Sequential Design is a core concept of the Waterfall Project Management method. In this design, each phase must be fully completed before moving on to the next one. It ensures meticulously crafted deliverables each time a phase completes, feeding into the success of the subsequent phase. While advantageous in producing high quality results, critics argue that this design lacks flexibility and adaptability to accommodate changes during the project lifecycle.

In Waterfall Project Management, an upfront detailed plan listing out the timeline and cost of each phase is drawn. This methodology values thorough planning at the outset to ensure time and budget constraints are adhered to. Because every subsequent phase is dependent on the preceding one, being on time and on budget is crucial. However, this strict adherence to predefined parameters could limit response to unexpected changes during project execution.

Waterfall methodology places great emphasis on documentation. Each phase's output is documented meticulously to facilitate smooth transition to the next phase. The belief is that well-documented results and processes contribute to effective team communication and understanding for all stakeholders. The downside is that it could potentially lead to excessive paperwork and lose focus from the real work or issues that need immediate attention.

Waterfall methodology typically involves the client at the beginning and end stages of the project. Detailed requirements are gathered at the onset, followed by extensive planning and sequential execution. The client sees the final product only at the end, not lending much space for them to make changes or provide incremental feedback. While this model can work for projects with stable requirements, it falls short with rapidly changing environments or when client collaboration is key.

Requirement Analysis is a critical phase of the waterfall project management approach where detailed requirements of the desired end product are recorded. These requirements are used throughout the project life cycle as a reference to ensure all software demands are met. This concept involves the identification of stakeholders, capturing their needs and expectations, analyzing them thoroughly, and documenting them in a formal and well-structured document known as the Requirement Specification Document. Failure to capture correct and complete requirements during this phase could lead to project failure as coding and testing would be based on misunderstood or incorrect requirements.

Designing is the second stage of the waterfall model. It is where system and software design is processed. The requirements identified in the first phase are translated into a software representation. The design phase is considered the stepping stone to physical construction, as the complete architectural blueprint of the project is laid out. This phase enables the developers to understand what exactly needs to be built and provides a detailed view of the system's behavior and how different components will interact with each other. With a good design in hand, a development team can reduce the complexity of the implementation phase.

Code Generation & Testing is an important stage in the waterfall model, where the actual code of the software is written based on the detailed design documentation. Also, each unit of the software is tested here to uncover and fix the issues as early as possible. The objective of this phase is to translate the design of the system into code in a suitable programming language, which can bring potential problems to the surface. The initial code is known for containing several bugs and errors, and therefore each piece of code is rigorously tested to ensure its correctness.

System integration is a critical phase of the waterfall methodology, where the individual units or modules of the software are combined and tested as a group. It ensures smooth interfacing between different modules and components. Also, it ensures that the integrated system functions as expected and satisfies the requirements. This process can discover issues that occur due to the interaction of different modules. It is crucial as software is rarely built in one piece but is constructed in parts or modules.

Implementation & Maintenance is the final stage in Waterfall Project Management, during which the developed software is delivered to the customer and put into use. During this phase, the focus is to ensure that the system continues to operate and meet the business objectives. Regular updates, repairing, and enhancements are part of this phase. The maintenance phase extends over a long period and involves correcting errors that were not discovered during the product's testing phase and improving the implementation of system units and enhancing the system's services as new requirements are discovered.

In Waterfall Project Management, the clear and precise definition of project goals and objectives is crucial. Prior to the project start, all aspects and elements of the project are thoroughly defined. This involves detailing all project requirements and expectations, thus providing a concrete plan for the entire project cycle. It is this meticulous pre-planning that makes Waterfall management a preferred choice for projects where requirements are long-term and unlikely to change. Understanding and defining goals and objectives at the start reduces the likelihood of errors and discrepancies later on in the project lifecycle.

The Waterfall methodology is characterized by its sequential approach. Projects are divided into clearly defined, distinct phases that follow a linear approach. Phases such as requirement gathering, analysis, design, development, testing, deployment, and maintenance must be completed in a specific order. No phase starts until the previous one is completely finalized and there is no or very limited overlapping in the phases. This approach ensures a high level of control and predictability in managing projects.

In the Waterfall model, regular monitoring and control ensure that the project is on the planned track in terms of project schedule, cost, and quality. Project performance data is constantly collected and compared to the project plan. If there is a deviation, corrective action is taken to put the project back on track. This step entails regular review meetings, performance reporting, and feedback cycles to ensure the project is progressing smoothly and as planned.

Waterfall model places a high emphasis on thorough and detailed documentation. At each phase's end, an extensive review and documentation ensure that all deliverables meet the predetermined standards and requirements. Not only does this provide a record of what was planned versus what was delivered, it also provides a reference point for future projects. Each documented phase is a ready reference manual for new team members and a guide for maintaining and upgrading the system in future.