Day & Time: Tuesday and Thursday 3:30pm — 5:20am First day of class: Tuesday, January 14 Location: Goldsmith Math 116 Instructor: Joel Bellaiche Office Hours: Thursday 2pm-3pm in Goldsmith Teaching assistant: Anna Medvedovski TA's office hours:Monday 2-3pm, Thursday 11am-12pm, or by appointment, in Goldsmith 103 Textbook:Calculus 2, linear and non-linear functions. F. J. Flanigan, J. L. Kazhdan, Second Edition Prerequisites: Math 22a or permission of the instructor Examinations: There will be two in class midterms and one final exam. |
Homework: There will be two kinds of homework:
Help: Help is available if you have trouble with homework or lecture material. My office hours are a good place to start. Discussions with your classmates can also be very helpful and are strongly encouraged.
Contents :
Class | Topic | Readings | Exercises | Due |
January 14 | Presentation of the course. Limit of vector-valued functions of one variable. | Section 4.1A | ||
January 16 | Continuity of vector valued functions. Parametrized curves. Derivatives of vector-valued functions | sections 4.1B, 4.2A, 4.2B | 4.1, exercises 1,2,6,10,11,13 | |
January 21 | Tangent map of a vector valued functions. Tangent of a curve. Acceleration. | 4.2BCDE | 4.2, exercises 1,2,3,10,15,16,21,26 | |
January 23 | Arc Length and Curvature. | 4.3 | Problems set 1 | |
January 28 | Curvature | 4.3 | Exercises 4.3. 1,4,17,20 | |
January 30 | Functions of several variables: Limit points and limits | 6.1 | 6.1:7,17,28 | Problems set 2 |
Feb 4 | Function of several variables: Continuity and directional derivatives | 6.1, 6.2 | 6.2:1,2 | |
Feb 6 | Directional and partial derivatives | 6.2,6.3 | 6.3:1,4,6 | |
Feb 11 | Total Differential and Partial derivatives. Gradients | 6.4,6.5 | 6.4:1,2,5 | Problems set 3 |
Feb 13 | No class due to snow. | |||
Feb 25 | The Chain Rule for functions of several variables. Maxima and Minima. | 6.5C | 6.5:2,3 | |
Feb 27 | Midterm I | Problems set 4 | ||
Mar 4 | Local Extrema are critical points. Taylor approximation and Taylor-Lagrange theorems | 7.1,7.2A, &.2B | 7.1:1,5,8,11 | |
Mar 6 | Quadratic forms and symmetric matrices. Taylor-Lagrange at order 2 for functions of several variables. The second-Derivative test | 7.2C, 7.2D, 7.3 | 7.3:1,2(a),(e),(i),(o),3,5,6,10 | |
Mar 11 | Global extrema. Constrained Extrema | 7.4,7.5A,B,C | Problems set 5 | |
Mar 13 | Constrained Extrema. Lagrange multipliers. | 7.5D | ||
Mar 18 | Lagrange multipliers. Applications | 7.5D | ||
Mar 20 | Vectors functions of several variables: differential calculus | 8.1,8.2 | ||
Mar 25 | Vector fields and gradients | 8.3,.8.4 | ||
Mar 27 | Midterm 2 | |||
Apr 1 | integration in R^2 | 9.1,9.2/td> | Problems set 6 | |
Apr 3 | Integration in R^2 | 9.2,9.3 | ||
Apr 8 | Integration in R^2: change of variables | Problems set 7 | ||
Apr 10 | Integration in R^n | |||
Apr 24 | Line integrals | Problems set 8 | ||
Apr 29 | Line integrals. Stokes Theorem | |||
May 8 | Final Exam | Practice Exercises | ||