Learning Outcomes |
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1 - Knowledge |
Theoretical - Conceptual |
1) Able to give a mathematical proof for the existence of limits and continuity of functions at specified points and calculate the limits of functions and determine their asymptotes using the limit laws and determine the points where a function is continuous.
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2) Able to use the mathematical definition of the derivative to derive the rules of differentiation, apply these basic rules, chain rule and implicit differentiation to calculate the derivatives of varies functions.
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3) Able to determine the intervals where the function is decreasing and increasing, determine the points where it has local extremum values, and inflection points and then sketch graphs of functions. Calculate the linear estimates of functions.
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4) Able to calculate indefinite integrals by using basic rules of integration and substitution. Write the expression of the fundamental theorem of calculus and apply it for evaluating definite integrals and derivatives of integrals with variable limits of integration and calculate the area between curves.
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5) Able to calculate the volumes of solid objects by using cross sections, volumes of objects obtained by revolving the areas between curves about varies axes, the arc length of curves and the surface areas of surfaces obtained by revolving the curves around varies axes.
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6) Able to find the analytical expressions for inverse functions where it is possible or use graphical methods to determine the behavior of inverse functions. Calculate the derivatives of inverse functions and transcendental functions and use them in evaluating definite and indefinite integrals.
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2 - Skills |
Cognitive - Practical |
3 - Competences |
Communication and Social Competence |
Learning Competence |
Field Specific Competence |
Competence to Work Independently and Take Responsibility |