Difference Equations to Differential Equations
An introduction to calculus
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The Calculus of Functions of Several Variables, is available
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For an alternative introduction to calculus, see Yet Another Calculus Text.
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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 poynomials
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 lineaer 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 by
Dan Sloughter.
This work comes with ABSOLUTELY NO WARRANTY.
This work is licensed under a Creative Commons
License.
Last modified: Tuesday 18 March 2008 9:18 EDT
113014