Calculus III
Text: Calculus Early Transcendentals (9th ed.), Stewart, Clegg, Watson.
| Section | Topics | Class |
|---|---|---|
| 12.2 | Vectors (omit applications) | 1 |
| 12.3 | The Dot Product (omit direction angles and cosines, work) | 1 |
| 12.4 | The Cross Product (omit torque) | 2 |
| 12.5 | Equations of Lines and Planes | 3 |
| 12.6 | Cylinders and Quadric Surfaces (review) | 4 |
| 14.1 | Functions of Several Variables | 4 |
| 14.2 | Limits and Continuity (only cover epsilon delta definition) | 5 |
| 14.3 | Partial Derivatives (omit PDEs) | 6 |
| 14.4 | Tangent Planes and Linear Approximations | 7 |
| 14.5 | The Chain Rule | 8 |
| EXAM | Exam 1: Monday 15 June | 9 |
| 14.6 | Directional Derivatives and the Gradient Vector | 10 |
| 14.7 | Maximum and Minimum Values | 11 |
| 15.1 | Double Integrals over Rectangles | 12 |
| 15.2 | Double Integrals over General Regions | 13 |
| 15.3 | Double Integrals in Polar Coordinates | 14 |
| 15.4 | Applications (omit gyration and probability) | 15 |
| EXAM | Exam 2: Monday 29 June | 16 |
| 15.6 | Triple Integrals | 17 |
| 15.7 | Triple Integrals in Cylindrical Coordinates | 18 |
| 15.8 | Triple Integrals in Spherical Coordinates | 18 |
| 10.1 | Curves Defined by Parametric Equations (omit graphing with technology) | 19 |
| 13.1 | Vector Functions and Space Curves (omit using technology) | 20 |
| 13.2 | Derivatives and Integrals of Vector Functions (omit integrals) | 21 |
| 13.3 | Arc Length and Curvature (omit curvature, normal and binormal vectors, torsion) | 21 |
| EXAM | Exam 3: Monday 13 July | 22 |
| 16.1 | Vector Fields | 23 |
| 16.2 | Line Integrals | 24 |
| 16.3 | The Fundamental Theorem for Line Integrals | 25 |
| 16.4 | Green's Theorem | 26 |
| 16.5 | Curl and Divergence (vector forms of Green's Theorem) | 27 |
| 7/22 | Review | 28 |
| FINAL | Final Exam: Tuesday 28 July | 3:30-5:45pm |
Grading Factors
HW Average: 2% of course grade.
Quiz Average: 13% of course grade.
Exam 1: 15% of course grade.
Exam 2: 15% of course grade.
Exam 2: 15% of course grade.
Final exam 40% of course grade
At the end of the course if your final exam grade is superior to any of your midterm exam grades, then you can use your final exam grade to replace all lower midterm exam average(s). For instance, if at the end of the semester your hw average is 92, your quiz average is 79, your midterm 1 grade is 70, midterm 2 grade is 0 (sick), midterm 3 grade is 88, and your final exam grade is 81 then your course grade will be computed as 2% * 92 + 13% * 79 + 15% * 88 + 70% * 81 = 82.01. One way to think of these grading factors is that your performance on the midterms cannot hurt your final grade, as compared to your final exam grade. You cannot drop your 2% hw grade, your 13% quiz average or your final exam grade. Your final exam grade will count at least 40% of your course grade.
With these grading factors you will be less stressed taking the midterms, knowing that you can replace a bad score with your final exam score. Moreover, if you feel ill or must assist a sick family member or friend, you can skip any assessment, except the final. You must take the final. If you are sick for the final, do not come to campus. There will be a make-up final exam for students who miss the final with a reason. The final will serve as the make-up for all midterms.
Exam questions will be similar to the suggested textbook homework questions, exact replicas sometimes. You should attempt all the assigned homework problems to learn the material and prepare for quizzes and exams. If you have done all assigned hw problems, there should be no surprises on quizzes and exams.
Exam Schedule
Exam 1: Monday 15 June
Exam 2: Monday 29 June
Exam 3: Monday 13 July
Office Hours
Tuesdays 5-6pm
Homework
You will submit homework in webassign.
Textbook Exercises vs. Textbook Examples
The best way to learn the material is to consistently do many suggested textbook exercises. It is better to spend a couple hours every day doing textbook exercises rather than spending the weekend before the exam cramming for eight hours a day. Consider the final exam like running a marathon and the problems as your training sessions. If you consistently do problems (train) then you will be well-prepared for the final exam. However if you have long gaps between working on problems you will always have difficulty getting back into the math mindset necessary to complete the problems. The first day of training is always the most painful. When I studied math in college I learned most by attempting to work out many of the odd numbered exercises in my textbooks and then checking my answers.
Textbook exercises are located at the end of each section in our book. Answers to the odd numbered exercises in the back of the book. Textbook examples are mixed into the section. Textbook examples always have a full written solution immediately underneath. These solutions are well-written and are one of the strengths of our textbook. Please cover up the solution and try to work it out yourself before reading the solution.
Flipped Classroom and Reading the Textbook
We will be practicing flipped classroom this semester. You will be reading (and watching videos) about the course topics before studying them in class with me. Having a rough idea of a course topic before learning studying it in class will give us more time to spend solving problems in class. Solving problems is the most important part of the course.
Learning to read a textbook is a crucial skill to master. Carefully reading a math textbook will help you in all of your future math courses at CCNY. Reading a math textbook is unlike reading the newspaper or a novel. You cannot just read the assigned pages in a math book and be done. It doesn't work like that. You must read a math book slowly, with diligence---and you must have a pencil and scrap paper by your side to work our the examples. It is best to cover up the solution to an example and attempt to work it out yourself before moving forward. It is usually impossible to work out a solution perfectly on first reading but it is important to try. Attempting a problem, or just trying to figure out what is being asked, is a great way to learn math.
There are some video links inside the reading. These can be helpful to ponder the topic from a different viewpoint.
