Contents

1. Introduction

2. Functions

   1. Domain and range

   2. Composition of functions

   3. Inverse functions

   4. Exponential functions

   5. Compound interest

   6. Logarithmic functions: base 10 and base e

   7. Properties of exponents and logarithms

   8. Logarithmic functions: other bases

3. Equations

   1. Calculations with linear equations

   2. Calculations with quadratic equations

   3. Gauss-Jordan elimination with two variables

   4. Gauss-Jordan elimination with three variables

4. Vectors

   1. Dot product, length/norm, angle, projection

   2. Equations of lines in R2

   3. Equations of planes in R3

   4. Gram-Schmidt orthonormalization in R2

   5. Gram-Schmidt orthonormalization in R3.

5. Matrices

   1. Multiplication, 2x2 matrix inverse, transpose

   2. Reflections and rotations in R2

   3. Projections in R2

   4. Combining transformations in R2

   5. Gauss-Jordan elimination to find matrix inverses

   6. Calculating determinants

   7. Eigenvalues and eigenvectors

   8. Diagonalization