Calculus With Analytic Geometry Pdf - Thurman Peterson

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Calculus with Analytic Geometry by Thurman Peterson: A Classic Textbook for Mathematics Students

Calculus with Analytic Geometry is a textbook written by Thurman Stewart Peterson, a professor of mathematics at the University of Michigan. The book was first published in 1960 by Harper and Row, and has been reprinted several times since then. It covers the topics of calculus and analytic geometry in a rigorous and comprehensive way, with numerous examples, exercises, and illustrations. The book is suitable for undergraduate students who have a solid background in algebra and trigonometry.

The book is divided into two parts: Part I deals with differential calculus and its applications, while Part II deals with integral calculus and its applications. The book also includes appendices on infinite series, differential equations, and vector analysis. Some of the topics covered in the book are:

Coordinates and lines

Functions and limits

Differentiation and applications

The mean value theorem and Taylor's theorem

Maxima and minima

Curves and curve sketching

Related rates and implicit differentiation

Integration and applications

The fundamental theorem of calculus

Techniques of integration

Improper integrals

Area, volume, and arc length

Polar coordinates and parametric equations

Conic sections and quadric surfaces

Multiple integrals and applications

Line integrals and surface integrals

Green's theorem, Stokes' theorem, and the divergence theorem

The book is praised for its clarity, rigor, and pedagogy. It provides a solid foundation for students who want to pursue further studies in mathematics or related fields. The book is also a valuable reference for teachers and researchers who are interested in calculus and analytic geometry.

The book can be accessed online for free from the Internet Archive[^3^]. Alternatively, it can be purchased from Google Books[^1^] [^2^] or other online retailers.

In this section, we will review some of the main concepts and results from the book. We will also provide some examples and exercises to test your understanding.

Coordinates and Lines

The book starts with a review of the Cartesian coordinate system and the distance formula. It then introduces the concept of slope and the equation of a line. The book also covers the topics of parallel and perpendicular lines, angle between two lines, and distance from a point to a line.

Example: Find the equation of the line that passes through the points (2, -3) and (-1, 4).

Solution: We first find the slope of the line using the formula:

$$m = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{4 - (-3)}{-1 - 2} = -\\frac{7}{3}$$

Then we use the point-slope form of the equation of a line:

$$y - y_1 = m(x - x_1)$$

Substituting one of the given points and the slope, we get:

$$y - (-3) = -\\frac{7}{3}(x - 2)$$

Simplifying, we get:

$$y + 3 = -\\frac{7}{3}x + \\frac{14}{3}$$

Or equivalently:

$$7x + 3y + 7 = 0$$

This is the equation of the line in standard form.

Functions and Limits

The book then introduces the concept of a function and its domain and range. It also covers the topics of graphs of functions, transformations of functions, inverse functions, and composite functions. The book then defines the concept of a limit and its properties. It also covers the topics of one-sided limits, infinite limits, limits at infinity, and continuity.

Example: Find $$\\lim_{x \\to 0} \\frac{\\sin x}{x}$$.

Solution: We cannot directly substitute x = 0 into the function, as it would result in an indeterminate form of type $$\\frac{0}{0}$$. We need to use some algebraic or trigonometric techniques to simplify the function. One way is to use the identity:

$$\\sin x = x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\cdots$$

This is an infinite series that approximates the value of sin x for small values of x. Using only the first two terms, we get:

$$\\sin x \\approx x - \\frac{x^3}{6}$$

Dividing both sides by x, we get:

$$\\frac{\\sin x}{x} \\approx 1 - \\frac{x^2}{6}$$

Now we can take the limit as x approaches 0:

$$\\lim_{x \\to 0} \\frac{\\sin x}{x} = \\lim_{x \\to 0} (1 - \\frac{x^2}{6}) = 1 - \\lim_{x \\to 0} \\frac{x^2}{6} = 1 - 0 = 1$$

This is the value of the limit. 061ffe29dd