Technical Calculus with Analytic Geometry (Dover Books on Mathematics)
Judith L. Gersting
Language: English
Pages: 528
ISBN: 048667343X
Format: PDF / Kindle (mobi) / ePub
This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.
Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, integration and using the integral. The last four chapters focus on derivatives of transcendental functions, patterns for integrations, series expansion of functions, and differential equations.
Throughout, the writing style is clear, readable and informal. Examples are abundant and have complete worked solutions. Practice problems appear in the body of the text in each section; these are relatively easy and are intended to be worked by the student as soon as they are encountered. Each new type of example in the text is followed by a practice problem that allows the student to gain immediate reinforcement in applying the problem-solving technique illustrated by the example. Answers to all practice problems are given at the back of the book, many with worked-out solutions.
Other learning aids include the division of complex problem-solving processes into a series of step-by-step tasks, numerous exercises at the end of each section and a Status Check at the end of each chapter that helps students review what they have learned. Additional review exercises and a glossary, with definitions and page references, round out the book.
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is a solution to this differential equation satisfying the boundary condition A = 2000 when t = 0. Figure 11-1 34. A body of mass m is hung on the end of a vertical spring of spring constant k; the body is pulled down and then released (see Figure 11-1). In the resulting harmonic motion, the displacement y of the body from its resting position is given by the differential equation Show that the function is a solution to this differential equation satisfying the boundary conditions y = 1 when
+ 2y = e−x subject to the boundary condition y = 3 when x = 0. Rewriting the equation in linear form, dy + 2y dx = e−x dx Here P = 2 and Q = e−x. e∫P dx = e∫2 dx = e2x The general solution is or ye2x = ex + c We find the particular solution by using the values from the boundary condition. 3 � e° = e° + c 3 = 1 + c c = 2 The solution is ye2x = ex + 2 or y = e−x + 2e−2x Exercises / Section 11.4 Exercises 1–18: Solve the given differential equation. 1. 2. 3. x dy = (5y + x +
circuit with L = 2 H, R = 50 Ω, C = 0.004 F, and E = 10 cos t V. 18. Find the steady-state solution for the current in a circuit with L = 10 H, R = 50 Ω, C = 0.06 F, and E = 56 sin 2t V. 19. Find the steady-state solution for the current in a circuit with L = 1 H, R = 8 Ω, C = 0.5 F, and E = 120 cos 4t V. 20. Find the steady-state solution for the charge in a circuit with L = 5 H, R = 4 Ω, C = 0.08 F, and E = 80 sin 3t V. 21. A box of weight 800 N, which is 0.5 m on a side, is floating in
itself appear in the answer. Practice 4. Integrate: The constant of integration, C, which enters into the indefinite integral, has a geometric interpretation. Suppose Figure 6-1 Then dF(x) = f(x) dx or dF(x)/dx = f(x). The function ∫ (x) is, therefore, the slope function for F(x). Integrating ∫ f(x) dx involves finding a function, given its slope function. For each slope function, there is a whole family of curves that have the same slope for each value of x (see Figure 6-1). Assigning a
bounded by y = 1/x2, x = , and y = x. 13. Find the smaller area bounded by y2 = −x − 2, y = 2x + 7, and y = 0. 14. Find the total area bounded by y = 2x2, y = x + 3, x = −2, and x = 0. 15. Find the volume generated by rotating the area in the first quadrant bounded by y = 3x2, x = 0, and y = 12 about the y-axis. 16. Find the volume generated by rotating the area of Exercise 11 about the x-axis. 17. Find the volume generated by rotating the area bounded by y = x4, y= 0, and x = 1 about the
