DIFFERENTIAL EQUATIONS & MATHEMATICAL MODELING

• Inverse Functions
• Finding derivatives of inverse functions
• The Chain Rule and an Interesting Derivative Worksheet
• Inverse Trigonometric Functions
• Finding derivatives of inverse trigonometric functions
• Tool for finding the inverse of a function
• Problems about inverse trigonometric functions
• Inverse Trigonometric Functions Worksheet
• Derivatives of Inverse Trigonometric Functions
• Differentiation of Inverse Trigonometric Functions
• Review problems for finding the derivative of inverse functions--Go to Calculus Book I,

then Derivatives, then Theory, then Inverse Functions

• Exponential Functions and Logarithms
• Lessons from precalculus
• Discussion of exponential functions with problems
• Definition of e
• Worksheet to calculate the derivative of y = e^x
• Animation of y = a^x as a changes; also shows slope of y = e^x is 1 at (0,1)
• Another demonstration of y = a^x to y = e^x
• Discussion of Derivative of natural logarithm expressions with problems
• The Derivative of the Natural Logarithm
• What is e?
• Definition of e
• Derivatives of logs and exponentials
• Logarithmic Differentiation -- a way to deal with complicated expressions
• Problems using logarithmic differentiation
• Derivatives & Integrals of Bases Other than e; Savings Account Formulas
• Lecture notes on the derivative of exponential and logarithmic functions

• Pictures of slope fields for parametrically defined derivatives
• Pictures of slope fields of first order differential equations
• Pictures of slope fields
• Problems to work on slope fields
• Graph solutions to differential equations applet
• Slope Fields discussion
• More discussion and exercises
• Even more discussion
• Instructions for using your calculator to graph a slope field

• Tool for integrating functions
• Tool to find definite integrals
• u-substitution applet
• Another u-substitution applet
• u-substitution
• Problems using u-substitution
• Problems with examples using u-substitution
• Discussion on integration by substitution with examples
• More on substitution
• Review problems for computing indefinite integrals with and without substitution--Go to Calculus Book II, then Chapter 1: Integration, then Section 2:  Indefinite Integrals.  Modules 1 - 4 have good problems to try.  Also Section 3:  Definite Integrals, Modules 1,2, and 3 is a good place to work.
• Find the error
• Integrate, using the Natural Logarithm & Integrate the rest of the Trigonometric Functions
• Review problems --Go to Calculus Book II, then Chapter 3:  Transcendental Functions.  Sections 1,2,3, and 6 have good problems to try.
• Graph a natural logarithm of your choosing and check its derivative
• Finding integrals of trigonometric functions -- includes integration by parts--also has good problems under Section 3 Exercises
• Integrate Exponential Functions
• Problems to work
• More problems with examples
• Integrating Trigonometric Functions
• Integration of trigonometric functions -- examples and problems to try
• Integrals of trigonometric functions
• Find the error
• Integrals Involving Inverse Trigonometric Functions
• Practice Multiple Choice Test -- more than just inverse trigonometric functions (questions written by Mrs. Halfacre)
• Tool for integrating functions -- offers suggestions and help
• Examples and Problems using logs and inverse trigonometric functions

• Good information on integration by parts with examples
• Integration by Parts
• Problems on Integration by Parts with examples
• More problems on Integration by Parts
• Integration by Parts applet
• Integrals of trigonometric functions, including integration by parts
• Find the error
• Find another error

• Graphs of exponentials & logarithms

• Separable Differential Equations
• Tool to solve differential equations by separating the variables
• Some applications using differential equations
• Problems using differential equations
• Discussion of differential equations solvable by separating variables
• Differential Equations solved in general by separating variables
• Derivatives & Integrals of Bases Other than e; Savings Account Formulas
• Lecture notes on the derivative of exponential and logarithmic functions
• Find the error
• Find another error

• Discussion of logistic equations
• Logistic Models
• Logistic problem about harvesting fish

• Explanation of Euler's Method
• Practice Problems using Euler's Method

• Lots of Integration Problems to do (Go to Integration Exercises in the left column)
  
• Lots of problems to try (Scroll down)
  
• Summary of the Integral (Scroll down)
  
• Review problems for solving differential equations, variables separable--Go to Calculus Book II, then Chapter 2:  Applications, then Section 4:  Assorted Applications, then Module 6:  Differential Equations
• Review derivatives of exponentials (do quiz 556)
  

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