Course Syllabus
Math 9
Welcome to Math 9! This course will study multivariable calculus, especially in dimensions 2 and 3. For example we will cover topics such as vectors, equations of lines and planes, arc length and curvature, partial derivatives and maxima and minima. To study these we will need to develop an understanding of one of the most ubiquitous tools in mathematics and science: Linear Algebra. The course will have a very geometric flavour and by translating questions into linear algebra we will gain a better understanding of the core concepts in multivariable calculus. We will switch between topics in multivariable calculus and linear algebra frequently throughout the term.
Both Math 9 and Math 11 are well suited for first-year students with a BC calculus background. In contrast to Math 11, however, Math 9 does not cover integral multivariable calculus. Students who take Math 9 and wish to complete the calculus sequence will go on to Math 13. Math 9 takes a more leisurely path through differentiable multi-variable calculus, while bringing in linear algebra to gain a deeper understanding.
| Prof: Kamran Kaveh |
Prof: Ciaran Schembri |
|
Location: Remote, with synchronous components (RSC) Class times: MWF 10:20-11:25am X-hour: Th 12:30-1:20 pm (same zoom link as class) Office: Kemeny 334 Office Hours: F3-4pm Email: Kamran.Kaveh@dartmouth.edu |
Location: Remote, with synchronous components (RSC) Class times: MWF 8:55-10:00am X-hour: Th 9:10-10:00 am (same zoom link as class) Office: Kemeny 338 Office Hours: W1-2pm Email: Ciaran.Schembri@dartmouth.edu |
Tutorials: Every Monday and Friday 4 - 6pm (except Oct 9th and 30th)
Grading: Your grade will be calculated in the following two ways and the highest will count:
Final Exam (35%), Midterm 1 (20%), Midterm 2 (20%), Homework (25%)
Final Exam (25%), Midterm 1 (25%), Midterm 2 (25%), Homework (25%)
Midterm 1: 9th Oct; Midterm 2: 2nd Nov; Final Exam: 3rd Dec
Homework: Homework is due at 4pm on Tuesdays. The homework with the lowest score will be dropped. Homework can be uploaded as a high-quality photo or scan. The Homework page is updated regularly and will be available shortly after handing in the previous one.
Late policy: The deadline is strict. The penalty for turning in late homework is 5% for each additional day. An extension is unlikely to be granted except for extenuating circumstances such as illness or a family emergency.
Textbook: Multivariable Calculus (8th edition) by James Stewart and
Linear Algebra Supplement for Math 9 (online source we provide) by Prof. Carolyn Gordon
Teaching Assistant: Ben Logsdon (ben@benlogsdon.org)
The following is a tentative syllabus for the course. This page will be updated.
| Lectures | Sections in Text | Brief Description |
|---|---|---|
| 9/14 M | Stewart 12.1 | Introduction and overview |
| 9/16 W | Stewart 12.1 | 3-d coordinate system and distance |
| 9/18 F | Stewart 12.2 | Vectors |
| 9/21 M | Linear Algebra 1.1-1.2 |
Linear equations and row reduction |
| 9/23 W | Linear Algebra 2.1 | Linear combinations and spanning sets |
| 9/25 F | Linear Algebra 2.3 | Vector equations of lines and planes |
| 9/28 M | Stewart 12.3 | Dot products and orthogonality |
| 9/30 W | Stewart 12.3-12.4 |
Projections, cross products |
| 10/2 F | Stewart 12.5 | Equations of lines and planes |
| 10/5 M | Stewart 12.6 | Quadric Surfaces |
| 10/7 W | Review | |
| 10/9 F | Exam 1: TBA | |
| 10/12M | Stewart 13.1 |
Vector valued functions, space curves |
| 10/14W | Stewart 13.2-13.3 |
Derivatives and integrals of vector valued functions, arclength and curvature |
| 10/16 F | Stewart 14.1 | Functions of several variables and level sets |
| 10/19 M | Linear Algebra 3.1-3.2 | Matrix Operations |
| 10/21 W | Stewart 14.3, Linear Algebra 4.1 | Partial derivatives and directional derivatives |
| 10/23 F | Linear Algebra 4.1 | Directional Derivatives |
| 10/26 M | Linear Algebra 4.2 | Differentiable functions and tangent planes |
| 10/28W | Linear Algebra 5.2 | Linear transformations and matrices |
| 10/30 F | Review | |
| 11/2 M | Exam 2: TBA | |
| 11/4 W | Linear Algebra 5.3-5.4 | Properties of linear transformations, rotations/reflections |
| 11/6 F | Linear Algebra 5.5-5.6 | Determinants and composition of linear transformations |
| 11/9 M | Linear Algebra 6.1-6.2 | Derivatives of real-valued functions |
| 11/11 W | Linear Algebra 6.2 | Derivatives of higher dimensions |
| 11/13 F | Stewart 14.6 Linear Algebra 6.4 |
The chain rule |
| 11/16 M | Stewart 14.7 | Min/Max for functions with several variables |
| 11/18 W | No Class | |
| 11/20 F | No Class | |
| 12/03 Th |
Final Exam: TBA |