- 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 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)

- 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

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