Competences

• • a)Manage a solid grasp of the prior principles of Calculus, both verbally and in writing as covered in Calculus I;
  • b)Deal with the theoretic knowledge behind maxima, minima, critical points and the first and second derivative for different functions and applying these results to analyse and to sketch/draw accurately;
  • c)Deal with derivatives to find the tangent, normal, and the relevant equation and interpret these results both verbally and graphically;
  • d)Apply derivatives in real-world applications such as maximising profits, minimising costs, involving two or more variables that change with respect to time, and using the chain rule to relate any rates of change of different situations;
  • e)Differentiate equations that are not explicitly solved for one variable in terms of another, also how to differentiate functions given in parametric form;
  • f)Manage, interpret and visualise Newton Raphson`s iterative method to find a closer value of a root of a function;
  • g)Apply integration for surfaces generated by revolving curves around an axis, and the length of the curve;
  • h)Apply integration to find the volume of solids using methods like the disk/shell method, taking good consideration of the axis considered and the different shapes/solids that can be formed.

Knowledge

• • • a)Develop thorough knowledge of both the theoretical and practical aspects of both differentiation and integration including trigonometric, exponential and logarithmic;
    • b)Develop knowledge of second-order differentiation and its interpretation;
    • c)Show proficiency in using derivatives to analyse the shape of graphs, including the critical points, inflection and concavity;
    • d)Explain how to apply differentiation to problems involving rates of change in variable real-world examples;
    • e)Gain knowledge and awareness of the applications of differentiation in physics and economics;
    • f)Gain knowledge of numerical methods for estimating differentiation and of the errors  associated with numerical differentiation and some integrations;
    • g)Develop knowledge of applications of integration such as length of arc of a curve, area of surface of revolution, volume of a solid of revolution;
    • h)Describe theoretical underpinnings, namely the relationship between continuity and differentiation, including points of non-differentiability and their significance;
    • i)Grasp knowledge of the mean value theorem and its implications in various mathematical and real-world scenarios;
    • j)Gain knowledge of integration techniques in solving first order differential equations and selected second-order differential equations;
    • k)Explain Calculus concepts clearly and concisely and engage in meaningful discussions fostering a deep understanding of Calculus.

Skills

• • a)Show strong foundational knowledge in Calculus and a strong ability to connect Calculus to real-world applications;
  • b)Show proficiency in using graphing calculators, software and online teaching platforms that can facilitate learning and provide visual understanding ;
  • c)Show pedagogical skills namely for curricular development, instructional strategies, and assessment techniques which determine the fundamentals of good teaching;
  • d)Practice communication skills namely the simplification of complex maths concepts in simple relatable terms and visualising maths through diagrams, software and online games to discussions;
  • e)Apply the concept of mean value in the context of integration to find the average value of a function;
  • f)Use pedagogical strategies to explain complex maths procedures in an accessible and engaging way and by applying technology for visual interpretations and problem-solving strategies to replace rote learning;
  • g)Create effective assessments that gauge understanding of advanced Calculus concepts.
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