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Introduction
Domain and range
Composition of functions
Inverse functions
Exponential functions
Compound interest
Logarithmic functions: base 10 and base e
Properties of exponents and logarithms
Logarithmic functions: other bases
Calculations with linear equations
Calculations with quadratic equations
Gauss-Jordan elimination with two variables
Gauss-Jordan elimination with three variables
Dot product, length/norm, angle, projection
Equations of lines in R2
Equations of planes in R3
Gram-Schmidt orthonormalization in R2
Gram-Schmidt orthonormalization in R3.
Multiplication, 2x2 matrix inverse, transpose
Reflections and rotations in R2
Projections in R2
Combining transformations in R2
Gauss-Jordan elimination to find matrix inverses
Calculating determinants
Eigenvalues and eigenvectors
Diagonalization
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A Compendium of Mathematics Problems Copyright © by Iain Pardoe is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.