Mathematics Projects
Second Semester Calculus
Projects available:
Project contributed by Neal Brand.
This project requires students to compute a certain probability.
No previous knowledge of probability or counting techniques is assumed.
Project teaches and provides practice in
- Basic counting
- Limits
- Riemann sums
- Improper integrals
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Project contributed by Neal Brand.
In this projects, students will derive the formula for the nth
Fibonacci number.
Project teaches and provides practice in
- Partial fraction decomposition
- Algebra of power series
- Deriving a power series
- Radius of convergence of a power series
Trigonometry without Geometry or Noncircular Trigonometry.
TeX version or
Postscript version.
Project contributed by Neal Brand.
This project gives an alternate definition to the trigonometric
functions which does not involve geometry.
Project teaches and provides practice in
- Defining functions in terms of integrals
- Inverse functions
- Fundemental theorem of calculus
- Deriving trigonometric identities based on alternate
definitions
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Project contributed by Neal Brand.
This project is an introduction to Fourier series. Students
should be able to compute integrals and have at least a basic ideas of what a
series is.
Project teaches and provides practice in
- Computation of integrals
- Introduction to Fourier series
- Trigonometric identities
- Use of Mathematica or Maple
- Trigonometry using Differential Equations. PDF
format.
Project contributed by Neal Brand.
This project gives an alternative definitions of the sine and cosine functions
involving a differential equation. Students are not expected to have any
background knowledge of differential equations.
Project teaches and provides practice in
- Defining functions using differential equations
- Chain rule
- Geometry of second derivative
- Periodic functions
- Mean value theorem implications
- The Exponential Function (Using Differential Equations)
PDF format.
Project contributed by Neal Brand.
This project is an introduction to differential equations. Students
can generally do this project as soon as they know the basic computational
techniques for taking derivatives. The purpose is to give students a
rigorous way to define the exponential function without first defining the
logarithmic function.
Project teaches and provides practice in
- Using uniqueness and existence theorems
- Induction
- Rules of differentiation
- The Exponetial Function (Power Series). PDF
format
Project contribute by Neal Brand
This project is an introduction to differential equations. Students
can generally do this project as soon as they know the basic computational
techniques for taking derivatives. The purpose is to give students a
rigorous way to define the exponential function without first defining the
logarithmic function.
Project teaches and provides practice in
- Computing interval of confergence
- Induction
- Taylor expansions
- Computations involving power series
Return to the UNT project home page.