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Mathematical Scholars Calculus 3
Gabriel Kerr
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Front Matter
1
Over(re)view
1.1
Arithmetic Review
1.1
Exercises
1.2
Sets and Functions Review
1.2
Exercises
1.3
Equations Review
1.3.1
General First Order ODE
1.3.2
Exercises
2
Linear Algebra
2.1
Matrices I
2.1
Exercises
2.2
Vector Spaces I
2.2
Exercises
2.3
Linear Transformations I
2.3
Exercises
2.4
Matrices II
2.4.1
Row Echelon Form
2.4.2
Row Reduction
2.4.3
Exercises
2.5
Vector Spaces II
2.5.1
Independence and Dimension
2.5.2
Annihilators
2.5.3
Exercises
2.6
Linear Transformations II
2.6
Exercises
2.7
Matrices III
2.7.1
Elementary Matrices
2.7.2
Determinants
2.7.3
Proof of Theorem 2.7.10
2.7.4
Formula for the Inverse
2.7.5
Exercises
3
Linear Geometry
3.1
Geometry I
3.1.1
Transpose Matrices
3.1.2
Dot Product
3.1.3
Other Examples
3.1.4
Exercises
3.2
Geometry II
3.2
Exercises
4
Linear Operators
4.1
Diagonalization
4.1.1
Eigenvalue Problem
4.1.2
Eigenvector Problem
4.1.3
Diagonalization Problem
4.1.4
Exercises
4.2
Jordan Normal Form
4.2
Exercises
4.3
The Spectral Theorem
4.3.1
Quadratic Forms
4.3.2
Covariance Matrices
4.3.3
Exercises
5
Ordinary Differential Equations
5.1
Paths
5.1.1
Curves vs. Paths
5.1.2
Tangent Vectors of Paths
5.1.3
The Geometry of Curves
5.1.4
Exercises
5.2
Linear Constant Coefficient ODE I
5.2
Exercises
5.3
Linear Constant Coefficient ODE II
5.3
Exercises
5.4
Linear Constant Coefficient ODE III
5.4.1
Higher order linear ODE’s
5.4.2
Exercises
5.5
Linear Ordinary Differential Equations
5.5.1
The Matrix Exponential
5.5.2
Higher order linear ODE’s II
5.5.3
Power Series Methods
5.5.4
Exercises
5.6
Laplace Transforms
5.6
Exercises
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.
