The ability to automatically monitor agricultural fields is an important capability in precision farming, enabling steps towards more sustainable agriculture. Precise, high-resolution monitoring is a key prerequisite for targeted intervention and the selective application of agro-chemicals. The main goal of this paper is developing a novel crop/weed segmentation and mapping framework that processes multispectral images obtained from an unmanned aerial vehicle (UAV) using a deep neural network (DNN). Most studies on crop/weed semantic segmentation only consider single images for processing and classification. Images taken by UAVs often cover only a few hundred square meters with either color only or color and near-infrared (NIR) channels. Although a map can be generated by processing single segmented images incrementally, this requires additional complex information fusion techniques which struggle to handle high fidelity maps due to their computational costs and problems in ensuring global consistency. Moreover, computing a single large and accurate vegetation map (e.g., crop/weed) using a DNN is non-trivial due to difficulties arising from: (1) limited ground sample distances (GSDs) in high-altitude datasets, (2) sacrificed resolution resulting from downsampling high-fidelity images, and (3) multispectral image alignment. To address these issues, we adopt a stand sliding window approach that operates on only small portions of multispectral orthomosaic maps (tiles), which are channel-wise aligned and calibrated radiometrically across the entire map. We define the tile size to be the same as that of the DNN input to avoid resolution loss. Compared to our baseline model (i.e., SegNet with 3 channel RGB (red, green, and blue) inputs) yielding an area under the curve (AUC) of [background=0.607, crop=0.681, weed=0.576], our proposed model with 9 input channels achieves [0.839, 0.863, 0.782]. Additionally, we provide an extensive analysis of 20 trained models, both qualitatively and quantitatively, in order to evaluate the effects of varying input channels and tunable network hyperparameters. Furthermore, we release a large sugar beet/weed aerial dataset with expertly guided annotations for further research in the fields of remote sensing, precision agriculture, and agricultural robotics.