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Advanced Engineering Mathematics Lecture Notes:
West Virginia Wesleyan College
Jesse Oldroyd
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Front Matter
Colophon
Acknowledgements
Preface
I
Linear Algebra
1
Introduction to Matrix Algebra
1.1
Matrices, Vectors and Linear Combinations
1.2
Matrix Multiplication
1.3
Systems of Linear Equations
1.4
Linear Independence
Span
Definition and Examples of Linear Independence
Bases in
\(\RR^n\)
1.5
Existence of Solutions
1.6
Determinants
1.7
Matrix Inverses
Computing the Inverse of a Matrix
The Invertible Matrix Algorithm
1.8
\(LU\)
Decomposition
2
Eigenvalues and Eigenvectors
2.1
Finding Eigenvalues and Eigenvectors
Computing Eigenvalues and Eigenvectors
Algebraic and Geometric Multiplicities of Eigenvalues
2.2
Eigenvalue Problems
2.3
Orthogonal Transformations
2.4
Diagonalization of Matrices
Eigenbases
Diagonalization
Diagonalizations of Symmetric and Hermitian Matrices
Analytic Functions of Matrices
II
Multivariable Calculus
3
Vector Derivatives
3.1
Inner Products and Cross Products
Inner Products
Cross Products
Computing Inner and Cross Products Using Technology
3.2
Vector Functions
Visualizing Vector Functions
Vector Functions and Motion
Derivatives of Vector Products
3.3
Arc Length and Components of Acceleration
Arc Length
Components of Acceleration
3.4
Gradients and Potentials
Gradients
Potential Functions
3.5
Divergence and Curl of Vector Fields
Divergence
Curl
3.6
Sage Examples
4
Vector Integrals
4.1
Line Integrals
Scalar Line Integrals
Line Integrals of Vector Fields
4.2
Path Independence and the Fundamental Theorem of Line Integrals
Path Independence
Fundamental Theorem of Line Integrals
4.3
Green's Theorem
Green's Theorem for Circulation Integrals
Green's Theorem for Flux Integrals
4.4
Surface Integrals
Surfaces in
\(\RR^3\)
Surface Integrals
4.5
The Divergence Theorem and Its Applications
The Divergence Theorem
Applications of the Divergence Theorem
Back Matter
A
GNU Free Documentation License
Index
Colophon
Colophon
Colophon
This book was authored in MathBook XML.