Homeworks are due Tuesdays at the beginning of class.

---

---

Homework #1 Read Stewart 10.1-10.3 (Strang 11.1-11.2) Due Tuesday August 28th. 10.1: 4, 6, 10, 14, 33 10.2: 3, 15, 17, 19, 29 10.3: 1, 3, 5, 6, 15, 17, 19, 20, 36

Notes We are studying Multivariable Calculus.  For this, we need some basic linear algebra. The terms vector and matrix have many meanings.  We're concerned with the mathematical ones, and we'll focus on their relationships with Euclidean space. Wikipedia Vector Matrix Unit Vector Dot Product Vector Projection Sailing into the wind Mathematica Demonstrations Vector Algebra Normalizing Vectors Terry Tao Sailing into the wind, or faster than the wind.

---

Homework #2 Read Stewart 10.4-10.5 (Strang 11.2-11.3) Due Tuesday Sept 4 10.4: 8, 11(pay attention to the direction of the arrows), 15,  25, 27, 32, 33 10.5: 23, 25, 33, 35, 38

Notes Wikipedia Right hand rule Cross Product Determinant

---

Homework #3 Read Stewart 10.5, 10.7 (Strang 11.3, 12.1) Due Tuesday Sept 11 10.5: 1, 4, 12, 14, 17, 47 10.7: 5, 7, 15, 17-22, 26, 27, 33, 45, 51, 56 (you may leave the answer in terms of inverse trig functions).

Notes We'll come back to 10.6 later. Wikipedia Parametric Equation Vector valued function Corriolis Effect Draining in bathtubs and toilets Test I We will have Test I in class on Tuesday Sept 18th. It will cover 10.1-10.5, 10.7-10.9

---

Homework #4 Read Stewart 10.8,10.9 (Strang 12.2 - 12.4) Study for Test I (in class, Tuesday Sept 18) Not Due 10.7: 57, 61, 63, 66 10.8: 1, 7, 11, 14, 30, (49, 50 optional) 10.9: 12, 28, 29, 33

Notes Test I We will have Test I in class on Tuesday Sept 18th. It will cover what we've done in hwks & class from 10.1-10.5, 10.7-10.9 Here is an example calculation of curvature and the components of acceleration. Admittedly, this one ends up being a bit more involved than will be on the test. Wolfram Alpha You can do 2 dimensional parametric plots in your web browser.   Try this. You can choose the range of the parameter too.  Like this. Wikipedia Curvature Frenet-Serret formulae

---

Homework #5 Read Stewart 10.6, 11.1 Due Tuesday September 25 10.6: 1, 3, 5, 7, 9, 25, 29 11.1: 22, 25, 31, 41-46 And watch this thing about Parabolas

Notes Stewart's TEC Go to http://www.stewartcalculus.com/tec/ Select the red book, Essential Calculus Browse Visuals and Modules Play with 10.6A and 10.6B Wolfram Alpha You can get a graph of surfaces and contour maps in your browser like this and this and this. Wikipedia Contours Level Set Wolfram Demonstrations Curvature and Torsion Curvature of the Trefoil Graph and Contour Plots

---

Homework #6 Read Stewart 11.2-11.4 Due Tuesday Oct 2 11.2: 3, 4, 23, 25 11.3: 3, 4, 5, 8, 11, 37, 43, 58ab, 60ab

Notes  Wikipedia Contours Level Set Partial Derivative Tangent Plane Implicit Function

---

Homework #7 Read Stewart 11.4-11.6 Due Tuesday Oct 9 11.4: 3, 19, 30 11.5: 3, 7, 20, 28, 31 11.6: 5, 9, 15, 17, 25, 26

Notes  Wikipedia Gradient Wave Equation Laplace's Equation

---

Homework #8 Read Stewart 11.6-11.7 Due Tuesday Oct 16 11.6: 28, 30, 31, 33, 37 11.7: 2, 7, 9, 13, 23, 25, 31, 35, 43

Notes  Wikipedia Second partial derivative test Newton's Method (for approximating roots) Methods for approximating square roots Wolfram Demonstrations Directional Derivatives in 3D Second-Order Partial Derivatives

---

Homework #9 Read Stewart 11.7-11.8 Study for Test 2 (in class Tues Oct 23) Not Due 11.8: 1, 5, 9, 13, 17, 21, 25, 29

Notes Wikipedia Optimization Lagrange multipliers Cobb-Douglas (economics) Viewing gasoline tax as a Lagrange multiplier. Wolfram Demonstrations Geometry of a Lagrange Multiplier Constrained Optimization Optimization of Cobb-Douglas

---

Homework #10 Read Stewart 12.1 Due Tuesday October 30th 12.1:  7, 9, 10, 11, 17

Notes Wikipedia Multiple Integral Iterated Integral Fubini's Theorem Wolfram Alpha An example of an iterated integral. inner integral outer/full integral