Spring  2024

To help you develop a solid understanding of what calculus is, and to equip you to use calculus effectively in subsequent courses and in your career. At the conclusion of this course you should:

• understand the fundamental concepts of calculus (functions, limits, derivatives, integrals, and transcendental functions)
• be able to apply the methods of calculus to solve real problems

Attendance is crucial for doing well in the course. Experience indicates that the students who do not attend the class regularly fail miserably. It is strongly recommended that you do not miss any class.

There will be one midterm test and a final exam. The final exam is a two-hour common comprehensive exam and there will be bi-weekly quizzes based on material covered in class. The quizzes will be 10-15 minutes long.

 2022 Final Exam (New! June 7)

2022 Spring Sample Final Exam

2017 SUMMER SAMPLE MIDTERM EXAM-II

2017 SUMMER SAMPLE MIDTERM EXAM

2017 Spring Sample Midterm Exam

2016 Spring Sample Final Exam I

2016 Spring Sample Final Exam II

2016 Spring Sample Final Exam III

2016 Spring Sample Final Exam IV

2016 Spring Midterm Exam

 2015 Spring Midterm Exam

2015 Spring Final Exam

Problem Set I

 Green’s/Stoke’s/Divergence Problems

Your grade will be calculated as follows:

40%Midterm Exam+ 60%Final Exam.

Unless otherwise indicated, all grades out of 100 will correspond to the following scale:

0 < F< 30, 31 < DF< 35, 36 < DD< 40,

41 < CD < 50,  51< CC < 60,  61 < CB < 70,

71 < BB< 80, 81 < BA< 90, 91 < A < 100.

From “Teaching at the University Level” by Stephen Zucker, Notices Amer. Math. Soc. 43(1996), p.863

1. You are no longer in high school. The great majority of you, not having done so already, will have to discard high school notions of teaching and learning and replace them by university-level notions. This may be difficult, but it must happen sooner or later, so sooner is better. Our goal is more than just getting you to reproduce what was told you in the classroom.

2. Expect to have material covered at two to three times the pace of high school. Above that, we aim for greater command of the material, especially the ability to apply what you have learned to new situations (when relevant).

3. Lecture time is at a premium, so it must be used efficiently. You cannot be “taught” everything in the classroom. It is YOUR responsibility to learn the material. Most of this learning must take place outside the classroom. You should be willing to put in two hours outside the classroom for each hour of class.

4. The instructor’s job is primarily to provide a framework, with some of the particulars, to guide you in doing your learning of the concepts and methods that comprise the material of the course. It is not to “program” you with isolated facts and problem types nor to monitor your progress.

5. You are expected to read the textbook for comprehension. It gives the detailed account of the material of the course. It also contains many examples of problems worked out, and these should be used to supplement those you see in the lecture. The textbook is not a novel, so the reading must often be slow-going and careful. However, there is the clear advantage that you can read it at your own pace. Use pencil and paper to work through the material and to fill in omitted steps.

6. (My additon) I want you to enjoy this class, but please respect my right to teach and your classmates’ rights to learn. I would like you to refrain from disruptive behavior (such as unnecessary talking), as well as from reading newspapers and other non-class materials during class. Also, please keep your cell phones turned off during class!!

• Three-Dimensional Coordinate Systems.
• Vectors.
• The Dot Product.
• The Cross Product.
• Equations of Lines and Planes.
• Cylinders and Quadric Surfaces.
• Cylindrical and Spherical Coordinates.

• Vector Functions and Space Curves.
• Derivatives and Integrals of Vector Functions.
• Arc Length and Curvature.
• Motion in Space: Velocity and Acceleration

• Functions of Several Variables.
• Limits and Continuity.
• Partial Derivatives.
• Tangent Planes and Linear Approximations.
• The Chain Rule.
• Directional Derivatives and the Gradient Vector.
• Maximum and Minimum Values.
• Lagrange Multipliers.

• Double Integrals over Rectangles.
• Iterated Integrals.
• Double Integrals over General Regions.
• Double Integrals in Polar Coordinates.
• Applications of Double Integrals.
• Surface Area.
• Triple Integrals.
• Triple Integrals in Cylindrical and Spherical Coordinates.
• Change of Variables in Multiple Integrals.

• Vector Fields.
• Line Integrals.
• The Fundamental Theorem for Line Integrals.
• Green’s Theorem.
• Curl and Divergence.
• Parametric Surfaces and Their Areas.
• Surface Integrals.
• Stokes’ Theorem.
• The Divergence Theorem.