Understand Basic Calculus Concepts

• Define calculus and understand the difference between differentiation and integration.

• Recognize the importance of calculus in solving real-life maritime problems, like calculating speed, distance, and rates of change.

Differentiation

• Understand the concept of a derivative as the rate of change of a function.

• Differentiate basic functions (like polynomials and trigonometric functions).

• Apply differentiation to solve problems involving velocity, acceleration, and rates of change in ship movements.

• Use differentiation to find maximum and minimum values, such as optimizing fuel consumption or cargo load.

Integration

• Understand integration as the process of finding the area under a curve or accumulating quantities.

• Integrate basic functions to solve practical problems.

• Apply integration to calculate distance traveled over time, area calculations, and fuel consumption over a period.

Apply Calculus in Maritime Operations

• Use differentiation to analyze changing conditions like speed and direction in navigation.

• Apply integration to calculate cargo volumes, displacement, and tank capacities.

• Solve problems related to tides, currents, and wave motions using calculus concepts.

Interpret and Communicate Calculus Data

• Interpret graphs and data involving rates of change and accumulated values.

• Clearly explain calculus-based solutions in reports and navigational planning.

Check and Verify Calculations

• Verify solutions by applying both differentiation and integration methods where applicable.

• Use estimation techniques to check the accuracy of calculus-based solutions.