions | 14.2/ #11,15,20-22,31,47,48,53,59 |
| 10 | 14.3 Partial Derivatives 14.4 The Chain Rule |
14.3/ #9,14-18,27,3046,67 14.4/ #7,28,29,33,39,44 |
| 11 | 14.5 Directional Derivatives and Gradient Vectors | 14.5/ #3-6,9,10,21,28,29,31 |
| 12 | Exam 1 covering 12.1-12.6, 13.1-13.3, 14.1, 14.2, 16.1 | |
| 13 | 14.6 Tangent Planes and Differentials | 14.6/ #5,9,13,19,21,31 |
| 14 | 14.7 Extreme Values and Saddle Points | 14.7/ #13,19,29,33,35,43,45,62 |
| 15 | 14.8 Lagrange Multipliers | 14.8/ #1,5,9,13,17,21,29 |
| 16 | 15.1 Double and Iterated Integrals Over Rectangles 15.2 Double Integrals over General Regions |
15.1/ #7,11,13,18,23,27,29,36 15.2/ #1-8,12,15,18,23,29,35,38,43,53 |
| 17 | 15.2 Double Integrals over General Regions 15.3 Area by Double Integration |
15.3/ #6-8,16,18,21 |
| 18 | 15.4 Double Integrals in Polar Form | 15.4/ #1-6,9,11,16,23,25,28,35 |
| 19 | 15.5 Triple Integrals in Rectangular Coordinates | 15.5/ #3,6,17,21,27,28,37,45 |
| 20 | 15.7 Triple Integrals in Cylindrical and Spherical Coordinates | 15.7/ #3-7,13-17,25,31,38,47,59,65 |
| 21 | 15.8 Substitution in Multiple Integrals | 15.8/ #1,3,6,7,9 |
| 22 | Exam 2 covering 14.3-14.8, 15.1-15.4 | |
| 23 | 16.2 Vector Fields & Line Integrals: Work, Circulation, Flux |
16.2/ #3,7,11,14,15,18,25,27,29,30,35,39,40,57,59 |
| 24 | 16.2 Vector Fields & Line Integrals: Work, Circulation, Flux 16.3 Path Independence, Conservative Fields, Potentials |
16.3/ #3,5,9,11,19,22,25,29,31 |
| 25 | 16.4 Green's Theorem in the Plane | 16.4/ #2,5,9,13,16,17,21,29,31,37 |
| 26 | 16.5 Surfaces and Area 16.6 Surface Integrals |
16.5/ #1,7,11,13,15,27,41,43 16.6/ #3,5,6,17,23,26,28,43 |
| 27 | 16.7 Stokes' Theorem | 16.7/ #5,7,11,19,23,28 |
| 28 | 16.8 The Divergence Theorem & A Unified Theory | 16.8/ #9,11,13,15,27,28 |
MyLab - Online Homework
Students are required to purchase access to MyLab Math to complete the online homework, and possibly quizzes and exams. The MyLab assignments are similar to the exercises in the official list of HW exercises. (The official HW exercises are not handed in for grading but instead form a significant, but not exhaustive, portion of your study guide for the course.) Each assignment will have a specific due date set by the professor, and these assignments must be completed online.
How to use MyLab properly:
If you take shortcuts like trying to find answers to MyLab problems from various "homework help" web services without solving all of the problems yourself in their entirety, then your performance on exams will suffer. Instead, use the built-in help tools within MyLab. This online homework exists primarily to give you feedback on your ability to calculate correct answers at early stages of the learning process. The homework is not intended to measure your mastery of the material; only the midterm exams and final exam measure mastery. Without doing well on the exams, it is impossible to pass the course, even with a perfect score on the homework. So be sure to take full advantage of MyLab to get as much feedback as possible on your problem-solving skills.
Getting started with MyLab:
- You will be able to access your MyLab course directly through your Canvas site for Math 251.
- In your Canvas site, navigate to MyLab and Mastering and follow the on-screen instructions to create a Pearson account (or link an existing Pearson account) to your Canvas account.
- You will automatically be enrolled in the MyLab course.
- If you switch to a different section of Math 251, you can enroll in your new section's MyLab course by following these same instructions.
Student support for MyLab:
- System RequirementsMyLab works on a series of pop-up screens. You MUST enable pop-ups when working in MyLab. For help on how to do this, as well as make sure your browser is up to date, use the link above.
- How to Use MyLab on a Mobile Device
This video shows you how to set up your mobile device with any necessary browser add-ons and apps to use MyLab properly. - Pearson Support Database
Use the above link to search Pearson's database for support topics (e.g., resetting password). - Contact SupportUse the above link to contact technical support. Fill out the required form and you will be immediately connected to a support agent based on your issue.
- Pearson sales representative: Melissa Blum is our Pearson Sales representative. If you are having technical issues, please first contact Technical Support. If you are still having issues after contacting Technical Support, please email Melissa Blum with the Incident Number you received from working with Technical Support. You must have an Incident Number for Melissa to be able to help.
Other information about MyLab:
- MyLab is an interactive, online homework system. The assignments follow the lecture topics.
- Questions are algorithmically generated to give each student their own random versions of the questions.
- After entering an incorrect answer, students are given helpful feedback and hints. Most exercises will also include learning aids, such as guided solutions and sample problems.
- You have three attempts to get an answer correct. If you use all three attempts, you will be told the correct answer and given a new, random version of the same problem. There is no limit to the number of versions of a particular problem you can be given. So you are strongly encouraged to work on a problem until you get the correct answer. There is no penalty for the number of attempts taken.
Grading Weights
| Component | Weight |
|---|---|
| Classwork | 20% of grade |
| ------------- | |
| Track 1: | Midterm 1 (24%), Midterm 2 (24%), Final Exam (32%) |
| Track 2: | Midterm 1 (20%), Midterm 2 (20%), Final Exam (40%) |
| ------------ | In order to pass the course with a C or higher, you must receive at least a 30 out of 150 on the final exam. That is, you must score at least a 20% on the final exam |
| Your score will be computed using both tracks and you will receive the highest grade |
Letter Grade Cutoffs
Solutions to practice exams and additional documents
Extra Problems 251 if you have finished working on the practice exams and additional review material provided by your instructor, you may want to check this list of problems if you want to do additional practice problems. Some of these are more conceptual in nature, so they may be useful to enhance your understanding of the course material. https://www.dropbox.com/scl/fi/zf60bu894t8bvf5j85nwl/extra-problems-251.pdf?rlkey=jb0yvp3962ji90p4wq377wt2c&st=pwazkd3n&dl=0
Practice Exams and Study Guides
https://www.dropbox.com/scl/fo/hbqc979lyn7y7qoa5jlsm/AMaNEKklTcGaaqgTniTgaGs?rlkey=zig2h25nkh2quk23ms0f3c94q&st=g24pfnuf&dl=0
Schedule of Sections:
01:640:250 - Introductory Linear Algebra
- Course Code: 01:640:250
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 3
- Counts toward math major/minor?: Yes
- Prerequisites: Math 112 or Math 115 or placement
General Information (Catalog listing)
Prerequisite: Precalculus (Math 115 or 111-112) or placement into calculus
Systems of linear equations, Gaussian elimination, matrices and determinants, vectors in two- and three-dimensional Euclidean space, vector spaces, introduction to eigenvalues and eigenvectors. Possible additional topics: systems of linear inequalities and systems of differential equations.
Updated description
Systems of linear equations, Gaussian elimination, Vectors in n-space, Span and linear independence of a set of vectors, Linear Transformations, Matrix algebra, Determinants, Vector spaces, Basis and dimension, Coordinate vectors and change of coordinates, Eigenvalues and eigenvectors, Diagonalization of a matrix, Geometry of vectors, Orthogonality, Symmetric matrices.
(current, 2025)
Textbook
Textbook: For current textbook please refer to our Master Textbook List page
The details of the syllabus and the timing of the midterm exams will vary from section to section. Each section of Math 250 has its own midterm exams and final exam. The final exam times are determined from the class meeting times. The room of the final exam may or may not be the usual lecture room! See the Final Exam schedule or the Math Department main website for updated details about final exams, when this information is available.
Course materials for all sections of Math 250
- Suggested syllabus ( PDF Format )
- Suggested homework problems ( coming soon )
Course materials for Math 250C1, C2, and C3 ---the MATLAB sections
Suggested examination review materials for all sections of Math 250
- Suggested review problems for First Midterm Exam: problems brief solutions
- Suggested review problems for Second Midterm Exam: problems brief solutions
- Suggested review problems for Final Exam: problems brief solutions
Students are expected to follow the Rutgers Standards of Academic Integrity on the assignments, quizzes and exams in the course.
Another Resource for MATLAB
(Note: for the MATLAB Assignments for the MATLAB Sections C1, C2, and C3, please refer to the Math 250C webpage instead)
- Matlab Tutorial (from MIT)
Schedule of Sections:
01:640:244 - Differential Equations for Engineering and Physics
- Course Code: 01:640:244
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 4
- Counts toward math major/minor?: Yes
- Prerequisites: Calc III
General Information
01:640:244 Differential Equations for Engineering and Physics (4)
First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations.
Prerequisite: CALC3. Credit restriction CR4.
Course Learning Goals: The specific learning goals for this course can be found on the document here. In addition, this document contains a list of recommended problems from each section of the textbook. These problems cover most of the essential topics that will be discussed during this course.
Textbook: The current textbook used for this course is Differential Equations: An Introduction for Engineers. This is a freely available textbook that was written to fit the desired structure and sequencing of this course. The PDF version can be found here: https://sites.rutgers.edu/matthew-charnley/course-materials/differential-equations-an-introduction-for-engineers/.
Special Accommodations: Students with disabilities requesting accommodations must follow the procedures outlined at https://ods.rutgers.edu/students/applying-for-services
Academic Integrity: All Rutgers students are expected to be familiar with and abide by the academic integrity policy (http://academicintegrity.rutgers.edu/academic-integrity-policy). Violations of the policy are taken very seriously.
Approximate Syllabus, Math 244
All section numbers refer to Charnley, Differential Equations: An Introduction for Engineers, version 0.9.
NOTE: This is a suggested syllabus, which individual instructors may revise.
| Lecture | Sections Covered | Assignments (Reading, MATLAB) | Lecture | Sections Covered | Assignments (Reading, MATLAB) | |
|---|---|---|---|---|---|---|
| 1 | 0.1, 0.2, 1.1, 1.2 | MATLAB 1 | 15 | Review, 2.7 | MATLAB 5 | |
| 2 | 1.3 | 16 | Exam 2 | |||
| 3 | 1.4 | 17 | 3.1, 3.2 | |||
| 4 | 1.2, 1.5, 1.6 | MATLAB 2 | 18 | 3.3 | ||
| 5 | 1.7, 1.8 | 19 | 3.4, 3.5 | |||
| 6 | 1.10, 1.11 | 20 | 3.6 | MATLAB 6 | ||
| 7 | Review | MATLAB 3 | 21 | Review, 4.1, 4.3 | ||
| 8 | Exam 1 | 22 | Exam 3 | |||
| 9 | 2.1 | 23 | 4.4 | |||
| 10 | 2.2 | MATLAB 4 | 24 | 4.5. 4.6. 4.7 | MATLAB 7 | |
| 11 | 2.3 | 25 | 4.8 | |||
| 12 | 2.4 | 26 | 5.1 | |||
| 13 | 2.5 | 27 | 5.2 | MATLAB 8 | ||
| 14 | 2.6 | 28 | 5.3, Review |
MATLAB in Math 244
Math 244 uses MATLAB assignments to given an opportunity for students to explore the computational side of differential equations and see how MATLAB can be used to solve and visualize these equations. Assignments and due dates will be decided by individual instructors. In order to complete the assignments, students will need the supplemental MATLAB functions as well as format files that outline the details of each assignment.
All of the information for these assignments are available to current students of Math 244. This is available on your section's Canvas site. There you will find information about when the assignments are due, how to submit them, and extra resources that are available to help with these assignments. The MATLAB On-Ramp can also be helpful for a review/introduction to Matlab if needed.
Schedule of Sections:
01:640:152 - Calculus II for the Mathematical and Physical Sciences
- Course Code: 01:640:152
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 4
- SAS Core Certified: QQ, QR
- Counts toward math major/minor?: Yes
- Prerequisites: Calc I (Math 135 or Math 151, not Math 130)
Math 152 (Calculus II for Math and Physical Sciences) is a continuation of Math 151, and is part of the three-semester calculus sequence for the mathematical and physical sciences at Rutgers University, New Brunswick. Math 152 covers the integral calculus and its applications, the theory of infinite series and power series, parametric curves, polar coordinates, and complex numbers.
All sections of Math 152 (other than asynchronous online sections) will have two lecture meetings and one workshop meeting per week. The Lecturer presents the course material during the lecture meetings. The workshop class is a smaller meeting with a Workshop Instructor (WI), where students engage in group work to solve in-depth problems related to the content delivered in the lectures. Workshops typically require students to complete a pre-class assignment, a write-up of their in-class activity results, and a short quiz following the problem-solving session. The workshop problems will form the basis for some of the problems that students will encounter on midterm quizzes and on the final exam.
The required textbook is Thomas' Calculus: Early Transcendentals (15th edition), by Hass, et al. with MyMathLab access code. You may use either the hardcover edition or the eBook; they contain exactly the same material. Both are available through the Rutgers bookstore, and the eBook can be purchased directly through the course canvas page.
- The ISBN for the physical textbook with MyMathLab access is 978-0137559756.
- The ISBN for the eBook with MyMathLab access is 978-0137560103.
Math 152 covers parts of Chapters 5, 6, 8, 10, 11 and 18 of the textbook. The course sets the following learning goals for each student:
- To use integrals to find volumes, arc lengths, and surfaces of revolution.
- To find antiderivatives using techniques including u-substitution, integration by parts, and trigonometric substitution.
- To determine whether an infinite series converges, and to find and use Taylor series and Taylor polynomials.
- To use derivatives and integrals with parametric equations, and with equations defined in polar coordinates.
- To use polar and exponential forms of a complex number.
A more detailed list of learning goals can be found here.
Typical Lecture Schedule (may vary slightly by semester)
| Lecture | Textbook Sections | Topics |
| 1 | 5.3, 5.5, 5.6, 8.1 | Review of basic integration formulas, average value, u-substitution, and area under curves |
| 2 | 6.1 | Volume by cross-sections (including disk/washer method) |
| 3 | 6.2 | Volume by shells; other applications |
| 4 | 6.3 | Arc length and surface area |
| 5 | 6.4 | Arc length and surface area |
| 6 | 8.2 | Integration by Parts |
| 7 | Midterm Exam 1 | |
| 8 | 8.3 | Trigonometric integrals |
| 9 | 8.4 | Trigonometric substitution |
| 10 | 8.8 | Improper Integrals |
| 11 | 10.1 | Sequences |
| 12 | 10.2 | Infinite series |
| 13 | 10.3 | The Integral Test |
| 14 | Midterm Exam 2 | |
| 15 | 10.4 | Comparison tests |
| 16 | 10.5 | Ratio/Root tests and absolute convergence |
| 17 | 10.6 | Alternating series and conditional convergence |
| 18 | 10.7 | Power series |
| 19 | 10.8 | Taylor and Maclaurin series |
| 20 | 10.9 | Convergence of Taylor series |
| 21 | 10.1 | Applications of Taylor series |
| 22 | Midterm Exam 3 | |
| 23 | 11.1, 11.2 | Parametrizations of plane curves; Calculus with parametric curves |
| 24 | 11.3,11.4 | Polar coordinates; graphing polar equations |
| 25 | 11.5 | Areas and lengths in polar coordinates |
| 26 | 18.1 | Arithmetic and Geometry of Complex Numbers |
| 27 | 18.1 | Euler's Theorem and Polar Forms of Complex Numbers; Finding complex roots of polynomials. |
Specific course information, resources, and policies for the current semester are available to course registrants through the Math 152: All Sections Canvas site.
Schedule of Sections:
01:640:151 - Calculus I for the Mathematical and Physical Sciences
- Course Code: 01:640:151
- Semester(s) Offered: Fall, Spring, Summer
- Credits: 4
- SAS Core Certified: QQ, QR
- Counts toward math major/minor?: Yes
- Prerequisites: Math 112 or Math 115 or placement
Math 151 (Calculus I for Math and Physical Sciences) is the first semester of the three-semester calculus sequence for the mathematical and physical sciences at Rutgers University, New Brunswick. Math 151 covers differential calculus of the elementary functions of a single real variable: the rational, trigonometric, and exponential functions and their inverses; various applications via the Mean Value Theorem; and an introduction to the integral calculus.
All sections of Math 151 will have two lecture meetings and one workshop meeting per week. The Lecturer presents the course material during the lecture meetings. The workshop class is a smaller meeting with a Workshop Instructor (WI), where students engage in group work to solve in-depth problems related to the content delivered in the lectures. Workshops typically require students to complete a pre-class assignment, a write-up of their in-class activity results, and a short quiz following the problem-solving session. The workshop problems will form the basis for some of the problems that students will encounter on midterm exams and on the final exam.
Textbook and Online Homework: The required textbook is Thomas' Calculus: Early Transcendentals (15th edition), by Hass, et al. with MyMathLab access code. Students may use either the hardcover edition or the eBook; they contain the same material. Students must purchase MyMathLab access with their textbook. Both are available through the Rutgers bookstore.
- The ISBN for the physical textbook with MyMathLab access is 978-0137559756.
- The ISBN for the eBook with MyMathLab access is 978-0137560103.
Math 151 covers Chapters 1-5 of the textbook. The course sets the following learning goals for each student:
- To acquire the ability to compute limits, derivatives, and integrals of certain algebraic, trigonometric, exponential, and logarithmic functions.
- To achieve understanding of the notions of continuity and differentiability.
- To develop the ability to use first and second derivatives to determine the shape of the graph of a function.
- To acquire practice solving optimization problems using calculus.
A more detailed list of learning goals can be found here.
Specific course information, resources, and policies for the current semester are available to course registrants through the Math 151: All Sections Canvas site.