Linear Algebra I - A collection of exercises and solution aimed for the first semester.

Linear Algebra II
- A collection of exercises and solution
aimed for the course Linear Algebra II.

Here is a phone version.

Email: per.w.alexandersson@gmail.com.

#Math 114 Fall 2016
## General info
Class time: Monday, Wednesday and Fridays: **13:00–14:00** in **A1**, start August 31.
Course material: **Thomas – Calculus Early Transcendentals, Upenn edition**
Office hours: DRL 4C19, Mondays, 15:00–17:00. My email: peal@sas.upenn.edu.
TAs: **Yubo Guo**, office hours TR 2-3 @ 3C17, **Yilun 'Ivan' Li**, office hours W 3-4, F 2-3 @ 3W8.
##Extra material
Here are some collections of practice problems and midterm solutions
The Jump
The London Eye Incident
Min/max problems
Professor A and the alternative scoring scheme
Integration problems
About the Jacobian
Midterm 1a, Midterm 1b
Midterm 2a, Midterm 2b.
Midterm 2 extra (with solutions)
Midterm 3 practice, (with solutions)
Midterm 3 (with solutions)
Midterm 3 extra (with solutions)
Midterm 4 (with solutions)
Important! List of old finals.
##Syllabus
See this page
for syllabus, core problems and so on. I might deviate from this slightly.
Math 114 covers multivariate calculus. It will start with things you are familiar with,
but the latter part of the course is dense with new material.
As a complement, some videos on multivariate calculus might be of use.
## Homework (updates regularly)
Turn in homework before class starts to me, with **name** and **recitation section** on top, sheets stapled together.
Homework due to *Mon Nov 28* **16.1: 1-8, 9 11, 14, 19, 20, 27 and 16.2: 2, 4, 7, 11, 15, 19, 20, 27, 30, 52
and 16.3: 1, 4, 8, 9, 19, 20, 27, 28, 30a, 30c, 33b**
Homework due to *Fri Dec 02* **16.4: 4, 7, 9, 11, 19, 27, 28 (if you want, 40, by Swedish mathematician) and 16.5: 4, 7, 8, 19, 23, 37, 41, 47**
Homework due to *Wed 07* **16.6: 2, 3, 7, 14, 17, 28, 38, 39 and 16.7: 3, 6, 7, 13, 19, 28**
Homework due to *Fri 09* **16.8: 5, 8, 9, 11, 15, 18, 28**
## Schedule
* *W - Aug 31* Section 12.1 Introduction. Read 12.1 yourself and make sure you are familiar with the equation for a sphere, cylinder, plane, and all that.
* *F - Sep 02* Section 12.2-12.3 Vectors, dot product.
* *M - Sep 05* No class
* *W - Sep 07* Section 12.4 Cross product.
* *F - Sep 09* Section 12.5 Lines and planes. Look through 11.6 and 12.6 yourself, I will not cover this much in class.
You may want to watch some Youtube video explaining these.
One reason we look at quadratic surfaces is that that they appear later in min/max problems.
* *M - Sep 12* Section 13.1-13.2 Curves in space and tangents. Projectile motion.
* *W - Sep 14* Section 13.1-13.2 More curves and projectile motion.
* *F - Sep 16* Section 13.3 Arc length / Midterm prep.
* *M - Sep 19* Midterm prep. Recommended preparation: this midterm (except 5) (solutions) and and these (except 9,11-16,18,22-25),
(answers).
* *W - Sep 21* Midterm.
* *F - Sep 23* Section 13.4 Curvature and normals
* *M - Sep 26* Section 13.5 Tangential and normal components of acceleration. Have a look yourself on Section 13.6.
* *W - Sep 28* Section 14.1 Functions of several variables
* *F - Sep 30* Section 14.2 Limits
* *M - Oct 03* Section 14.3 Partial derivatives
* *W - Oct 05* Section 14.4 The chain rule. See this PDF for computing second derivative.
* *F - Oct 07* Fall break
* *M - Oct 10* Section 14.5. Directional derivatives and gradients. Note: Drop period ends
* *W - Oct 12* Section 14.6 Tangent planes
* *F - Oct 14* Section 14.7 Extreme values and saddle points, extra exercises here.
* *M - Oct 17* Section 14.8 Lagrange multipliers
* *W - Oct 19* Section 15.1-15.2 Double integrals.
* *F - Oct 21* Section 15.3 More double integrals, 15.4(?) integrals with polar coordinates.
* *M - Oct 24* Midterm review.
* *W - Oct 26* Midterm.
* *F - Oct 28* Section 15.4 More integrals and polar
* *M - Oct 31* Section 15.5, 15.7 Triple integrals
* *W - Nov 02* Section 15.7, 15.8 Substitutions
* *F - Nov 04* Section 15.6 Moments, center of mass
* *M - Nov 07* Section 16.1 Line integrals
* *W - Nov 09* Section 16.2 Vector fields
* *F - Nov 11* Section 16.3 Path independence and conservation. Note, Last day to withdraw from course.
* *M - Nov 14* Midterm review
* *W - Nov 16* Midterm! Solutions a
* *F - Nov 18* Section 16.4 Greens theorem
* *M - Nov 21* Section 16.5 Surfaces and area
* *W - Nov 23* Review (Old finals problems related to Section 16.1-16.5)
* *F - Nov 25* No class (Thanksgiving)
* *M - Nov 28* Section 16.6 Surface integrals
* *W - Nov 30* Section 16.7 Stokes theorem
* *F - Dec 02* Section 16.8 Divergence theorem
* *M - Dec 05* Extra
* *W - Dec 07* Finals practice
* *F - Dec 09* Finals practice
* *M - Dec 12* Finals practice - last day of class
* *M - Dec 19* 09:00-11:00 Final Exam (Cohen Hall/17), be in time, and bring Penn ID!
* *Thursday Jan 12* Postponed final, in case of conflict. Room A1 from 6pm to 8pm.
## Grading
The grading will be weighted as follows: 30% final, 45% midterms (most likely three midterms), 15% homework, 10% recitation activities.
All sections of math-114 will have a common final. The result of the final determines the distribution of grades in individual sections.
That is, a strong class with many A's on the final, will result in that many A's as final grade in that class.