Homework for Math 3354 and Math 3355

Brainfood Problems for Math 3354

• Brainfood #1: Parametric Curves
• Brainfood #2: Cross-Sections of Surfaces
• Brainfood #3: Numerical Derivatives and the Chain Rule
• Brainfood #4: Study for Exam
• Brainfood #5: Gradients and Level Sets
• Brainfood #6: Critical Points
• Brainfood #7: Lagrange Multipliers
• Brainfood #8: Jacobians and Tangent Planes Revisited
• Brainfood #9: Multivariable Limits and Continuity
• Brainfood #10: Hamiltonian Vector Fields and Chain Rule
• Brainfood #11: Some fun with Eigenvectors and Eigenvalues
• Brainfood #12: Dynamics of a Shock Absorber

Gateway Problems for Math 3354

Gateway 1 10/2 Answers

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)

Gateway 2 10/9 Answers

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)

Gateway 3 10/16 Answers

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

#1a,f #3a (Gradients)

Gateway 4 10/23 Study for Exam

Gateway 5 10/30 Answers

4.5

#2a,d,e (Find critical points)

5.1

#1b,c (more critical points)

Gateway 6 11/6 Answers

5.2

#6a,g (Classify critical points)

5.3

#3a,b #7a,b (Max/Min and Lagrange Multipliers)

Gateway 7 11/13 Answers

4.4

#4c,d (Chain Rule = Derivatives of the restrictions of functions to parametrized curves)

Also, study for exam and Gateway II

Gateway 8 11/20 Answers

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

Gateway 11 Answers

3.1 (BDH)

#5, 17, 24 (Linear Systems of Differential Equations)

3.2 (BDH)

#17a, 19a, 30, 31 (Eigenvalues and Eigenvectors)

Gateway 12 Answers

3.2 (BDH)

#17b, 19b, 26 (Skip 3rd) (Solutions to Linear ODEs)

Gateway 13 Answers

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