Connected Calculus The Connected Curriculum Project

#### Contents

Models, Data, and Curve Fitting -- A Guide to this Chapter.

• The Mean and the Median
• Linear Models
• Linear Regression
• Exponential Models
• Logistic Models
• Periodic Models
• Contents
Estimation and Limits -- A Guide to this Chapter. Sequences and Discrete Dynamical Systems -- A Guide to this Chapter. Derivatives and Differention -- A Guide to this Chapter.
Graphing -- A Guide to this Chapter.
• Interpreting the First Derivative -- Increasing and Decreasing, Local and Global Extremums
• Interpreting the Second Derivative -- Concavity and Points of Inflection
• Symmetry
• Cartesian Coordinates
• Polar Coordinates
• Parametric Equations
• Implicit Functions
• Contents
Optimization -- A Guide to this Chapter.
• Optimization on a Closed and Bounded Interval -- The Extreme Value Theorem
• Optimization on a Closed and Bounded Interval -- A Recipe
• Optimization on a Close and Bounded Interval -- Examples
• Optimization on Other Domains -- Techniques
• Optimization on Other Domains -- Examples
• Optimization -- Using A Computer or Graphing Calculator
• Optimizing a Function of More than One Variable -- Using Partial Derivatives
• Optimizing a Function of More Than One Variable -- The Method of Steepest Descent
• Optimizing a Function of More Than One Variable -- Using a Computer or Graphing Calculator
• Optimizing a Function of More Than One Variable -- Examples
• Contents
Integrals and Integration -- A Guide to this Chapter.
• Area
• Summation or "Sigma" Notation
• From Velocity to Displacement
• Riemann Sums
• The Definite Integral -- Definition
• The Definite Integral -- Exotic Multiplication
• Accumulation Functions
• The Fundamental Theorem of Calculus -- the Ho-Hum Theorem of Calculus
• Antidifferentiation -- Basic Formulas
• Linearity of the Intgeral
• The Chain Rule Revisited -- Change of Variables
• Integration by Parts
• Trigonometric Substitution
• Contents
Differential Equations and Continuous Models -- A Guide to this Chapter.
Series -- A Guide to this Chapter.
• Geometric Series
• Convergence
• The One-Way Convergence Test
• The Integral Test
• Comparison Theorems
• The Ratio Test
• Power Series
• Power Series Solutions of Initial Value Problems
• Taylor Series
• Taylor's Theorem
• Fourier Series
• Contents
Numerical Methods -- A Guide to this Chapter.
• Solving Equations
• Estimating the First Derivative
• Estimating the Second Derivative
• Estimating the Integral
• The Right Hand Rule
• The Left Hand Rule
• The Midpoint Rule
• The Trapezoid Rule
• Simpson's Rule
• Initial Value Problems
• Euler's Method for One Variable
• Euler's Method for Several Variables
• The Modified Euler's Method
• Fourth Order Runge-Kutta
• Round-Off Error
• Propogation of Errors
• Taylor Series
• Interpolation
• Linear Interpolation
• Splines
• Contents

Copyright c 1995 by Frank Wattenberg, Department of Mathematics, Carroll College, Helena, MT 59625