Competences

• • a)Represent and use mathematical symbols and notations efficiently and present verbally and in writing the concept of a limit which underpins the definition of differentiation;
  • b)Represent both verbally and in writing, the differentiation from first principle, graphically as a slope of the tangent at a point and analytically as a rate of change;
  • c)Carry out proficiently the differentiation of different types of functions namely linear, quadratic, cubic, rational, exponential and logarithmic and trigonometric;
  • d)Choose the appropriate method of differentiation for a given function, namely sum, difference, product, quotient and composite functions, parametric and implicit differentiation;
  • e)Manage verbally and in writing the integration of different functions as the inverse process of differentiation;
  • f)Manage verbally and in writing the integration method from first principle and graphically as the accumulated change in area under a given function within a specified interval;
  • g)Carry out proficiently the appropriate methods of integration namely by sight, by substitution and by parts;
  • h)Manage proficiently Simpson`s Rule and Trapezium rule as an estimate procedure to calculate the area under a curve.

Knowledge

• • a)Explain abstract calculus concepts in an accessible and understandable way;
  • b)Identify the fundamental concept in differentiation that focuses on how a function`s output changes, with respect to the changes in its input;
  • c)Identify the behaviour of functions and  graphs and calculate the gradient/slope of a curve at any point as compared to the slope of a line;
  • d)Identify and recall the different types of functions (linear, quadratic, cubic, exponential, logarithmic, rational trigonometric and beyond;
  • e)Recall and identify differentiation rules and types:  power, sum, product, quotient, chain rule, implicit and parametric;
  • f)Identify which type of differentiation is required, and the actual technique depending on the given expression;
  • g)Describe graphical interpretations, visualise and explain derivatives, and use of graphing tools;
  • h)Explain the concept of integration  as the inverse process of differentiation and as the accumulated change in area within a specified interval;
  • i)Recall and identify integration rules: definite, indefinite, by recognition, by sight, and by parts;
  • j)Compare Simpson`s Rule and Trapezium rule as an estimate procedure to find the area under a curve and as a comparison with the exact procedure of the area under the curve by the Integration process.

Skills

• • a)Demonstrate adequate manipulation of algebraic terms and geometric results to present answers reduced and simplified to lowest terms;
  • b)Apply the differentiation process from 1st principle;
  • c)Communicate verbally about differentiation, clearly, concisely and analytically and show good core techniques across all types of derivative methods and strong problem solving skills to improve and strengthen overall teaching skills;
  • d)Demonstrate the ability to apply abstract concepts and principles in the nature of mathematics to employ and refines one`s power of abstraction and generalisations;
  • e)Reflect critically one`s own work and of others, to extend the understanding of mathematics;
  • f)Explore mathematical topics from theoretically, practically and analytically;
  • g)Apply the integration concept, the constant rule and indefinite and definite rule;
  • h)Use varying methods of learning and resources in the delivery of work to cater for all learning types.
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