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Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children’s greater depth maths skills and knowledge. These Pupil Resources comprise: · High-quality mathematical investigations that spark curiosity · Extensive opportunities for children to explore different maths concepts and develop their range of problem solving strategies · Photocopiable pages with visual representations for every investigation,  prompts and word banks to help children discuss and develop their ideas.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children's greater depth maths skills and knowledge. This Teacher's Guide: * Shows you what greater depth maths looks like and how to assess for it * Provides ready-to-teach sequences and PowerPoints for developing greater depth mathematicians, with support for modelling key strategies, questions to scaffold children's learning and examples of age-appropriate responses * Contains 'Stumble support' to provide inclusive greater depth maths opportunities for all children.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children's greater depth maths skills and knowledge. These Pupil Resources comprise: * High-quality mathematical investigations that spark curiosity * Extensive opportunities for children to explore different maths concepts and develop their range of problem solving strategies * Photocopiable pages with visual representations for every investigation, prompts and word banks to help children discuss and develop their ideas.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children's greater depth maths skills and knowledge. This Teacher's Guide: * Shows you what greater depth maths looks like and how to assess for it * Provides ready-to-teach sequences and PowerPoints for developing greater depth mathematicians, with support for modelling key strategies, questions to scaffold children's learning and examples of age-appropriate responses * Contains 'Stumble support' to provide inclusive greater depth maths opportunities for all children.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children's greater depth maths skills and knowledge. These Pupil Resources comprise: * High-quality mathematical investigations that spark curiosity * Extensive opportunities for children to explore different maths concepts and develop their range of problem solving strategies * Photocopiable pages with visual representations for every investigation, prompts and word banks to help children discuss and develop their ideas.
Greater Depth Maths is a flexible resource that can be used alongside your existing scheme of work to support pupils who are ready to extend their mathematical thinking. It provides a structured approach for systematically developing children’s greater depth maths skills and knowledge. This Teacher’s Guide: · Shows you what greater depth maths looks like and how to assess for it · Provides ready-to-teach sequences  and PowerPoints for developing greater depth mathematicians, with support for modelling key strategies, questions to scaffold children’s learning and examples of age-appropriate responses · Contains ‘Stumble support’ to provide inclusive greater depth maths opportunities for all children.
Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed - boundary, decentralized, distributed, and Lagrangian control - corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
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