Mastering the TI-89 Titanium Graphing Calculator

The TI-89 Titanium has the faintly comic dignity of an instrument thathas outlived several fashions. It is no longer new enough to frighten themarketplace, nor old enough to be harmless. Its virtue lies elsewhere: itremains a compact symbolic workstation, able to calculate numerically,manipulate algebraically, draw graphs, store procedures, and expose theoperator who asked an imprecise question. That last service is among itsfinest, though it seldom receives a medal.This book is written for the student, engineer, examiner, teacher,analyst, solitary investigator, impatient apprentice, returning scholar,nocturnal problem-solver, and practical mathematician who wishes touse the calculator without becoming its clerk. The tone is deliberatelyargumentative. A calculator result is never accepted merely because thescreen is confident. It is compared with a model, an assumption, adomain, a graph, a limiting case, or a unit.The work also follows a typographical discipline. Where equations areneeded, variables are defined, notation is translated into meaning, andderivations are supplied. No expression is allowed to fall from the skydressed as authority. The attached mathematical-notation model hastherefore been treated not as decoration, but as a compact constitutionfor clarity.The reader should keep the calculator near the page. This is a manual ofaction as much as explanation. Keystrokes are not charms; they arereproducible instructions. Enter them, predict the output, test the result,and then ask whether the answer deserves citizenship in the problem.A scientific calculator is often introduced as a convenience. Thedescription is true in the same way that a library is a convenient pile ofpaper. The TI-89 Titanium deserves a sterner definition. It is a numericalengine, a symbolic algebra system, a graphing environment, a matrixlaboratory, a statistics desk, a financial worksheet, and a programmablecompanion. Each of these offices has its own grammar; confusion beginswhen one office impersonates another.This book therefore proceeds by dialectic. First comes the mathematicalclaim; then the contrary temptation; then the calculator procedure; thenthe verification. The device may solve an equation, but the operator mustdecide whether the equation represented the problem. The device mayplot a curve, but the investigator must decide whether the window liedby omission. The device may return an exact symbolic form, butexactness without assumptions is merely punctual vanity.The structure of the book follows the original table of contents. The earlychapters establish the body of the instrument and the grammar of entry.Algebra and functions follow; graphing opens the visible theatre;calculus and differential equations extend the inquiry; linear algebra andstatistics give the machine its heavier mathematical furniture; units,science, finance, and programming complete the applied arc.The method is practical but not servile. At every stage, the calculator isused as a disciplined assistant. It does not replace derivation, judgement,or mathematical memory. It makes their absence harder to excuse.

The TI-89 Titanium has the faintly comic dignity of an instrument thathas outlived several fashions. It is no longer new enough to frighten themarketplace, nor old enough to be harmless. Its virtue lies elsewhere: itremains a compact symbolic workstation, able to calculate numerically,manipulate algebraically, draw graphs, store procedures, and expose theoperator who asked an imprecise question. That last service is among itsfinest, though it seldom receives a medal.This book is written for the student, engineer, examiner, teacher,analyst, solitary investigator, impatient apprentice, returning scholar,nocturnal problem-solver, and practical mathematician who wishes touse the calculator without becoming its clerk. The tone is deliberatelyargumentative. A calculator result is never accepted merely because thescreen is confident. It is compared with a model, an assumption, adomain, a graph, a limiting case, or a unit.The work also follows a typographical discipline. Where equations areneeded, variables are defined, notation is translated into meaning, andderivations are supplied. No expression is allowed to fall from the skydressed as authority. The attached mathematical-notation model hastherefore been treated not as decoration, but as a compact constitutionfor clarity.The reader should keep the calculator near the page. This is a manual ofaction as much as explanation. Keystrokes are not charms; they arereproducible instructions. Enter them, predict the output, test the result,and then ask whether the answer deserves citizenship in the problem.A scientific calculator is often introduced as a convenience. Thedescription is true in the same way that a library is a convenient pile ofpaper. The TI-89 Titanium deserves a sterner definition. It is a numericalengine, a symbolic algebra system, a graphing environment, a matrixlaboratory, a statistics desk, a financial worksheet, and a programmablecompanion. Each of these offices has its own grammar; confusion beginswhen one office impersonates another.This book therefore proceeds by dialectic. First comes the mathematicalclaim; then the contrary temptation; then the calculator procedure; thenthe verification. The device may solve an equation, but the operator mustdecide whether the equation represented the problem. The device mayplot a curve, but the investigator must decide whether the window liedby omission. The device may return an exact symbolic form, butexactness without assumptions is merely punctual vanity.The structure of the book follows the original table of contents. The earlychapters establish the body of the instrument and the grammar of entry.Algebra and functions follow; graphing opens the visible theatre;calculus and differential equations extend the inquiry; linear algebra andstatistics give the machine its heavier mathematical furniture; units,science, finance, and programming complete the applied arc.The method is practical but not servile. At every stage, the calculator isused as a disciplined assistant. It does not replace derivation, judgement,or mathematical memory. It makes their absence harder to excuse.