Darin Stephenson | Hope College | Department of Mathematics

This page will contain details about a textbook I am writing for our sophomore sequence, Math 231-232. As I learn about errors and omissions in the text, I will post corrections here.

Table of Contents

The Geometry of Rⁿ
Matrices and Linear Systems
Vector Spaces
Linear Transformations
Eigenvalues and Eigenvectors
First Order Differential Equations
Linear Differential Equations
Systems of Differential Equations
Functions of Several Variables (planned)
Differentiation (planned)
Integration (planned)
Calculus on Vector Fields (planned)

Errata for the 2007-08 version (Version 1.5):

On page 30, Exercise 16 should say "a vector in R³" rather than R².
On page 30, there is an error in Exercise 22. There is not a single point that is equidistant from three points in R³.
On page 104, Exercise 8 of Section 2.5 should really be in Section 2.7, since the concept of rank has not yet been defined.
On page 110, the reference to Theorem 2.85 in Exercise 3 is incorrect. The exercise should reference Theorem 2.52.
On page 110, Exercise 4 of Section 2.6 should really be an exercise for Section 2.7, since the concept of rank has not yet been define.
On page 111, in the definition of rank(A), the second occurrence of "rref(A)" should be "rank(A)".
Theorem 2.68 on page 119 should read "If e is an ERO of the form..." There is an extra word "the" in the theorem statement.
On page 134 in Exercise 1(f), the definition of odd function should read "f(-x)=-f(x) for all x", not "f(-x)=-f(-x) for all x".
On page 135, the final sentence of Exercise 9 should read "Prove that Cⁿ(R) is a subspace of F(R)." In the proof of this given on page 414, you also need to replace C^infinity(R) with F(R) everywhere.
On page 190, Theorem 4.15 should read
1. ker f= NS(A) and therefore the null(f)=null(A)
2. im f= CS(A) and therefore rank(f)=rank(A)
On page 408, the answer to Section 1.4 exercise 3(b) should be the vector (5,-5,-30).
On page 408, in the solution of Section 1.5 exercises 13 and 15, you may be more comfortable using s and t as the parameters, rather than u and v. (In essence, it doesn't matter, since they are "dummy variables.")
On page 409, the answer to Section 1.6 #5 should be 12 (not 30).
On page 409, in the solution of Section 2.2 exercise 3, the variables x and y are reversed. The solution should read x = -14/25 and y = -73/25.

Multivariable Mathematics I & II

Linear Algebra, Differential Equations, and Vector Calculus with Applications



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