Technical Calculus with Analytic Geometry (4 STU SOL)

Technical Calculus with Analytic Geometry (4 STU SOL)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 437 p.
  • 言語 ENG,ENG
  • 商品コード 9780495105459
  • DDC分類 515.15

Table of Contents

    1 Introduction to Analytic Geometry            1  (50)
1.1 The Cartesian Coordinate System 1 (2)
1.2 The Slope 3 (1)
1.3 The Straight Line 4 (3)
1.4 Curve Sketching 7 (11)
1.5 Curves with Graphing Utilities 18 (2)
1.7 The Circle 20 (3)
1.8 The Parabola 23 (4)
1.9 The Ellipse 27 (5)
1.10 The Hyperbola 32 (5)
1.11 Translation of Axes; Standard 37 (14)
Equations of the Conics
Chapter 1 Review 43 (8)
2 Introduction to Calculus: The Derivative 51 (28)
2.1 Functions and Intervals 51 (2)
2.2 Limits 53 (3)
2.4 The Derivative by the Four-Step 56 (3)
Process
2.5 Derivatives of Polynomials 59 (1)
2.6 Instantaneous Rates of Change 60 (2)
2.7 Differentiation Formulas 62 (7)
2.8 Implicit Differentiation 69 (3)
2.9 Higher Derivatives 72 (7)
Chapter 2 Review 74 (5)
3 Applications of the Derivative 79 (38)
3.1 The First-Derivative Test 79 (4)
3.2 The Second-Derivative Test 83 (10)
3.3 Exploring with Graphing Utilities 93 (4)
3.4 Applications of Minima and Maxima 97 (7)
3.5 Related Rates 104(6)
3.6 Differentials 110(7)
Chapter 3 Review 111(6)
4 The Integral 117(30)
4.1 Antiderivatives 117(1)
4.2 The Area Problem 118(1)
4.3 The Fundamental Theorem of Calculus 119(1)
4.5 Basic Integration Formulas 119(4)
4.6 Area Between Curves 123(6)
4.7 Improper Integrals 129(4)
4.8 The Constant of Integration 133(6)
4.9 Numerical Integration 139(8)
Chapter 4 Review 142(5)
5 Applications of the Integral 147(46)
5.1 Means and Root Mean Squares 147(1)
5.2 Volumes of Revolution: Disk and 148(5)
Washer Methods
5.3 Volumes of Revolution: Shell Method 153(8)
5.4 Centroids 161(12)
5.5 Moments of Inertia 173(6)
5.6 Work and Fluid Pressure 179(14)
Chapter 5 Review 189(4)
6 Derivatives of Transcendental Functions 193(34)
6.1 Review of Trigonometry 193(2)
6.2 Derivatives of Sine and Cosine 195(3)
Functions
6.3 Other Trigonometric Functions 198(4)
6.4 Inverse Trigonometric Functions 202(2)
6.5 Derivatives of Inverse Trigonometric 204(3)
Functions
6.6 Exponential and Logarithmic Functions 207(3)
6.7 Derivative of the Logarithmic Function 210(2)
6.8 Derivative of the Exponential Function 212(3)
6.9 L'Hospital's Rule 215(1)
6.10 Applications 216(5)
6.11 Newton's Method 221(6)
Chapter 6 Review 223(4)
7 Integration Techniques 227(40)
7.1 The Power Formula Again 227(2)
7.2 The Logarithmic and Exponential Forms 229(4)
7.3 Trigonometric Forms 233(3)
7.4 Further Trigonometric Forms 236(6)
7.5 Inverse Trigonometric Forms 242(3)
7.6 Integration by Trigonometric 245(6)
Substitution
7.7 Integration by Parts 251(3)
7.8 Integration of Rational Functions 254(5)
7.9 Integration by Use of Tables 259(8)
Chapter 7 Review 261(6)
8 Parametric Equations, Vectors, and Polar 267(22)
Coordinates
8.1 Vectors and Parametric Equations 267(4)
8.2 Arc Length 271(2)
8.3 Polar Coordinates 273(3)
8.4 Curves in Polar Coordinates 276(3)
8.5 Areas in Polar Coordinates 279(10)
Chapter 8 Review 286(3)
9 Three Dim. Space; Partial Derivatives; 289(48)
Multiple Integrals
9.1 Surfaces in Three Dimensions 289(7)
9.2 Partial Derivatives 296(4)
9.3 Applications of Partial Derivatives 300(7)
9.4 Curve Fitting 307(2)
9.5 Iterated Integrals 309(5)
9.6 Volumes by Double Integration 314(6)
9.7 Mass, Centroids, and Moments of 320(7)
Inertia
9.8 Volumes in Cylindrical Coordinates 327(10)
Chapter 9 Review 330(7)
10 Infinite Series 337(24)
10.1 Introduction to Infinite Series 337(1)
10.2 Tests for Convergence 338(4)
10.3 Maclaurin Series 342(3)
10.4 Operations with Series 345(1)
10.5 Computations with Series; 346(5)
Applications
10.6 Fourier Series 351(10)
Chapter 10 Review 358(3)
11 First-Order Differential Equations 361(28)
11.1 What is a Differential Equation? 361(2)
11.2 Separation of Variables 363(5)
11.3 First-Order Linear Differential 368(5)
Equations
11.4 Applications of First-Order 373(8)
Differential Equations
11.5 Numerical Solutions 381(8)
Chapter 11 Review 383(6)
12 Higher-Order Linear Differential 389(30)
Equations
12.1 Higher-Order Homogeneous 389(3)
Differential Equations
12.2 Auxiliary Equations with Repeating 392(4)
or Complex Roots
12.3 Nonhomogeneous Equations 396(10)
12.4 Applications of Second-Order 406(13)
Equations
Chapter 12 Review 414(5)
13 The Laplace Transform 419
Sections 13.1-13.3 419(6)
13.4 Solution of Linear Equations by 425
Laplace Transforms
Chapter 13 Review 434