Phl 410 Textbook Exercises 7.9.1 7.9.2 and 7.9.3 Solutions
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This book provides a complete course for first-year engineering mathematics. Whichever field of engineering you are studying, you will be most likely to require knowledge of the mathematics presented in this textbook. Taking a thorough approach, the authors put the concepts into an engineering context, so you can understand the relevance of mathematical techniques presented and gain a fuller appreciation of how to draw upon them throughout your studies. This MyMathLab edition comes with student access to MyMathLab Global(R), a powerful online homework, tutorial and self study system to enrich your learning. Containing hundreds of extra practice questions to support your study of each topic in the book - MyMathLab Global provides automatic, instant feedback and support tools to help you better understand the mathematical concepts.
Table of Contents
Guided tour xxi
Preface xxiv
About the authors xxvii
Chapter 1 Numbers, Algebra and Geometry 1 (62)
1.1 Introduction 2 (1)
1.2 Number and arithmetic 2 (10)
1.2.1 Number line 2 (1)
1.2.2 Rules of arithmetic 3 (4)
1.2.3 Exercises (1-5) 7 (1)
1.2.4 Inequalities 7 (1)
1.2.5 Modulus and intervals 8 (3)
1.2.6 Exercises (6-10) 11 (1)
1.3 Algebra 12 (21)
1.3.1 Algebraic manipulation 13 (6)
1.3.2 Exercises (11-16) 19 (1)
1.3.3 Equations, inequalities and identities 20 (7)
1.3.4 Exercises (17-28) 27 (1)
1.3.5 Suffix, sigma and pi notation 27 (3)
1.3.6 Factorial notation and the binomial 30 (3)
expansion
1.3.7 Exercises (29-31) 33 (1)
1.4 Geometry 33 (11)
1.4.1 Coordinates 33 (1)
1.4.2 Straight lines 33 (2)
1.4.3 Circles 35 (3)
1.4.4 Exercises (32-38) 38 (1)
1.4.5 Conics 38 (6)
1.4.6 Exercises (39-41) 44 (1)
1.5 Numbers and accuracy 44 (12)
1.5.1 Representation of numbers 45 (2)
1.5.2 Rounding, decimal places and 47 (2)
significant figures
1.5.3 Estimating the effect of rounding 49 (5)
errors
1.5.4 Exercises (42-55) 54 (1)
1.5.5 Computer arithmetic 55 (1)
1.5.6 Exercises (56-58) 56 (1)
1.6 Engineering applications 56 (3)
1.7 Review exercises (1-25) 59 (4)
Chapter 2 Functions 63 (121)
2.1 Introduction 64 (1)
2.2 Basic definitions 64 (23)
2.2.1 Concept of a function 64 (9)
2.2.2 Exercises (1-6) 73 (1)
2.2.3 Inverse functions 74 (4)
2.2.4 Composite functions 78 (3)
2.2.5 Exercises (7-13) 81 (1)
2.2.6 Odd, even and periodic functions 82 (5)
2.2.7 Exercises (14-15) 87 (1)
2.3 Linear and quadratic functions 87 (11)
2.3.1 Linear functions 87 (2)
2.3.2 Least squares fit of a linear 89 (4)
function to experimental data
2.3.3 Exercises (16-22) 93 (1)
2.3.4 The quadratic function 94 (3)
2.3.5 Exercises (23-28) 97 (1)
2.4 Polynomial functions 98 (16)
2.4.1 Basic properties 99 (1)
2.4.2 Factorization 100 (2)
2.4.3 Nested multiplication and synthetic 102 (3)
division
2.4.4 Roots of polynomial equations 105 (7)
2.4.5 Exercises (29-37) 112 (2)
2.5 Rational functions 114 (14)
2.5.1 Partial fractions 116 (6)
2.5.2 Exercises (38-41) 122 (1)
2.5.3 Asymptotes 123 (3)
2.5.4 Parametric representation 126 (2)
2.5.5 Exercises (42-46) 128 (1)
2.6 Circular functions 128 (24)
2.6.1 Trigonometric ratios 129 (2)
2.6.2 Exercises (47-53) 131 (1)
2.6.3 Circular functions 132 (6)
2.6.4 Trigonometric identities 138 (4)
2.6.5 Amplitude and phase 142 (3)
2.6.6 Exercises (54-65) 145 (1)
2.6.7 Inverse circular (trigonometric) 146 (2)
functions
2.6.8 Polar coordinates 148 (3)
2.6.9 Exercises (66-70) 151 (1)
2.7 Exponential, logarithmic and hyperbolic 152 (12)
functions
2.7.1 Exponential functions 152 (3)
2.7.2 Logarithmic functions 155 (2)
2.7.3 Exercises (71-79) 157 (1)
2.7.4 Hyperbolic functions 157 (5)
2.7.5 Inverse hyperbolic functions 162 (2)
2.7.6 Exercises (80-87) 164 (1)
2.8 Irrational functions 164 (9)
2.8.1 Algebraic functions 165 (1)
2.8.2 Implicit functions 166 (4)
2.8.3 Piecewise defined functions 170 (2)
2.8.4 Exercises (88-97) 172 (1)
2.9 Numerical evaluation of functions 173 (6)
2.9.1 Tabulated functions and interpolation 174 (4)
2.9.2 Exercises (98-103) 178 (1)
2.10 Engineering application: a design problem 179 (2)
2.11 Review exercises (1-23) 181 (3)
Chapter 3 Complex Numbers 184 (45)
3.1 Introduction 185 (1)
3.2 Properties 186 (22)
3.2.1 The Argand diagram 186 (1)
3.2.2 The arithmetic of complex numbers 187 (3)
3.2.3 Complex conjugate 190 (1)
3.2.4 Modulus and argument 191 (4)
3.2.5 Exercises (1-14) 195 (1)
3.2.6 Polar form of a complex number 196 (4)
3.2.7 Euler's formula 200 (2)
3.2.8 Exercises (15-18) 202 (1)
3.2.9 Relationship between circular and 202 (4)
hyperbolic functions
3.2.10 Logarithm of a complex number 206 (1)
3.2.11 Exercises (19-24) 207 (1)
3.3 Powers of complex numbers 208 (8)
3.3.1 De Moivre's theorem 208 (4)
3.3.2 Powers of trigonometric functions and 212 (3)
multiple angles
3.3.3 Exercises (25-32) 215 (1)
3.4 Loci in the complex plane 216 (5)
3.4.1 Straight lines 216 (1)
3.4.2 Circles 217 (2)
3.4.3 More general loci 219 (1)
3.4.4 Exercises (33-41) 220 (1)
3.5 Functions of a complex variable 221 (2)
3.5.1 Exercises (42-45) 223 (1)
3.6 Engineering application: alternating 223 (2)
currents in electrical networks
3.6.1 Exercises (46-47) 225 (1)
3.7 Review exercises (1-34) 225 (4)
Chapter 4 Vector Algebra 229 (67)
4.1 Introduction 230 (1)
4.2 Basic definitions and results 231 (45)
4.2.1 Cartesian coordinates 231 (2)
4.2.2 Scalars and vectors 233 (2)
4.2.3 Addition of vectors 235 (6)
4.2.4 Cartesian components and basic 241 (6)
properties
4.2.5 Complex numbers as vectors 247 (2)
4.2.6 Exercises (1-16) 249 (2)
4.2.7 The scalar product 251 (6)
4.2.8 Exercises (17-30) 257 (1)
4.2.9 The vector product 258 (10)
4.2.10 Exercises (31-42) 268 (1)
4.2.11 Triple products 269 (6)
4.2.12 Exercises (43-51) 275 (1)
4.3 The vector treatment of the geometry of 276 (11)
lines and planes
4.3.1 Vector equation of a line 276 (7)
4.3.2 Vector equation of a plane 283 (3)
4.3.3 Exercises (52-67) 286 (1)
4.4 Engineering application: spin-dryer 287 (3)
suspension
4.4.1 Point-particle model 287 (3)
4.5 Engineering application: cable stayed 290 (2)
bridge
4.5.1 A simple stayed bridge 290 (2)
4.6 Review exercises (1-24) 292 (4)
Chapter 5 Matrix Algebra 296 (121)
5.1 Introduction 297 (2)
5.2 Definitions and properties 299 (29)
5.2.1 Definitions 301 (3)
5.2.2 Basic operations of matrices 304 (4)
5.2.3 Exercises (1-10) 308 (2)
5.2.4 Matrix multiplication 310 (4)
5.2.5 Exercises (11-16) 314 (1)
5.2.6 Properties of matrix multiplication 315 (10)
5.2.7 Exercises (17-33) 325 (3)
5.3 Determinants 328 (13)
5.3.1 Exercises (34-50) 340 (1)
5.4 The inverse matrix 341 (6)
5.4.1 Exercises (51-59) 345 (2)
5.5 Linear equations 347 (30)
5.5.1 Exercises (60-71) 354 (2)
5.5.2 The solution of linear equations: 356 (13)
elimination methods
5.5.3 Exercises (72-80) 369 (2)
5.5.4 The solution of linear equations: 371 (6)
iterative methods
5.5.5 Exercises (81-86) 377 (1)
5.6 Rank 377 (10)
5.6.1 Exercises (87-95) 385 (2)
5.7 The eigenvalue problem 387 (16)
5.7.1 The characteristic equation 387 (2)
5.7.2 Eigenvalues and eigenvectors 389 (6)
5.7.3 Exercises (96-97) 395 (1)
5.7.4 Repeated eigenvalues 396 (4)
5.7.5 Exercises (98-102) 400 (1)
5.7.6 Some useful properties of eigenvalues 400 (2)
5.7.7 Symmetric matrices 402 (1)
5.7.8 Exercises (103-107) 403 (1)
5.8 Engineering application: spring systems 403 (4)
5.8.1 A two-particle system 404 (1)
5.8.2 An n-particle system 404 (3)
5.9 Engineering application: steady heat 407 (4)
transfer through composite materials
5.9.1 Introduction 407 (1)
5.9.2 Heat conduction 408 (1)
5.9.3 The three-layer situation 408 (2)
5.9.4 Many-layer situation 410 (1)
5.10 Review exercises (1-26) 411 (6)
Chapter 6 An Introduction to Discrete 417 (49)
Mathematics
6.1 Introduction 418 (1)
6.2 Set theory 418 (11)
6.2.1 Definitions and notation 419 (1)
6.2.2 Union and intersection 420 (2)
6.2.3 Exercises (1-8) 422 (1)
6.2.4 Algebra of sets 422 (5)
6.2.5 Exercises (9-17) 427 (2)
6.3 Switching and logic circuits 429 (13)
6.3.1 Switching circuits 429 (1)
6.3.2 Algebra of switching circuits 430 (6)
6.3.3 Exercises (18-29) 436 (1)
6.3.4 Logic circuits 437 (4)
6.3.5 Exercises (30-31) 441 (1)
6.4 Propositional logic and methods of proof 442 (15)
6.4.1 Propositions 442 (2)
6.4.2 Compound propositions 444 (3)
6.4.3 Algebra of statements 447 (3)
6.4.4 Exercises (32-37) 450 (1)
6.4.5 Implications and proofs 450 (6)
6.4.6 Exercises (38-47) 456 (1)
6.5 Engineering application: expert systems 457 (2)
6.6 Engineering application: control 459 (3)
6.7 Review exercises (1-23) 462 (4)
Chapter 7 Sequences, Series and Limits 466 (73)
7.1 Introduction 467 (1)
7.2 Sequences and series 467 (7)
7.2.1 Notation 467 (2)
7.2.2 Graphical representation of sequences 469 (3)
7.2.3 Exercises (1-13) 472 (2)
7.3 Finite sequences and series 474 (7)
7.3.1 Arithmetical sequences and series 474 (1)
7.3.2 Geometric sequences and series 475 (2)
7.3.3 Other finite series 477 (3)
7.3.4 Exercises (14-25) 480 (1)
7.4 Recurrence relations 481 (13)
7.4.1 First-order linear recurrence 482 (3)
relations with constant coefficients
7.4.2 Exercises (26-28) 485 (1)
7.4.3 Second-order linear recurrence 486 (8)
relations with constant coefficients
7.4.4 Exercises (29-35) 494 (1)
7.5 Limit of a sequence 494 (8)
7.5.1 Convergent sequences 495 (2)
7.5.2 Properties of convergent sequences 497 (2)
7.5.3 Computation of limits 499 (2)
7.5.4 Exercises (36-40) 501 (1)
7.6 Infinite series 502 (7)
7.6.1 Convergence of infinite series 502 (2)
7.6.2 Tests for convergence of positive 504 (3)
series
7.6.3 The absolute convergence of general 507 (1)
series
7.6.4 Exercises (41-49) 508 (1)
7.7 Power series 509 (9)
7.7.1 Convergence of power series 509 (2)
7.7.2 Special power series 511 (6)
7.7.3 Exercises (50-56) 517 (1)
7.8 Functions of a real variable 518 (7)
7.8.1 Limit of a function of a real variable 518 (4)
7.8.2 One-sided limits 522 (2)
7.8.3 Exercises (57-61) 524 (1)
7.9 Continuity of functions of a real variable 525 (7)
7.9.1 Properties of continuous functions 525 (2)
7.9.2 Continuous and discontinuous functions 527 (2)
7.9.3 Numerical location of zeros 529 (3)
7.9.4 Exercises (62-69) 532 (1)
7.10 Engineering application: insulator chain 532 (1)
7.11 Engineering application: approximating 533 (2)
functions and Pad? approximants
7.12 Review exercises (1-25) 535 (4)
Chapter 8 Differentiation and Integration 539 (140)
8.1 Introduction 540 (1)
8.2 Differentiation 541 (16)
8.2.1 Rates of change 541 (1)
8.2.2 Definition of a derivative 542 (2)
8.2.3 Interpretation as the slope of a 544 (2)
tangent
8.2.4 Differentiable functions 546 (1)
8.2.5 Speed, velocity and acceleration 547 (1)
8.2.6 Exercises (1-7) 548 (1)
8.2.7 Mathematical modelling using 549 (7)
derivatives
8.2.8 Exercises (8-18) 556 (1)
8.3 Techniques of differentiation 557 (35)
8.3.1 Basic rules of differentiation 558 (2)
8.3.2 Derivative of xr 560 (4)
8.3.3 Exercises (19-23) 564 (1)
8.3.4 Differentiation of polynomial 564 (3)
functions
8.3.5 Differentiation of rational functions 567 (1)
8.3.6 Differentiation of composite functions 568 (5)
8.3.7 Differentiation of inverse functions 573 (1)
8.3.8 Exercises (24-31) 574 (1)
8.3.9 Differentiation of circular functions 575 (4)
8.3.10 Extended form of the chain rule 579 (2)
8.3.11 Exercises (32-34) 581 (1)
8.3.12 Differentiation of exponential and 581 (5)
related functions
8.3.13 Exercises (35-43) 586 (1)
8.3.14 Parametric and implicit 586 (5)
differentiation
8.3.15 Exercises (44-54) 591 (1)
8.4 Higher derivatives 592 (8)
8.4.1 The second derivative 592 (4)
8.4.2 Exercises (55-67) 596 (1)
8.4.3 Curvature of plane curves 597 (3)
8.4.4 Exercises (68-71) 600 (1)
8.5 Applications to optimization problems 600 (11)
8.5.1 Optimal values 600 (9)
8.5.2 Exercises (72-81) 609 (2)
8.6 Numerical differentiation 611 (2)
8.6.1 The chord approximation 611 (2)
8.6.2 Exercises (82-86) 613 (1)
8.7 Integration 613 (12)
8.7.1 Basic ideas and definitions 613 (3)
8.7.2 Mathematical modelling using 616 (4)
integration
8.7.3 Exercises (87-95) 620 (1)
8.7.4 Definite and indefinite integrals 620 (3)
8.7.5 The Fundamental Theorem of Calculus 623 (2)
8.7.6 Exercise (96) 625 (1)
8.8 Techniques of integration 625 (21)
8.8.1 Integration as antiderivative 625 (11)
8.8.2 Exercises (97-104) 636 (1)
8.8.3 Integration by parts 637 (3)
8.8.4 Exercises (105-107) 640 (1)
8.8.5 Integration by substitution 640 (5)
8.8.6 Exercises (108-116) 645 (1)
8.9 Applications of integration 646 (11)
8.9.1 Volume of a-solid of revolution 646 (1)
8.9.2 Centroid of a plane area 647 (2)
8.9.3 Centre of gravity of a solid of 649 (1)
revolution
8.9.4 Mean values 649 (1)
8.9.5 Root mean square values 650 (1)
8.9.6 Arclength and surface area 650 (6)
8.9.7 Exercises (117-125) 656 (1)
8.10 Numerical evaluation of integrals 657 (10)
8.10.1 The trapezium rule 657 (6)
8.10.2 Simpson's rule 663 (3)
8.10.3 Exercises (126-131) 666 (1)
8.11 Engineering application: design of 667 (2)
prismatic channels
8.12 Engineering application: harmonic 669 (2)
analysis of periodic functions
8.13 Review exercises (1-39) 671 (8)
Chapter 9 Further Calculus 679 (85)
9.1 Introduction 680 (1)
9.2 Improper integrals 680 (6)
9.2.1 Integrand with an infinite 681 (3)
discontinuity
9.2.2 Infinite integrals 684 (1)
9.2.3 Exercise (1) 685 (1)
9.3 Some theorems with applications to 686 (7)
numerical methods
9.3.1 Rolle's theorem and the first mean 686 (3)
value theorems
9.3.2 Convergence of iterative schemes 689 (4)
9.3.3 Exercises (2-7) 693 (1)
9.4 Taylor's theorem and related results 693 (19)
9.4.1 Taylor polynomials and Taylor's 693 (3)
theorem
9.4.2 Taylor and Maclaurin series 696 (5)
9.4.3 L'H?pital's rule 701 (1)
9.4.4 Exercises (8-20) 702 (1)
9.4.5 Interpolation revisited 703 (1)
9.4.6 Exercises (21-23) 704 (1)
9.4.7 The convergence of iterations 705 (1)
revisited
9.4.8 Newton-Raphson procedure 706 (3)
9.4.9 Optimization revisited 709 (1)
9.4.10 Exercises (24-27) 709 (1)
9.4.11 Numerical integration 709 (2)
9.4.12 Exercises (28-31) 711 (1)
9.5 Calculus of vectors 712 (3)
9.5.1 Differentiation and integration of 712 (2)
vectors
9.5.2 Exercises (32-36) 714 (1)
9.6 Functions of several variables 715 (24)
9.6.1 Representation of functions of two 715 (2)
variables
9.6.2 Partial derivatives 717 (4)
9.6.3 Directional derivatives 721 (3)
9.6.4 Exercises (37-46) 724 (1)
9.6.5 The chain rule 725 (4)
9.6.6 Exercises (47-55) 729 (1)
9.6.7 Successive differentiation 729 (4)
9.6.8 Exercises (56-64) 733 (1)
9.6.9 The total differential and small 733 (3)
errors
9.6.10 Exercises (65-72) 736 (1)
9.6.11 Exact differentials 737 (2)
9.6.12 Exercises (73-75) 739 (1)
9.7 Taylor's theorem for functions of two 739 (15)
variables
9.7.1 Taylor's theorem 740 (3)
9.7.2 Optimization of unconstrained 743 (5)
functions
9.7.3 Exercises (76-84) 748 (1)
9.7.4 Optimization of constrained functions 749 (4)
9.7.5 Exercises (85-90) 753 (1)
9.8 Engineering application: deflection of a 754 (2)
built-in column
9.9 Engineering application: streamlines in 756 (3)
fluid dynamics
9.10 Review exercises (1-35) 759 (5)
Chapter 10 Introduction Ordinary Differential 764 (109)
Equations
10.1 Introduction 765 (1)
10.2 Engineering examples 765 (5)
10.2.1 The take-off run of an aircraft 765 (2)
10.2.2 Domestic hot-water supply 767 (1)
10.2.3 Hydro-electric power generation 768 (1)
10.2.4 Simple electrical circuits 769 (1)
10.3 The classification of differential 770 (6)
equations
10.3.1 Ordinary and partial differential 771 (1)
equations
10.3.2 Independent and dependent variables 771 (1)
10.3.3 The order of a differential equation 772 (1)
10.3.4 Linear and nonlinear differential 773 (1)
equations
10.3.5 Homogeneous and nonhomogeneous 774 (1)
equations
10.3.6 Exercises (1-2) 775 (1)
10.4 Solving differential equations 776 (7)
10.4.1 Solution by inspection 776 (1)
10.4.2 General and particular solutions 777 (1)
10.4.3 Boundary and initial conditions 778 (3)
10.4.4 Analytical and numerical solution 781 (1)
10.4.5 Exercises (3-6) 782 (1)
10.5 First-order ordinary differential 783 (19)
equations
10.5.1 A geometrical perspective 783 (3)
10.5.2 Exercises (7-10) 786 (1)
10.5.3 Solution of separable differential 786 (2)
equations
10.5.4 Exercises (11-17) 788 (1)
10.5.5 Solution of differential equations 789 (2)
of dx/dt = f(x/t) form
10.5.6 Exercises (18-22) 791 (1)
10.5.7 Solution of exact differential 791 (3)
equations
10.5.8 Exercises (23-30) 794 (1)
10.5.9 Solution of linear differential 795 (4)
equations
10.5.10 Solution of the Bernoulli 799 (2)
differential equations
10.5.11 Exercises (31-38) 801 (1)
10.6 Numerical solution of first-order 802 (9)
ordinary differential equations
10.6.1 A simple solution method: Euler's 803 (2)
method
10.6.2 Analysing Euler's method 805 (3)
10.6.3 Using numerical methods to solve 808 (2)
engineering problems
10.6.4 Exercises (39-45) 810 (1)
10.7 Engineering application: analysis of 811 (5)
damper performance
10.8 Linear differential equations 816 (10)
10.8.1 Differential operators 816 (2)
10.8.2 Linear differential equations 818 (6)
10.8.3 Exercises (46-54) 824 (2)
10.9 Linear constant-coefficient differential 826 (13)
equations
10.9.1 Linear homogeneous 826 (5)
constant-coefficient equations
10.9.2 Exercises (55-61) 831 (1)
10.9.3 Linear nonhomogeneous 832 (6)
constant-coefficient equations
10.9.4 Exercises (62-65) 838 (1)
10.10 Engineering application: second order 839 (14)
linear constant-coefficient differential
equations
10.10.1 Free oscillations of elastic systems 839 (4)
10.10.2 Free oscillations of damped elastic 843 (3)
systems
10.10.3 Forced oscillations of elastic 846 (4)
systems
10.10.4 Oscillations in electrical circuits 850 (1)
10.10.5 Exercises (66-73) 851 (2)
10.11 Numerical solution of second- and 853 (8)
higher-order differential equations
10.11.1 Numerical solution of coupled, 853 (3)
first-order equations
10.11.2 State-space representation of 856 (3)
higher-order systems
10.11.3 Exercises (74-79) 859 (2)
10.12 Qualitative analysis of second-order 861 (5)
differential equations
10.12.1 Phase-plane plots 861 (4)
10.12.2 Exercises (80-81) 865 (1)
10.13 Review exercises (1-35) 866 (7)
Chapter 11 Introduction to Laplace Transforms 873 (51)
11.1 Introduction 874 (2)
11.2 The Laplace transform 876 (21)
11.2.1 Definition and notation 876 (2)
11.2.2 Transforms of simple functions 878 (3)
11.2.3 Existence of the Laplace transform 881 (2)
11.2.4 Properties of the Laplace transform 883 (8)
11.2.5 Table of Laplace transforms 891 (1)
11.2.6 Exercises (1-3) 892 (1)
11.2.7 The inverse transform 892 (1)
11.2.8 Evaluation of inverse transforms ` 893 (2)
11.2.9 inversion using the first shift 895 (2)
theorem
11.2.10 Exercise (4) 897 (1)
11.3 Solution of differential equations 897 (13)
11.3.1 Transforms of derivatives 897 (2)
11.3.2 Transforms of integrals 899 (1)
11.3.3 Ordinary differential equations 900 (6)
11.3.4 Exercise (5) 906 (1)
11.3.5 Simultaneous differential equations 907 (2)
11.3.6 Exercise (6) 909 (1)
11.4 Engineering applications: electrical 910 (10)
circuits and mechanical vibrations
11.4.1 Electrical circuits 910 (5)
11.4.2 Mechanical vibrations 915 (4)
11.4.3 Exercises (7-12) 919 (1)
11.5 Review exercises (1-18) 920 (4)
Chapter 12 Introduction to Fourier Series 924 (49)
12.1 Introduction 925 (1)
12.2 Fourier series expansion 926 (28)
12.2.1 Periodic functions 926 (1)
12.2.2 Fourier's theorem 927 (1)
12.2.3 The Fourier coefficients 928 (3)
12.2.4 Functions of period 2π 931 (7)
12.2.5 Even and odd functions 938 (4)
12.2.6 Even and odd harmonics 942 (2)
12.2.7 Linearity property 944 (2)
12.2.8 Convergence of the Fourier series 946 (3)
12.2.9 Exercises (1-7) 949 (2)
12.2.10 Functions of period T 951 (2)
12.2.11 Exercises (8-13) 953 (1)
12.3 Functions defined over a finite interval 954 (7)
12.3.1 Full-range series 954 (2)
12.3.2 Half-range cosine and sine series 956 (4)
12.3.3 Exercises (14-23) 960 (1)
12.4 Differentiation and integration of 961 (5)
Fourier series
12.4.1 Integration of a Fourier series 961 (3)
12.4.2 Differentiation of a Fourier series 964 (1)
12.4.3 Exercises (24-26) 965 (1)
12.5 Engineering application: analysis of a 966 (3)
slider-crank mechanism
12.6 Review exercises (1-21) 969 (4)
Chapter 13 Data Handling and Probability Theory 973 (65)
13.1 Introduction 974 (1)
13.2 The raw material of statistics 975 (5)
13.2.1 Experiments and sampling 975 (1)
13.2.2 Histograms of data 975 (3)
13.2.3 Alternative types of plot 978 (2)
13.2.4 Exercises (1-5) 980 (1)
13.3 Probabilities of random events 980 (12)
13.3.1 Interpretations of probability 980 (1)
13.3.2 Sample space and events 981 (1)
13.3.3 Axioms of probability 982 (2)
13.3.4 Conditional probability 984 (4)
13.3.5 Independence 988 (3)
13.3.6 Exercises (6-23) 991 (1)
13.4 Random variables 992 (21)
13.4.1 Introduction and definition 992 (1)
13.4.2 Discrete random variables 993 (1)
13.4.3 Continuous random variables 994 (1)
13.4.4 Propertiesof density and 995 (3)
distribution functions
13.4.5 Exercises (24-31) 998 (1)
13.4.6 Measures of location and dispersion 998 (4)
13.4.7 Expected values 1002 (1)
13.4.8 Independence of random variables 1003 (1)
13.4.9 Scaling and adding random variables 1004 (3)
13.4.10 Measures from sample data 1007 (4)
13.4.11 Exercises (32-48) 1011 (2)
13.5 Important practical distributions 1013 (16)
13.5.1 The binomial distribution 1013 (2)
13.5.2 The Poisson distribution 1015 (3)
13.5.3 The normal distribution 1018 (3)
13.5.4 The central limit theorem 1021 (3)
13.5.5 Normal approximation to the binomial 1024 (2)
13.5.6 Random variables for simulation 1026 (1)
13.5.7 Exercises (49-65) 1027 (2)
13.6 Engineering application: quality control 1029 (3)
13.6.1 Attribute control charts 1029 (2)
13.6.2 United States standard attribute 1031 (1)
charts
13.6.3 Exercises (66-67) 1032 (1)
13.7 Engineering application: clustering of 1032 (3)
rare events
13.7.1 Introduction 1032 (1)
13.7.2 Survey of near-misses between 1033 (2)
aircraft
13.7.3 Exercises (68-69) 1035 (1)
13.8 Review exercises (1-13) 1035 (3)
Appendix I Tables 1038 (6)
AI.1 Some useful results 1038 (3)
AI.2 Trigonometric identities 1041 (1)
AI.3 Derivatives and integrals 1042 (1)
AI.4 Some useful standard integrals 1043 (1)
Answers to Exercises 1044 (38)
Index 1082
Phl 410 Textbook Exercises 7.9.1 7.9.2 and 7.9.3 Solutions
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