Teacher Delivery Guide Pure Core 8.05 Surfaces and Partial Differentiation OCR Subject Content Stage 2 learners Stage 1 learners should… should additionally… Ref. 8.05 Surfaces and Partial Differentiation 8.05a 3-D surfaces a) Be able to work with functions of two variables, given either b) Extend their knowledge of surfaces to those defined by 8.05b explicitly in the form or implicitly in the form , and understand functions of more than two variables, and incorporating and use the fact that this equation, and its partial derivatives, trigonometric functions, logarithms and exponentials. relate to a 3-D surface. An informal understanding only of how the partial derivatives relate to the surface is required. Functions will involve sums and products of powers of x and y only. Issues relating to domains and ranges will not be considered beyond the appreciation that, for example the surface has no point at which . 8.05c Sections and c) Be able to sketch sections and contours, and know how contours these are related to the surface. i.e. Sections of the form or and contours of the form . 8.05d Partial d) Be able to find first and second derivatives, including mixed differentiation derivatives. Learners will be expected to recognise and use both notations for first- and second-order partial derivatives, including mixed ones. e g. , and , . Includes the Mixed derivative theorem; namely, that or for f. suitably well-defined, continuous functions
Teacher Delivery Guide Pure Core 8.05 Surfaces and Partial Differentiation OCR Ref. Subject Content Stage 1 learners should… Stage 2 learners should additionally… 8.05 Surfaces and Partial Differentiation 8.05a 8.05b 3-D surfaces a) Be able to work with functions of two variables, given either explicitly in the form or implicitly in the form , and understand and use the fact that this equation, and its partial derivatives, relate to a 3-D surface. An informal understanding only of how the partial derivatives relate to the surface is required. Functions will involve sums and products of powers of x and y only. Issues relating to domains and ranges will not be considered beyond the appreciation that, for example the surface has no point at which . b) Extend their knowledge of surfaces to those defined by functions of more than two variables, and incorporating trigonometric functions, logarithms and exponentials. 8.05c Sections and contours c) Be able to sketch sections and contours, and know how these are related to the surface. i.e. Sections of the form or and contours of the form . 8.05d Partial differentiation d) Be able to find first and second derivatives, including mixed derivatives. Learners will be expected to recognise and use both notations for first- and second-order partial derivatives, including mixed ones. e g. , and , . Includes the Mixed derivative theorem; namely, that or for suitably well-defined, continuous functions f.
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