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The entry into higher mathematics begins with calculus. Rarely, however, does the calculus student recognize the full power and applications for the mathematical concepts and tools that are taught. Frank R. Giordano, Maurice D. Weir, and William P. Fox produced A First Course in Mathematical Modeling a unique text designed to address this shortcoming and teach the student how to identify, formulate, and interpret the real world in mathematical terms. Mathematical modeling is the application of mathematics to explain or predict real world behavior. Often real world data are collected and used to veriiy or validate (and sometimes formulate) a hypothetical model or scenario. Inevitably, in such situations, it is desirable and necessary to have computational support available to analyze the large amounts of data. Certainly this eliminates the tedious and inefficient hand calculations necessary to validate and apply the model (assuming the calculations can even be reasonably done by hand). The primary purpose of Mathematical Modeling Using Microsoft Excel is to provide instructions and examples for using the spreadsheet program Microsoft Excel to support a wide range of mathematical modeling applications. Microsoft Excel is a powerful spreadsheet program which allows the user to organize numerical data into an easy to follow on-screen grid of columns and rows. Our version of Excel is based on Microsoft Windows. In this text, it is not the intent to teach mathematical modeling, but rather to provide computer support for most of the modeling topics covered in A First Course in Mathematical Modeling. The examples given here are support that text as well, http://archive.org/details/mathematicalmode1094526053, Captain, United States Army, Approved for public release; distribution is unlimited.

Mathematical modeling forms a bridge between the study of mathematics and the application of mathematics with the intent of explaining or predicting real world behavior. In their book A First Course in Mathematical Modeling, Frank R. Giordano, Maurice D. Weir, and William P. Fox provide an introduction to the entire modeling process. Model verification, an important step(in the modeling process, often requires the analysis of vast amounts of data, making computational support essential. Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process through the employment of MATLAB's powerful computational capabilities. In it, the reader is led through a series of examples, each building upon the previous, which apply MATLAB's computational power to various modeling scenarios. While not intended as a text in modeling, Mathematical Modeling Using MA TIAB is a useful resource for the novice modeler interested in tackling problems too large to be performed manually, http://archive.org/details/mathematicalmode109458655, Captain, United States Army, Approved for public release; distribution is unlimited.

The Unmanned Ground Vehicle/System Joint Project Office is currently developing a family of untanned ground systems that may have the potential to give the ground combat commander the ability to gain a decisive advantage in the battle for information dominance. By harnessing the power of robotics in a reconnaissance, surveillance and target acquisition role, the UGV is designed to provide the maneuver battalion commander with the ability to extend his influence beyond the capabilities of traditional scouts. This thesis examined the Unmanned Ground Vehicle Medium (UGVM) using the Joint Conflict and Tactical Simulation (JCATS) model to evaluate the impact of changes to performance characteristics of the system. The scenario used for the simulation was based on Exercise KERNEL BLITZ (KB), a biennial joint amphibious operation conducted on the West Coast of the United States. The UGVM's communication limitations and speed were varied in the JCATS simulations. Measures of effectiveness (MOEs) for these changes included total blue detections, blue detections over time, total blue kills, and blue losses over time.

Mathematical modeling forms a bridge between the study of mathematics and the application of mathematics with the intent of explaining or predicting real world behavior. In their book A First Course in Mathematical Modeling, Frank R. Giordano, Maurice D. Weir, and William P. Fox provide an introduction to the entire modeling process. Model verification, an important step(in the modeling process, often requires the analysis of vast amounts of data, making computational support essential. Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process through the employment of MATLAB's powerful computational capabilities. In it, the reader is led through a series of examples, each building upon the previous, which apply MATLAB's computational power to various modeling scenarios. While not intended as a text in modeling, Mathematical Modeling Using MA TIAB is a useful resource for the novice modeler interested in tackling problems too large to be performed manually

The entry into higher mathematics begins with calculus. Rarely, however, does the calculus student recognize the full power and applications for the mathematical concepts and tools that are taught. Frank R. Giordano, Maurice D. Weir, and William P. Fox produced A First Course in Mathematical Modeling a unique text designed to address this shortcoming and teach the student how to identify, formulate, and interpret the real world in mathematical terms. Mathematical modeling is the application of mathematics to explain or predict real world behavior. Often real world data are collected and used to veriiy or validate (and sometimes formulate) a hypothetical model or scenario. Inevitably, in such situations, it is desirable and necessary to have computational support available to analyze the large amounts of data. Certainly this eliminates the tedious and inefficient hand calculations necessary to validate and apply the model (assuming the calculations can even be reasonably done by hand). The primary purpose of Mathematical Modeling Using Microsoft Excel is to provide instructions and examples for using the spreadsheet program Microsoft Excel to support a wide range of mathematical modeling applications. Microsoft Excel is a powerful spreadsheet program which allows the user to organize numerical data into an easy to follow on-screen grid of columns and rows. Our version of Excel is based on Microsoft Windows. In this text, it is not the intent to teach mathematical modeling, but rather to provide computer support for most of the modeling topics covered in A First Course in Mathematical Modeling. The examples given here are support that text as well

The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab, which assists the student in translating the theory into a computer language. At the Naval Postgraduate School, Maple is the software used most commonly in the Mathematics Department, requiring a similar instructing tool. Mathematical Modeling Using Maple follows the lead of Mathematical Modeling With Minitab, and assists the student in grasping the concepts of the modeling class without getting slowed down by the syntax of Maple.

The Javelin antitank weapon system will replace the Dragon m Infantry and Combat Engineer battalions on a one for one basis. The tactics and techniques for Javelin employment will closely mirror those used for Dragon and TOW missile systems. This thesis examines the effectiveness of Javelin versus Dragon and examines a different employment method. The thesis goals are: • To investigate the suitability of Janus(A) to model the employment of various weapon systems. • To compare Javelin against Dragon, using measures of effectiveness and performance outlined in the Test and Evaluation Plan (TEP). • To examine how changes in the composition and tactical employment of anti-armor weapon systems influence their lethality and survivability, potentially suggesting a more effective employment method. The data generated from the simulated force-on-force scenarios is analyzed using graphical, statistical, and mathematical modeling techniques. The results could benefit the Army's Training and Doctrine Command in their combat development and combat effectiveness analysis.

Visualization is key in helping a student understand the fundamentals of Calculus. The new generation of computer literate students, raised in a video-based environment, will expect more than the traditional chalkboard methods in assisting them in this visualization. By integrating computers into the classroom and developing software to assist in mathematics instruction, we can enhance student comprehension of, and ability to apply, mathematics in solving real world problems of interest to the military. As evidenced by the success of both the Apple Macintosh and Windows software, mouse driven, graphical user interfaces (GUI's) represent a powerful and frequently-used tool in the computing environment. GUI's improve the visual capabilities in computing software, simplify program execution, and reduce the time required to become proficient with the software. When designed correctly, the GUI-based software can significantly improve the way in which people interact with computers. This thesis lays the framework and develops multi-platform GUI software modules needed for the instruction of Calculus

The Janus combat simulation offers the user a wide variety of weather effects options to employ during the execution of any simulation run, which can directly influence detection of opposing forces. Realistic weather effects are required if the simulation is to accurately reproduce "real world" results. This thesis examines the mathematics of the Janus Weather Effects Models. A weather effect option in Janus is the Sky-to-Ground Brightness Ratio (SGR). SGR affects an optical sensors ability to detect targets. It is a measure of the sun angle in relation to the horizon. A review of the derivation of SGR is performed and an analysis of SGR's affect on the number of optical detections and detection ranges is performed using an unmanned aerial vehicle (UA V) search scenario. For comparison, the UAVs are equipped with a combination of optical and thermal sensors.

This thesis describes, extends and explores the validity of Hatzopoulos Naval Combat Model of modern surface warship missile engagements. An extensive sensitivity analysis is conducted to determine how the model's output is affected by changes in force alertness and scouting effectiveness. The approach taken is to analyze the sensitivity of combat (missile exchange) results first through the use of ratios, and second by examining partial derivatives. Two ratios are developed. The first is a ratio of remaining staying power after the exchange of salvos. The second is a fractional exchange ratio, which compares the fraction of combat power remaining on the two sides after an exchange. The robustness of the fractional exchange ratio as an indicator of success in naval salvo warfare was demonstrated.

The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to the real world phenomena, and laymen have enjoyed much of the popular literature and television programs that the field has fostered. Unfortunately, the mathematics associated with these subjects has made them inaccessible to most undergraduates, even if they have a strong back ground in mathematics. This thesis presents the basic ideas of fractal geometry and chaotic dynamical systems in a setting that can by understood by undergraduate students who have has a course in advanced calculus. We hope it will allow them to gain an appreciation of the fields and motivate them to pursue further study.

This report develops a modern naval combat model. It deals with naval surface missile combat and models the attrition as a force-on-force process described in discrete time steps, or slaves. The degradation of each force is expressed in terms of remaining staying power and combat power in both opponents. It is based on Lt. Beall's model, but since it deals with missile warfare it incorporates several human factors that affect the outcome of a naval battle: specifically scouting effectiveness, leadership, morale, and training.

This thesis is a tutorial for Command, Control, and Communications (C3) students and synthesizes the essence of electronic communications systems and related frequency spectrums into an integrated set of illustrations. The objective is to help the C3 student focus his or her attention on the performed operations and transformations in order to acquires a better understanding for the processes involved. The first major illustration show how the various components of a communication system are related. These components include analog and digital signals, multiplexing, modulation, and various transmission mediums. Central to any communications system is the limitations imposed by bandwidth and noise. The concept of bandwidth is developed through Fourier analysis. An integrated set of graphics shows the relationship between the time and frequency domains and illustrates how the bandwidth increases as the pulse width decreases. Transmitting information often requires higher data rates which, in turn, require higher frequencies. Radio wave propagation is frequency dependent and a chart is developed showing the different categories of radio wave propagation as they relate to atmospheric layers and frequency. Finally, a chart relating transmission medium attenuation, noise sources, and various radio wave terminology is given.

Quantitative analysis, specifically in this thesis which studies the Quantified Judgment Model (QJM), has been used consistently as a method of analyzing ground combat. If the QJM model is to be used as a basis for making' important ground combat decisions, then its internal mathematical consistency and military soundness must be fIrmly established. A universal requirement is that any model be both reasonable and valid, in which case the model itself must be able to withstand careful scrutiny. In the case of the QJM, a dimensional analysis to ensure ,.' mathematical consistency of the variables and submodels is one test of the reasonableness of the model. Dimensional analysis tests are applied in this thesis to examine the validity of the QJM. We also perfonn some analyses to determine how sensitive the outcomes predicted by the mooel are to the values of several of the coefficients appearing in its submodels. The fInal chapter presents our conclusions and recommendations for further investigation of the QJM.

This thesis provides usage and cost data on programmable hand-held calculators (PHHC's) in the operating force of the U.S. Marine Corps (USMC). In 1978 PHHC's that computerized aircraft performance charts were procured for USMC AV-8A pilots. During 1979 the U.S. Army successfully tested and began procuring a PHHC for use by artillery fire directions centers (FDC's). USMC artillery batteries will receive this PHHC in 1981 In 1980 the Army tested and approved procurement of PHHC's for mortar FDC's. In September 1980 Beech Aircraft Corporation started selling a PHHC module which enabled Super King Air pilots to enjoy 10% fuel savings. In February 1981 Naval Air Systems Command began reviewing a proposal to provide a PHHC for the CH-53E. Each of these systems is described, and available cost information in analyzed. In order to do their jobs faster and more accurately, several individuals have written or purchased software for their personal PHHC's. Four examples which have application in the USMC are presented and explained.

Six false alarms occurred at NORAD in 1978, 1979, and 1980. These false alarms subsequently regenerated interest in launch policies and the increased possibility of accidental nuclear war, which motivated this investigation. We construct a new model to address several questions: What is the sequence of events and reasonable timing between events in the missile warning system? How much time do decision makers have to respond to a threat? What effects do United States launch policies have on decision-making time? How likely is accidental nuclear war? The results show that accidental nuclear war is not very probable with launch-under-attack, but significantly more likely if the United States adopts a launch-on-warning policy. The final decision and responsibility to use these policies, once they are implemented, rests entirely with the President of the United States.

The Janus combat simulation offers the user a wide variety of weather effects options to employ during the execution of any simulation run, which can directly influence detection of opposing forces. Realistic weather effects are required if the simulation is to accurately reproduce "real world" results. This thesis examines the mathematics of the Janus Weather Effects Models. A weather effect option in Janus is the Sky-to-Ground Brightness Ratio (SGR). SGR affects an optical sensors ability to detect targets. It is a measure of the sun angle in relation to the horizon. A review of the derivation of SGR is performed and an analysis of SGR's affect on the number of optical detections and detection ranges is performed using an unmanned aerial vehicle (UA V) search scenario. For comparison, the UAVs are equipped with a combination of optical and thermal sensors., http://archive.org/details/amathematicalnal1094543026, U.S. Navy (USN) author, Approved for public release; distribution is unlimited.

The Javelin antitank weapon system will replace the Dragon m Infantry and Combat Engineer battalions on a one for one basis. The tactics and techniques for Javelin employment will closely mirror those used for Dragon and TOW missile systems. This thesis examines the effectiveness of Javelin versus Dragon and examines a different employment method. The thesis goals are: • To investigate the suitability of Janus(A) to model the employment of various weapon systems. • To compare Javelin against Dragon, using measures of effectiveness and performance outlined in the Test and Evaluation Plan (TEP). • To examine how changes in the composition and tactical employment of anti-armor weapon systems influence their lethality and survivability, potentially suggesting a more effective employment method. The data generated from the simulated force-on-force scenarios is analyzed using graphical, statistical, and mathematical modeling techniques. The results could benefit the Army's Training and Doctrine Command in their combat development and combat effectiveness analysis., http://archive.org/details/javelinnalysisus1094542928, U.S. Army (USA) author, Approved for public release; distribution is unlimited.

Quantitative analysis, specifically in this thesis which studies the Quantified Judgment Model (QJM), has been used consistently as a method of analyzing ground combat. If the QJM model is to be used as a basis for making' important ground combat decisions, then its internal mathematical consistency and military soundness must be fIrmly established. A universal requirement is that any model be both reasonable and valid, in which case the model itself must be able to withstand careful scrutiny. In the case of the QJM, a dimensional analysis to ensure ,.' mathematical consistency of the variables and submodels is one test of the reasonableness of the model. Dimensional analysis tests are applied in this thesis to examine the validity of the QJM. We also perfonn some analyses to determine how sensitive the outcomes predicted by the mooel are to the values of several of the coefficients appearing in its submodels. The fInal chapter presents our conclusions and recommendations for further investigation of the QJM., http://archive.org/details/dimensionalnalys1094526997, Captain, United States Marine Corps, Approved for public release; distribution is unlimited.

This thesis describes, extends and explores the validity of Hatzopoulos Naval Combat Model of modern surface warship missile engagements. An extensive sensitivity analysis is conducted to determine how the model's output is affected by changes in force alertness and scouting effectiveness. The approach taken is to analyze the sensitivity of combat (missile exchange) results first through the use of ratios, and second by examining partial derivatives. Two ratios are developed. The first is a ratio of remaining staying power after the exchange of salvos. The second is a fractional exchange ratio, which compares the fraction of combat power remaining on the two sides after an exchange. The robustness of the fractional exchange ratio as an indicator of success in naval salvo warfare was demonstrated., http://archive.org/details/sensitivitynalys1094528525, Lieutenant Commander, Hellenic Navy, Approved for public release; distribution is unlimited.

The Unmanned Ground Vehicle/System Joint Project Office is currently developing a family of untanned ground systems that may have the potential to give the ground combat commander the ability to gain a decisive advantage in the battle for information dominance. By harnessing the power of robotics in a reconnaissance, surveillance and target acquisition role, the UGV is designed to provide the maneuver battalion commander with the ability to extend his influence beyond the capabilities of traditional scouts. This thesis examined the Unmanned Ground Vehicle Medium (UGVM) using the Joint Conflict and Tactical Simulation (JCATS) model to evaluate the impact of changes to performance characteristics of the system. The scenario used for the simulation was based on Exercise KERNEL BLITZ (KB), a biennial joint amphibious operation conducted on the West Coast of the United States. The UGVM's communication limitations and speed were varied in the JCATS simulations. Measures of effectiveness (MOEs) for these changes included total blue detections, blue detections over time, total blue kills, and blue losses over time., http://archive.org/details/annalysisoftacti109457954, Captain, United States Marine Corps ., Approved for public release; distribution is unlimited.

Six false alarms occurred at NORAD in 1978, 1979, and 1980. These false alarms subsequently regenerated interest in launch policies and the increased possibility of accidental nuclear war, which motivated this investigation. We construct a new model to address several questions: What is the sequence of events and reasonable timing between events in the missile warning system? How much time do decision makers have to respond to a threat? What effects do United States launch policies have on decision-making time? How likely is accidental nuclear war? The results show that accidental nuclear war is not very probable with launch-under-attack, but significantly more likely if the United States adopts a launch-on-warning policy. The final decision and responsibility to use these policies, once they are implemented, rests entirely with the President of the United States., http://archive.org/details/theprobabilityof1094521501, Lieutenant, United /states Navy, Approved for public release; distribution is unlimited.

This thesis provides usage and cost data on programmable hand-held calculators (PHHC's) in the operating force of the U.S. Marine Corps (USMC). In 1978 PHHC's that computerized aircraft performance charts were procured for USMC AV-8A pilots. During 1979 the U.S. Army successfully tested and began procuring a PHHC for use by artillery fire directions centers (FDC's). USMC artillery batteries will receive this PHHC in 1981 In 1980 the Army tested and approved procurement of PHHC's for mortar FDC's. In September 1980 Beech Aircraft Corporation started selling a PHHC module which enabled Super King Air pilots to enjoy 10% fuel savings. In February 1981 Naval Air Systems Command began reviewing a proposal to provide a PHHC for the CH-53E. Each of these systems is described, and available cost information in analyzed. In order to do their jobs faster and more accurately, several individuals have written or purchased software for their personal PHHC's. Four examples which have application in the USMC are presented and explained., http://archive.org/details/programmablehand1094520652, Major, United States Marine Corps, Approved for public release; distribution is unlimited.

Visualization is key in helping a student understand the fundamentals of Calculus. The new generation of computer literate students, raised in a video-based environment, will expect more than the traditional chalkboard methods in assisting them in this visualization. By integrating computers into the classroom and developing software to assist in mathematics instruction, we can enhance student comprehension of, and ability to apply, mathematics in solving real world problems of interest to the military. As evidenced by the success of both the Apple Macintosh and Windows software, mouse driven, graphical user interfaces (GUI's) represent a powerful and frequently-used tool in the computing environment. GUI's improve the visual capabilities in computing software, simplify program execution, and reduce the time required to become proficient with the software. When designed correctly, the GUI-based software can significantly improve the way in which people interact with computers. This thesis lays the framework and develops multi-platform GUI software modules needed for the instruction of Calculus, http://archive.org/details/integratingcompu1094530883, U.S. Army (USA) author

This thesis is a tutorial for Command, Control, and Communications (C3) students and synthesizes the essence of electronic communications systems and related frequency spectrums into an integrated set of illustrations. The objective is to help the C3 student focus his or her attention on the performed operations and transformations in order to acquires a better understanding for the processes involved. The first major illustration show how the various components of a communication system are related. These components include analog and digital signals, multiplexing, modulation, and various transmission mediums. Central to any communications system is the limitations imposed by bandwidth and noise. The concept of bandwidth is developed through Fourier analysis. An integrated set of graphics shows the relationship between the time and frequency domains and illustrates how the bandwidth increases as the pulse width decreases. Transmitting information often requires higher data rates which, in turn, require higher frequencies. Radio wave propagation is frequency dependent and a chart is developed showing the different categories of radio wave propagation as they relate to atmospheric layers and frequency. Finally, a chart relating transmission medium attenuation, noise sources, and various radio wave terminology is given., http://archive.org/details/electroniccommun1094527714, Captain, United States Air Force, Approved for public release; distribution is unlimited.

The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab, which assists the student in translating the theory into a computer language. At the Naval Postgraduate School, Maple is the software used most commonly in the Mathematics Department, requiring a similar instructing tool. Mathematical Modeling Using Maple follows the lead of Mathematical Modeling With Minitab, and assists the student in grasping the concepts of the modeling class without getting slowed down by the syntax of Maple., http://archive.org/details/mathematicalmode1094532216, NA, U.S. Navy (U.S.N.) author, Approved for public release; distribution is unlimited.

The study of fractal geometry and chaotic dynamical systems has received considerable attention in the past decade. Motivated by the interesting computer graphics produced by these fields, mathematicians have attempted to formalize the theoretical structure of the results, physicists have attempted to apply the theory to the real world phenomena, and laymen have enjoyed much of the popular literature and television programs that the field has fostered. Unfortunately, the mathematics associated with these subjects has made them inaccessible to most undergraduates, even if they have a strong back ground in mathematics. This thesis presents the basic ideas of fractal geometry and chaotic dynamical systems in a setting that can by understood by undergraduate students who have has a course in advanced calculus. We hope it will allow them to gain an appreciation of the fields and motivate them to pursue further study., http://archive.org/details/fractalsndchaos1094528232, Captain, United States Army, Approved for public release; distribution is unlimited.