Calculus: Difference Equations to Differential Equations

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Chapter 1: Sequences, limits, and difference equations

Section 1.1: Calculus: Areas and tangents (244 kb)
- Java applet: Area of a circle
- Java applet: Tangent line for a parabola
Section 1.2: Sequences (354 kb)
Section 1.3: The sum of a sequence (328 kb)
Section 1.4: Difference equations (360 kb)
Section 1.5: Nonlinear difference equations (283 kb)
- Java applet: Inhibited population growth

Chapter 2: Functions and their properties

Section 2.1: Functions and their graphs (488 kb)
Section 2.2: Trigonometric functions (435 kb)
Section 2.3: Limits and the notion of continuity (483 kb)
Section 2.4: Continuous functions (250 kb)
Section 2.5: Some consequences of continuity (275 kb)

Chapter 3: Best affine approximations

Section 3.1: Best affine approximations (356 kb)
Section 3.2: Best affine approximations, derivatives, and rates of change (359 kb)
Section 3.3: Differentiation of polynomials and rational functions (240 kb)
Section 3.4: Differentiation of compositions of functions (242 kb)

dcs@math.furman.edu