Difference Equations to Differential Equations

An introduction to calculus

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ChapterSectionAppletDate PostScriptPDF

Sequences, limits,
and difference equations
Calculus: areas and tangents Area of a circle
Tangent line for a parabola
04-07-02
154 kb
103 kb
Sequences
11-07-04
235 kb
129 kb
The sum of a sequence
08-21-04
128 kb
110 kb
Difference equations
04-07-02
210 kb
113 kb
Nonlinear difference equations Inhibited population growth 04-07-02
291 kb
106 kb

Functions and
and their properties
Functions and their graphs
04-07-02
406 kb
132 kb
Trigonometric functions Square wave approximation
Sound wave approximation
04-07-02
413 kb
138 kb
Limits and the notion of continuity
08-25-02
355 kb
141 kb
Continuous functions
10-01-04
188 kb
103 kb
Some consequences of continuity
04-02-02
202 kb
105 kb

Best affine
approximations
Best affine approximations Affine approximations 04-07-02
206 kb
111 kb
Best affine approximations, derivatives and rates of change
04-07-02
210 kb
118 kb
Differentiation of polynomials and rational functions
04-07-02
112 kb
95 kb
Differentiation of compositions of functions
04-07-02
190 kb
120 kb
Differentiation of trigonometric functions
04-07-02
143 kb
97 kb
Newton's method Newton's method 04-07-02
140 kb
90 kb
Rolle's Theorem and the Mean Value Theorem
04-07-02
281 kb
134 kb
Finding maximum and minimum values
04-07-02
425 kb
148 kb
The geometry of graphs
04-07-02
307 kb
107 kb

Integration The definite integral
06-21-02
574 kb
188 kb
Numerical approximations of definite integrals Numerical integration rules 04-07-02
257 kb
136 kb
The fundamental theorem of calculus Cumulative area 04-07-02
267 kb
133 kb
Using the fundamental theorem Change of variable 04-07-02
117 kb
106 kb
More techniques of integration
04-07-02
106 kb
196 kb
Improper integrals
04-07-02
472 kb
148 kb
More on area
04-07-02
323 kb
106 kb
Distance, position, and the length of curves
04-07-02
289 kb
114 kb

Polynomial approximations
and Taylor series
Polynomial approximations Taylor polynomials 04-07-02
297 kb
124 kb
Taylor's Theorem
04-07-02
112 kb
99 kb
Infinite series revisited
04-07-02
165 kb
102 kb
Infinite series: the comparison test
04-07-02
103 kb
92 kb
Infinite series: the ratio test
04-07-02
82 kb
80 kb
Infinite series: absolute convergence
04-07-02
95 kb
85 kb
Power series
04-07-02
122 kb
104 kb
Taylor series
04-07-02
135 kb
92 kb
Some limit calculations
04-07-02
106 kb
97 kb

More transcendental
functions
The exponential function
09-16-04
182 kb
123 kb
The natural logarithm function
04-07-02
127 kb
102 kb
Models of growth and decay
04-07-02
166 kb
119 kb
Integration of rational functions
04-07-02
89 kb
81 kb
Inverse trigonometric functions
04-07-02
175 kb
114 kb
Trigonometric substitutions
04-07-02
107 kb
90 kb
Hyperbolic functions
04-07-02
208 kb
102 kb

The complex plane The algebra of complex numbers
04-07-02
173 kb
119 kb
The calculus of complex functions
06-15-04
168 kb
132 kb
Complex-valued functions: motion in the plane Projectile motion 04-07-02
186 kb
134 kb
The two-body problem
04-07-02
271 kb
126 kb

Differential equations Numerical solutions of differential equations Euler's method 04-07-02
229 kb
130 kb
Separation of variables
04-07-02
165 kb
106 kb
First order linear differential equations
10-16-02
146 kb
98 kb
Second order linear differential equations
04-07-02
186 kb
101 kb
Applications: pendulums and mass-spring systems
04-07-02
304 kb
129 kb
The geometry of solutions: the phase plane Phase plane for a pendulum 04-07-02
373 kb
154 kb
Power series solutions
04-07-02
125 kb
101 kb



Copyright © 1997, 2000 by Dan Sloughter.

This work comes with ABSOLUTELY NO WARRANTY.

Creative Commons License
This work is licensed under a Creative Commons License.


Last modified: 13:57 UTC 07 March 2017