A small group of profit seeking publishers dominates the American textbook market and guides the learning of the majority of our nation’s calculus students. The College Board’s AP Calculus curriculum is a de facto national standard for this gateway course that is critically important to 21st century STEM careers. A multi-representational understanding of calculus is a central pillar of the AP curriculum. This dissertation asks whether this multi-representational vision is manifest in popular calculus textbooks. This dissertation began with a survey of all AP Calculus AB Examination free response items, 2002-2011, and found that students score worse on items characterized by numerical anchors or verbal targets. Based on previously elucidated models, a new cognitive model of five levels and six principles is developed for the purpose of calculus textbook task analysis. This model explicates complexity as a function of representational input and output. Eight popular secondary calculus textbooks were selected for study based on Amazon sales rank data. All verbally anchored mathematical tasks (n=555) from sections of those books concerning the mean value theorem and all AP Calculus AB prompts (n=226) were analyzed for cognitive complexity and representational diversity using the model. The textbook study found that calculus textbooks underrepresented the numerical anchor and verbal target. It found that the textbooks were both explicitly and implicitly less cognitively complex than the AP test. The article suggested that textbook tasks should be less dense, avoid cognitive attenuation, move away from the stand-alone item, juxtapose anchor representations, scaffold student solutions, incorporate previously considered overarching concepts and include more profound follow-up questions. To date there have been no studies of calculus textbook content based on established research on cognitive learning. Given the critical role that their calculus course plays in the lives of hundreds of thousands of students annually, it is incumbent upon the College Board to establish a textbook review process at the very least in the same vain as the teacher syllabus auditing process established in recent years.

Having an engine model that is accurate but not too complicated is desirable when working with on-board diagnosis or engine control. In this thesis a four state mean value model is introduced. To make the model usable in an on-line automotive application it is discrete and simulated with a fixed step size solver. Modelling is done with simplicity as main object. Some simple static models are also presented. To validate the model measuring is carried out in a Scania R124LB truck with a 12 liter six-cylinder turbo charged diesel engine. In general, for this relatively simple model, the mean errors must be considered low. The inlet manifold pressure mean error during highway driving is 3.4\%.

Over the last years, the emission and on board diagnostics legislations for heavy duty trucks are getting more and more strict. An accurate engine model that is possible to execute in the engine control system enables both better diagnosis and lowered emissions by better control strategies. The objective of this thesis is to extend an existing mean value diesel engine model, to include turbo compound. The model should be physical, accurate, modular and it should be possible to execute in real time. The calibration procedure should be systematic, with some degree of automatization. Four different turbo compound models have been evaluated and two models were selected for further evaluation by integration with the existing model. The extended model showed to be quite insensitive to small errors in the compound turbine speed and hence, the small difference in accuracy of the tested models did not affect the other output signals significantly. The extended models had better accuracy and could be executed with longer step length than the existing model, despite that more complexity were added to the model. For example, the mean error of the intake manifold pressure at mixed driving was approximately 3.0%, compared to 5.8% for the existing model. The reasons for the improvements are probably the good performance of the added submodels and the systematic and partly automatized calibration procedure including optimization.

VehProLib is one of many libraries being developed for the object oriented multi-domain language Modelica. The layout and the current status of the library are shown. The aims of the library are to provide the user with a number of different components with different levels of complexity. The components included range from mean value engine components to in-cylinder models. An efficient way to handle parameters using records is provided. Different bus systems are implemented and discussed. Furthermore are replaceable fluid models introduced in the library. It will be shown that Modelica is a very efficient way to create an advanced modelling library.

Because of new emission and on board diagnostics legislations, heavy truck manufacturers are facing new challenges when it comes to improving the engines and the control software. Accurate and real time executable engine models are essential in this work. One successful way of lowering the NOx emissions is to use Exhaust Gas Recirculation (EGR). The objective of this thesis is to create a mean value model for Scania's next generation EGR system consisting of a poppet valve and a two stage cooler. The model will be used to extend an existing mean value engine model. Two models of different complexity for the EGR system have been validated with sufficient accuracy. Validation was performed during static test bed conditions. The resulting flow models have mean relative errors of 5.0% and 9.1% respectively. The temperature model suggested has a mean relative error of 0.77%.

Due to stricter emission legislation, there is a need for more efficient control of diesel engines with exhaust gas recirculation(EGR). In particular, it is important to estimate the air/fuel ratio accurately in transients. Therefore a new engine gas flow model has been developed. This model divides the gas into one part for oxygen and one part for inert gases. Based on this model an observer has been designed to estimate the oxygen concentration in the gas going into the engine, which can be used to calculate the air/fuel ratio. This observer can also be used to estimate the intake manifold pressure. The advantage of estimating the pressure, instead of low pass filtering the noisy signal, is that the observer does not cause time delay.

Since measurements in engine test cells are closely coupled with high costs it is of interest to use physically interpretable engine models instead of engine maps. Such engine models can also be used to do off-line tests of how new or altered components affects engine performance. In the thesis an existing mean value engine model will be extended with a model of a compressor bypass valve. A controller for that valve will also be developed. The purpose with that controller is to save torque and boost pressure but at the same time avoid having the compressor entering surge during fast closing transients in the throttle position. Both the extension and controller is successfully developed and implemented. The extension lowers the pressure after the compressor and increases the pressure before the compressor when the bypass valve is being opened and the controller shows better results in simulations than the controller used in the research lab. By using the proposed controller, as much as 5 percent higher torque can be achieved in simulations. Finally there is a discussion on wastegate control alternatives and the use of TOMOC for optimization of wastegate control.

The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational points on certain algebraic varieties in function fields. The aim is to establish asymptotic relations that are relatively robust to changes in the characteristic of the base finite field. More notably, in the case when the characteristic is "small", the results are sharper than their integer analogues.

Modern engines are faced with increasingly stringent requirements for reduced fuel consumptionand lower emissions. A technique which can partly be used to reduce emissionsof nitrogen oxides is recirculation of combusted gases (Exhaust Gas Recirculation, EGR). Ingasoline engines, it also has the advantage that it can save fuel by reducing pumping losses.To large mixture of EGR in the air to the cylinders will however affect the combustion stabilitynegatively. To investigate EGR rate and dynamics with respect to different actuatorinputs, the thesis develops an engine model that includes EGR. The model focus on the airflow in the engine and extends an existing mean value engine model. Two types of EGRsystemare investigated. They are short-route EGR which is implemented between intakemanifold and exhaust manifold and long-route EGR which is implemented between compressorand turbine. The work provides a simulation study that compares both stationaryand transient properties of the two EGR-systems, such as fuel consumption, maximum EGR,and rise time with respect to different actuators.

The ring of polynomials over a finite field has many arithmetic properties similar to those of the ring of rational integers. In this thesis, we apply the Hardy-Littlewood circle method to investigate the density of rational points on certain algebraic varieties in function fields. The aim is to establish asymptotic relations that are relatively robust to changes in the characteristic of the base finite field. More notably, in the case when the characteristic is "small", the results are sharper than their integer analogues.