![]() ![]() This class will be integrating active learning methods including in class worksheets, group work, and in class presentations and discussions. Demonstrate problem-solving skills, by analyzing a problem, hypothesizing the outcome, and applying the techniques learned in class to solve the problem. Write coherent and logical solutions to mathematical problems. Demonstrate ability to effectively interpret and use functions of several variables including finding limits, the use of partial derivatives, and finding and analyzing critical points of these functions with and without constraints. Understand the concepts of vectors, and vector valued functions in two and three dimensions. Understand lines, curves, planes, surfaces and graphs of functions in two variables in three dimensional coordinate systems Specific topics include: vectors, dot and cross products, equations of lines and planes, polar, cylindrical and spherical coordinates, differentiation of vector functions, velocity and acceleration, arc length, parametric surfaces, functions of several variables, partial derivatives, tangent plane and linear approximations, chain rule for partial derivatives, directional derivative and gradient, max-min problems for functions of several variables, Lagrange multipliers. it will develop techniques to obtain local linear approximations of functions (of multiple variables) in order to analyze and optimize quantities. This course will extend the methods of single-variable calculus to functions of many variables, i.e. ![]() At UIC she has been a member of the Developmental Math Task Force, which is a part of the Student Success Initiative, as well as a Master Teaching Scholar for the second year of the Center for Teaching and Learning Communities. Outside of teaching she received the Best Practices University Excellence Award, and the Campus Partner Award (Student Affairs) at Northwestern. Awards during the 15-year career at Northwestern include 10 teaching awards, including the Northwestern WCAS Teaching Alumni award, the Northwestern Charles Deering McCormick University Distinguished Lecturer Award, and eight-time recipient of the ASG Honor Roll. Prior to coming to UIC and NU, she taught at Brandeis, Tufts, Wellesley and Harvard. Martina Bode was the director of calculus at Northwestern University for 15 years before accepting her position as director of calculus at UIC in the fall of 2015. Differential Calculus of Multivariable FunctionsÄifferential Calculus of Multivariable Functions (230-CN-62) Instructors.Thus, we consider #f(x) = tan^2(x) = tan(x)tan(x)# so that we can deal with #tan(x)#, for which we know the derivative. However, the derivative for #f(x) = tan^2(x)# is not one of the elementary 6 trigonometric derivatives. In this case, expressing the function as a product is easier because the basic derivatives for the six primary trig functions ( #sin(x), cos(x), tan(x), csc(x), sec(x), cot(x)#) are known, and are, respectively, #cos(x), -sin(x), sec^2(x), -csc(x)cot(x), sec(x)tan(x), -csc^2(x)# For example, when looking at the function #f(x) = tan^2(x)#, it is easier to express the function as a product, in this case namely #f(x) = tan(x)tan(x)#. The product rule is used primarily when the function for which one desires the derivative is blatantly the product of two functions, or when the function would be more easily differentiated if looked at as the product of two functions. The product rule for derivatives states that given a function #f(x) = g(x)h(x)#, the derivative of the function is #f'(x) = g'(x)h(x) + g(x)h'(x)# ![]()
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