# Linear Algebra and Intermediate Calculus, part 2 (MATH 22b, Spring 2014)

 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.

Assessment: The course grades will be computed as follows:
25% Homework
35% Midterms
40% Final exam

Homework: There will be two kinds of homework:

• Exercises give you a chance to practice and check that you have understood the material. They will not be collected.
• Graded homework: There will be ten graded homework, about one every week or a little less, at dates to be announced in class and on this web page. The two lowest grades of the 10 will be dropped.

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 :

• Vector-valued functions and their derivatives and integrals
• Functions of several variables and their derivatives
• Extrema problems for scalar-valued function of several variables.
• Integration of functions of several variables
• Stokes's formula

## Schedule of Lectures

 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