tailieunhanh - Ebook Calculus, early transcendentals (9th edition): Part 2

(BQ) Part 2 book "Calculus, early transcendentals" has contents: Mathematical modeling with differential equations, infinite series; parametric and polar curves; conic sections; parametric and polar curves; conic sections; vector valued functions; partial derivatives; multiple integrals, topics in vector calculus,. and other contents. | October 13, 2008 14:26 m91-ch08 Sheet number 1 Page number 561 cyan magenta yellow black 8 Photo by Milton Bell, Texas Archeological Research Laboratory, The University of Texas at Austin. In the 1920’s, excavation of an archeological site in Folsom, . uncovered a collection of prehistoric stone spearheads now known as “Folsom points.” In 1950, carbon dating of charred bison bones found nearby confirmed that human hunters lived in the area between 9000 . and 8000 . We will study carbon dating in this chapter. MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS Many of the principles in science and engineering concern relationships between changing quantities. Since rates of change are represented mathematically by derivatives, it should not be surprising that such principles are often expressed in terms of differential equations. We introduced the concept of a differential equation in Section , but in this chapter we will go into more detail. We will discuss some important mathematical models that involve differential equations, and we will discuss some methods for solving and approximating solutions of some of the basic types of differential equations. However, we will only be able to touch the surface of this topic, leaving many important topics in differential equations to courses that are devoted completely to the subject. MODELING WITH DIFFERENTIAL EQUATIONS In this section we will introduce some basic terminology and concepts concerning differential equations. We will also discuss the general idea of modeling with differential equations, and we will encounter important models that can be applied to demography, medicine, ecology, and physics. In later sections of this chapter we will investigate methods that may be used to solve these differential equations. TERMINOLOGY Table differential equation order dy = 3y dx 1 d2y dy −6 + 8y = 0 dx 2 dx 2 dy d 3y −t + (t 2 – 1)y = e t dt 3 dt 3 y′− y = e2x 1 y′′+ y′ = cos .

• Toán học
• Early transcendentals
• Mathematical modeling
• Differential equations
• Infinite series
• Polar curves
• Conic sections
• Vector valued functions
• Anton Calculus Early Transcendentals 9th
• Limits and continuity
• The derivative
• The derivative in graphing and applications
• Principles of integral evaluation
• Partial derivativesrinciples of integral evaluation
• Calculus early transcendentals
• Functions and models
• Limits and derivatives
• Applications of differentiation
• Applications of integration
• Techniques of integration
• Further applications of integration
• Parametric equations
• Polar coordinates
• Infinite sequences
• Vector functions
• Partial derivatives
• Vector calculus
• Essential calculus
• Functions and limits
• Inverse functions
• Inverse trigonometric functions
• Multiple integrals
• Topics in differentiation
• The derivative in graphing
• The definite integral
• Averaging
• Conservation of mass
• Multiphase flow models
• Multiphase flow notation
• distribution functions
• the geometry of space
• further applications
• integration
• The subject of rock mechanics
• Content of this book
• Geological setting
• Natural rock environments
• Stress as a point property
• Aerodynamics for Engineering Students
• Wing geometry
• Thickness distribution
• Two dimensional flow
• Component velocities
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