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Starting in 1996,
Alexa Internet has been donating their crawl data to the Internet Archive. Flowing in every day, these data are added to the
Wayback Machine after an embargo period.
The Wayback Machine - https://web.archive.org/web/20110715014621/http://math.furman.edu:80/~dcs/book/
Difference Equations to Differential Equations
An introduction to calculus
Each section of the text is in Portable Document Format (PDF). PDF viewers are availablehere and here.
A PostScript version may be foundhere (the old homepage).
Difference Equations to Differential Equations was written with the helpofTex,DVIPS,xdvi,PDFTeX,XEmacs,nedit,XFig,epstopdf,pstoedit,Acrobat Reader® andMathematica®.
A companion multi-variable calculus text,The Calculus of Functions of Several Variables, is availablehere.
For an alternative introduction to calculus, seeYet Another Calculus Text.
Answers for selected problems are availablehere.
Send e-mail toDan Sloughter to report any errors.
Chapter 1: Sequences, limits, and difference equations
- Calculus: areas and tangents
- Applet:Area of a circle
- Applet:Tangent line for a parabola
- Sequences
- The sum of a sequence
- Difference equations
- Nonlinear difference equations
Chapter 2: Functions and their properties
- Functions and their graphs
- Trigonometric functions
- Applet:Square wave approximation
- Applet:Sound wave approximation
- Limits and the notion of continuity
- Continuous functions
- Some consequences of continuity
Chapter 3: Best affine approximations
- Best affine approximations
- Applet:Affine approximations
- Best affine approximations, derivatives, and rates of change
- Differentiation of polynomials and rational functions
- Differentiation of compositions of functions
- Differentiation of trigonometric functions
- Newton's method
- Applet:Newton's method
- Rolle's Theorem and the Mean Value Theorem
- Finding maximum and minimum values
- The geometry of graphs
Chapter 4: Integration
- The definite integral
- Numerical approximations of definite integrals
- Applet:Numerical integration rules
- The fundamental theorem of calculus
- Applet:Cumulative area
- Using the fundamental theorem
- Applet:Change of variable
- More techniques of integration
- Improper integrals
- More on area
- Distance, position, and the length of curves
Chapter 5: Polynomial approximations and Taylor series
- Polynomial approximations of definite integrals
- Applet:Taylor polynomials
- Taylor's Theorem
- Infinite series revisited
- Infinite series: the comparison test
- Infinite series: the ratio test
- Infinite series: absolute convergence
- Power series
- Taylor series
- Some limit calculations
Chapter 6: More transcendental functions
- The exponential function
- The natural logarithm function
- Models of growth and decay
- Integration of rational functions
- Inverse trigonometric functions
- Trigonometric substitutions
- Hyperbolic functions
Chapter 7: The complex plane
- The algebra of complex numbers
- The calculus of complex functions
- Complex-valued functions: motion in the plane
- Applet:Projectile motion
- The two-body problem
Chapter 8: Differential equations
- Numerical solutions of differential equations
- Applet:Euler's method
- Separation of variables
- First order linear differential equations
- Second order linear differential equations
- Applications: pendulums and mass-spring systems
- The geometry of solutions: the phase plane
- Applet:Phase plane for a pendulum
- Power series solutions
Copyright © 1997, 2000 byDan Sloughter.
This work comes with ABSOLUTELY NO WARRANTY.
This work is licensed under aCreative CommonsLicense.
Last modified: Monday 30 June 2008 17:30 EDT
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