CHAPTER FOURAdvanced Topics: Taylor Series, Numerical Integration, and Differential Equations
Chapters 1–3 established the fundamental concepts of calculus. This chapter introduces three tools for putting calculus into action. Taylor's theorem provides a mathematical tool for representing any function that can be differentiated into a form that lends itself to computation, numerical integration describes the first step in evaluating integrals that have no analytical solution, and differential equations introduces the mathematical structure in which scientific problems are frequently posed.
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4.1 Taylor Series
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The mathematical functions reviewed in Chapter 1—exponentials, logarithms, and the trigonometric functions—have been ...
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