# Homework for Math 3354 and Math 3355

Howework for Math 3354 and Math 3355 will consist of two types of problems, gateway and brainfood problems. The gateway problems involve routine computations which every student should master. The brainfood problems are in-depth problems which not only challenge the student to discover the deeper mathematical meanings, but also understand the real world constraints involved.

## Gateway Problems for Math 3354

Each of the following sets of problems are due on Wednesdays along with the Brainfood problems for the week. As with any homework list, these problems are subject to change.

3.1
#3a,d, #6c (Parametric curves)
3.2
#1a,b,g, #4d (More parametric curves)
3.3
#3a,d #6a,d (Derivatives of parametric curves)

2.1
#2a,b #6b (part i) (Vectors)
2.2
#1a,d #14a,b (Write Plane in #14 as a parametrization)
2.3
#5a,b (Write Planes as parametrizations)

1.2
#7a,c (Cross-sections)
4.3
#1c,d #3a,c (Partial derivatives)
4.2
#2a,b,c #5a,b,c (Directional derivatives)
4.4
#5a,b (Directional derivatives)
4.5

Gateway 4 10/23 Study for Exam

4.5
#2a,d,e (Find critical points)
5.1
#1b,c (more critical points)

5.2
#6a,g (Classify critical points)
5.3
#3a,b #7a,b (Max/Min and Lagrange Multipliers)

4.4
#4c,d (Chain Rule = Derivatives of the restrictions of functions to parametrized curves)
Also, study for exam and Gateway II

3.5
#2a,b and evaluate Df at each critical point (Critical points; linearization)
4.4
#1a,b and write tangent planes as graphs over (x,y). That is, f(x0,y0)+Df(x0,y0)(x-x0,y-y0))

Gateway 9 11/27
1.3
#4b,c (Neighborhoods)
4.1
#6a,b #7a,b 8d (Continuity)
4.4
#3a,b (Differentiability)

## Gateway Problems for Math 3355

Week 1
3.1 (BDH)
#5, 17, 24 (Linear Systems of Differential Equations)
3.2 (BDH)
#17a, 19a, 30, 31 (Eigenvalues and Eigenvectors)
3.2 (BDH)
#17b, 19b, 26 (Skip 3rd) (Solutions to Linear ODEs)
3.4 (BDH)
#1, 6, 12ab (Linear ODEs with complex solutions)
Week 4-5
6.3 (DF)
#2 do first and third parts, 7c,d,e (polar coordinates)
6.5 (DF)
#1a,b,c do first and third parts (cylindrical coordinates)
Week 6-7
6.1 (DF)
#3b,c,d, 4d
6.2 (DF)
#3c
6.4 (DF)
#7b, 8a,d
Week 8
6.3 (DF)
#9a
6.5 (DF)
#1a,b,c (do first and third parts)
6.6 (DF)
#3d, 6c