Intro

• Systems of Units


  • cgs system
  • mks system
  • Engineering system
• mks system


  Also known as the International System of Units (SI)
• Units in the cgs system

  • centimeter (cm)
  • gram (g)
  • second (s)
  • dyne
• Units in the mks system

  • meter (m)
  • kilogram (kg)
  • second (s)
  • newton (nt)
• Units in the Engineering system

  • foot (ft)
  • slug
  • second (s)
  • pound (lb)
• 1 inch (in.) 2.540000 cm
• 1 foot (ft) 12 in. 30.480000 cm
• 1 yard (yd) 3 ft 91.440000 cm
• 1 statute mile (mi) 5280 ft 1.609344 km
• 1 nautical mile 6080 ft 1.853184 km
• 1 acre 4840 yd2 4046.8564 m2
• 1 mi2 640 acres 2.5899881 km2
• 1 fluid ounce 1/128 U.S. gallon 231/128 in.3 29.573730 cm3
• 1 U.S. gallon 4 quarts (liq) 8 pints (liq) 128 fl oz 3785.4118 cm3
• 1 British Imperial and Canadian gallon 1.200949 U.S. gallons 4546.087 cm3
• 1 slug 14.59390 kg
• 1 pound (lb) 4.448444 nt
• 1 newton (nt) 105 dynes
• 1 British thermal unit (Btu) 1054.35 joules
• 1 joule 107 ergs
• 1 calorie (cal) 4.1840 joules
• 1 kilowatt-hour (kWh) 3414.4 Btu 3.6 • 106 joules
• 1 horsepower (hp) 2542.48 Btu/h 178.298 cal/sec 0.74570 kW
• 1 kilowatt (kW) 1000 watts 3414.43 Btu/h 238.662 cal/s
• °F °C • 1.8 32
• 1° 60 3600 0.017453293 radian
• GUIDES AND MANUALS


  • Maple Computer Guide
  • Mathematica Computer Guide
  • Student Solutions Manual and Study Guide
  • Instructor's Manual
• PARTS AND CHAPTERS OF THE BOOK

  • PART A: Chaps. 1–6 Ordinary Differential Equations (ODEs)
  • PART B: Chaps. 7–10 Linear Algebra. Vector Calculus
  • PART C: Chaps. 11–12 Fourier Analysis. Partial Differential Equations (PDEs)
  • PART D: Chaps. 13–18 Complex Analysis, Potential Theory
  • PART E: Chaps. 19–21 Numeric Analysis
  • PART F: Chaps. 22–23 Optimization, Graphs
  • PART G: Chaps. 24–25 Probability, Statistics
• The driving force in engineering mathematics is the rapid growth of technology and the sciences. New areas—often drawing from several disciplines—come into existence.
• Modeling


  • The process in engineering, physics, computer science, biology, chemistry, environmental science, economics, and other fields whereby a physical situation or some other observation is translated into a mathematical model
  • The mathematical model could be a system of differential equations, a probabilistic model, a linear programming problem, a financial problem leading to an algebraic equation that has to be solved by Newton's method, and many others
  • The next step is solving the mathematical problem obtained by one of the many techniques covered in Advanced Engineering Mathematics
  • The third step is interpreting the mathematical result in physical or other terms to see what it means in practice and any implications
  • Finally, we may have to make a decision that may be of an industrial nature or recommend a public policy
• While we cannot predict what the future holds, we do know that the student has to practice modeling by being given problems from many different applications as is done in this book. We teach modeling from scratch, right in Sec. 1.1, and give many examples in Sec. 1.3, and continue to reinforce the modeling process throughout the book.
• Judicious use of powerful software

  • For numerics (listed in the beginning of Part E) and statistics (Part G) is of growing importance
  • Projects in engineering and industrial companies may involve large problems of modeling very complex systems with hundreds of thousands of equations or even more. They require the use of such software
  • Our policy has always been to leave it up to the instructor to determine the degree of use of computers, from none or little use to extensive use
• The beauty of engineering mathematics

  • Engineering mathematics relies on relatively few basic concepts and involves powerful unifying principles
  • We point them out whenever they are clearly visible, such as in Sec. 4.1 where we "grow" a mixing problem from one tank to two tanks and a circuit problem from one circuit to two circuits, thereby also increasing the number of ODEs from one ODE to two ODEs
  • This is an example of an attractive mathematical model because the "growth" in the problem is reflected by an "increase" in ODEs
• To clearly identify the conceptual structure of subject matters


  • Complex analysis (in Part D) is a field that is not monolithic in structure but was formed by three distinct schools of mathematics. Each gave a different approach, which we clearly mark
  • The first approach is solving complex integrals by Cauchy's integral formula (Chaps. 13 and 14), the second approach is to use the Laurent series and solve complex integrals by residue integration (Chaps. 15 and 16), and finally we use a geometric approach of conformal mapping to solve boundary value problems (Chaps. 17 and 18)
  • Learning the conceptual structure and terminology of the different areas of engineering mathematics is very important for three reasons: 1) It allows the student to identify a new problem and put it into the right group of problems, 2) The student can absorb new information more rapidly by being able to fit it into the conceptual structure, 3) Knowledge of the conceptual structure and terminology is also important when using the Internet to search for mathematical information
• The problem sets have been revised and rebalanced with some problem sets having more problems and some less, reflecting changes in engineering mathematics. There is a greater emphasis on modeling. Now there are also problems on the discrete Fourier transform (in Sec. 11.9).
• Chap. 5, on series solutions of ODEs and special functions, has been shortened. Chap. 11 on Fourier Analysis now contains Sturm–Liouville problems, orthogonal functions, and orthogonal eigenfunction expansions (Secs. 11.5, 11.6), where they fit better conceptually (rather than in Chap. 5), being extensions of Fourier's idea of using orthogonal functions.
• In order to give the student a better idea of the structure of the material (see Underlying Theme 4 above), we have entirely rewritten the openings of parts and chapters. Furthermore, large parts or individual paragraphs of sections have been rewritten or new sentences inserted into the text. This should give the students a better intuitive understanding of the material (see Theme 3 above), let them draw conclusions on their own, and be able to tackle more advanced material. Overall, we feel that the book has become more detailed and leisurely written.
• Upon the explicit request of the users, the answers provided in the Student Solutions Manual and Study Guide are more detailed and complete. More explanations are given on how to learn the material effectively by pointing out what is most important.
• Historical footnotes are there to show the student that many people from different countries working in different professions, such as surveyors, researchers in industry, etc., contributed to the field of engineering mathematics. It should encourage the students to be creative in their own interests and careers and perhaps also to make contributions to engineering mathematics.
• Parts of Chap. 1 on first-order ODEs are rewritten. More emphasis on modeling, also new block diagram explaining this concept in Sec. 1.1. Early introduction of Euler's method in Sec. 1.2 to familiarize student with basic numerics. More examples of separable ODEs in Sec. 1.3.