On successful completion of this module the student should be able to:1. Calculate first and second order partial derivatives. 2. Find equations of tangent lines to curves and tangent planes to surfaces.3. Determine rates of change using the chain rule. 4. Find approximate values of functions and percentage changes. 5. Calculate directional derivatives.6. Find and classify critical points of functions of several variables.7. Solve constrained extremum problems using the method of Lagrange multipliers. 8. Solve linear constant coefficient differential equations by various methods.

1. Functions of several variables; 2. Partial derivatives, chain rule, linear approximation; 3. Gradient and directional derivatives; 4. Second order partial derivatives and the Hessian matrix; 5. The Jacobian matrix, chain rule and inverse function theorem; 6. Maxima and minima, classification of critical points; 7. Constrained optimization and Lagrange multipliers; 8. Higher order linear differential equations with constant coefficients; 9. (Time permitting) The Laplace transform.

The student must have taken modules in Calculus of a single variable whose content includes the basics of differential and integral calculus. The student should also have taken an Algebra module whose learning outcomes include a working knowledge of vector geometry in 2 and 3 dimensions as well as an appreciation of matrix techniques.

• Group/class feedback, post-assessment

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