viii
CONTENTS
3.20. Arc length 3.21. Curvature 3.22. Acceleration In plane motion............ 3.23. Theorem of the mean..
4.
14 15 15 15
I7
4.15. 4.16. 4.17. 4.18. 4.19. 4.20. 4.21. 4.22. 4.23. 4.24. 4.25. 4.26.
28 28 28 28 29 29 30 30 30 30 30 31 32 33
5.15. Undetermined coefficients 5.16. Variation of parameters 5.17. The Cauchy - Euler "homogeneous linear equation" 5.18. Simultaneous differential equations 5.19. First order partial differential equations.. 5.20. Second order partial differential equations .. 5.21. Runge-Kutta method of finding numerical solutions .. . . . . . . . . ..
Scalars . . . . . . . . . . . . . .. Vectors Components.......... Sums and products by scalars
39 39 39 40
28
34 35
36 36 37 37
39
VECTOR ANALYSIS • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "
6.1. 6.2. 6.3. 6.4.
17
Mean values 24 Inequalities.......... 24 Improper integrals. . . . 25 Definite integrals of functions . . . . . . . . .. 25 Plane area 25 Length of arc . . . . . . .. 25 Volumes 25 Curves and surfaces in space.. . . . . . . . . . .. 26 Change of variables In multiple integrals .. 26 Mass and density .... 26 Moment and center of gravity. . . . .. . . . . .. 27 Moment of inertia and radius of gyration .. 27
DIFFERENTIAL EQUATIONS . . . . . • . . . . . . . . . . . . . . . . . • . . . . . . . . . . . ,
5.1. Classification.......... 5.2. Solutions 5.3. First order and first degree. . . . . . . . . . . .. 5.4. Variables separable 5.5. Linear in y 5.6. Reducible to linear 5.7. Homogeneous 5.8. Exact equations 5.9. First order and higher degree :... 5.10. Equations solvable for p 5.11. Clairaut's form 5.12. Second order 5.13. Linear equations 5.14. Constant coefficients..
6.
15 16
INTEGRAL CALCULUS........................................
4.1. Indefinite integral 17 4.2. Indefinite integrals of functions 18 4.3. Polynomials 18 4.4. Simple rational fractions 18 4.5. Rational functions .... 18 4.6. Trigonometric functions 19 4.7. Exponential and hyperbolic functions. . 20 4.8. Radicals . . . . . . . . . . .. 20 4.9. Products . . . .. 21 4~10. Trigonometric or exponential integrands .. 21 4.11. Algebraic integrands .. 22 4.12. Definite integral.. . . .. 22 4.13. Approximation rules 23 4.14. Linearity properties .. 24
5.
3.24. Indeterminate forms .. 3.25. Taylor's theorem .... 3.26. Differentiation of integrals
6.5. The scalar or dot product, VI' V2 • • • • • • • • 40 6.6. The vector or cross product, Vi X V, 40 6.7. The triple scalar product 41
39