MATH 051 SURVEY OF CALCULUS Lehigh

Math 23 Sections 110-113 B. Dodson Week 2 Homework: 12.2 vectors: unit, standard unit, notations 12.3 dot product: orthogonal, proj, comp 12.4 cross product: formula, properties Problem 12.2.25: Find a unit vector u that has the same direction as a

Math 205, Summer II 2007 B. Dodson Text - Peterson-Sochacki -1. Course Info 2. Week 1 Homework: 1.1 (1st half), 1.2 Intro -An m n matrix A is an array with m horizontal rows; n vertical columns i, jth entry ai,j in the ith row, and jth column. row v

Week 8: 1. 6.1 1st order systems of DE (briefly!) 2. 5.4 Eigenvalues and Eigenvectors 3. 5.5 Eigenspaces and Diagonalization - A vector v = 0 in Rn (or in Cn ) is an eigenvector with eigenvalue of an n-by-n matrix A if Av = v. We re-write the vector

Math 23 B. Dodson Week 6 Homework: 14.2 limits 14.3 partial derivatives, 2nd order deriv Week 6 Homework: 14.2 limits Problem 14.2.6: Find the limit lim(x,y)(6,3) (xy cos (x - 2y) . Solution: We see that the function f (x, y) = xy cos (x - 2y) is co

Week 4a: 4.3 Undetermined Coef [Tables] TABLE of trial yp : Usual trial yp F (x) ceax ceax cos(bx) or ceax sin(bx) cxk Usual yp = A0 eax yp = eax (A0 cos(bx)+ B0 sin(bx) yp = A0 + A1 x + + Ak xk Modified When: The root associated with F (x) is NO

Week 3b: 3.6 Cooling/Mixing [see Cooling example, week 3] [3.9 Numerical Solutions [Euler, Maple\'s dsolve/numeric] not collected 4.1 Higher Order DE 4.2 Constant Coef, Homogeneous DE - Problem: A 200L tank is half full of a solution containing 100g o

MATH 43 Policy Statement Fall, 2007 1. Instructor: B. Dodson, Room 207 XS, Phone x8-3745, Email bad0. 2. Text: Poole, Linear Algebra: A Modern Introduction, 2nd Edtn. Selected portions of Chapters 1 - 5, plus Section 7.3 will be covered. 3. Attend

MATH 43 Selected Solutions to Exam 1 Sample/Review October, 2007 1. Sample exam, #5 from Fall 2006: The augmented matrix has 1 -1 -1 2 | 1 0 0 1 -1 | 1 as a row echelon matrix (not unique), and 0 0 0 0 | 0 1 -1 0 1 | 2 0 0 1 -1 | 1 as as its

Week 3: 1. 1.5 Determinants 2. 1.6 Properties of Dets 3. 2.1 Vector Spaces - 2 1 We compute det 4 2 9 5 5 3 using the 1 (first) row expansion (by minors): det(A) = 2 2 5 4 2 4 3 3 +5 -1 9 5 9 1 1 = 2(2 - 15) - (4 - 27) + 5(20 - 18) = 2(-13) - (