* Math 17B
SUPPLEMENTARY CLASS HANDOUTS *

* Last Update: February 25, 2015
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kouba@math.ucdavis.edu*

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- SUPPLEMENTARY CLASS HANDOUTS

- Proof of Two Summation Formulas

- Limit Definition of Definite Integral

- An Example of a Definite Integral

- Properties of Definite Integrals

- Even and Odd Functions

- The Mean Value Theorem for Definite Integrals and Two Fundamental Theorems of Calculus

- The Average Value of a Function

- Formulas for Computing Volume

- A Formula for Arc Length

- An Example of Arc Length

- The Derivative of Arctangent

- Integration Formulas

- Estimating the Value of Definite Integrals Using the Midpoint and Trapezoidal Rules

- Constructing Taylor Polynomials

- A Function and its Taylor Polynomials

- Examples Using Taylor Polynomials and Taylor Error

- A Differential Equation Representing Logistic Growth

- Finding Equations and Growth Rates from Semi-Log Graphs

- Plotting Data on Semi-Log Graph Paper

- Differential Equations Representing Mixture Problems and Solutions

- An Example Illustrating Direction Fields

- An Example Illustrating the Classification (Stable or Unstable) of Equilibria

- The Allee Effect , A Biological Example of an Unstable Equilibrium as an Extinction Threshold

- Determining Inverses of Matrices and Computing Determinants of 2x2 Matrices

- What the Heck is a Leslie Matrix

- Rotation Matrices in Two-Dimensional Space

- Determining Eigenvalues and Eigenvectors for a Two-by-Two Matrix

- Leslie Matrices, Eigenvalues, and Stable Age Distributions

- Using Eigenvalues and Eigenvectors to Solve Matrix Algebra Problems

- Using Vectors to Determine Equations for Lines and Planes

- An Alternate Formula for the Dot Product

- Functions of Exponential Order

- A List of Laplace Transform Formulas

- A Laplace Transform Example Using Integration by Parts Twice

- Proof of Two Summation Formulas