This course extends the basic operation skills of calculus to infinite series, differential calculus for multivariable functions, integral calculus for multivariable functions, integration of multi-vector valued functions.

By the end of this course students will be able to:

· state what is meant by a sequence and series, find limits of sequence;

· apply criteria for convergence of series with terms of the same sign or alternating sign; distinguish between absolute convergence and conditional convergence;

· establish conditions for convergence of power series, other functional series and Taylor series;

· derive Maclaurin expansions of elementary transcedental functions such as sin(x) and cos(x);

·  apply direct and indirect expansion methods of some simple functions to applications of power series in approximate calculations;

· apply calculus to parametric functions and vector-valued functions;

· understand the inner and cross products of vectors, and apply them to lines and planes in space;

· introduce the polar coordinates and the related equations;

· calculate partial derivatives, total differential and high-order partial derivatives of multivariable functions;

· find the derivative of implicit functions;

· explain the concepts of directional derivative and gradient and calculate them in two and three dimensions;

· apply partial derivatives to find the tangent plane and normal line of a surface;

· locate extreme values of a multivariable function, both unconstrained and under given conditions, and apply the Lagrange multiplier method;

· describe the meaning of double integrals (Cartesian coordinates and Polar coordinates) and evaluate them; similarly for triple integral (Cartesian coordinates, Polar coordinates and Spherical coordinates);

· evaluate open and closed line integrals of vector functions, aware that the results depends on the path in general;

· determine whether a line integral is independent of path;

· apply Green’s theorem to integrals in the plane;

· express given surfaces in an appropriate form and evaluate surface integrals over both open and closed surfaces;

· apply the theorems of Green, Gauss and Stokes to line, surface and volume integrals and explain their significance in engineering;

· explain what is meant by conservative, irrotational and solenoidal fields and explain their physical meaning.

Thomas' Calculus, 12th edition

George B. Thomas

Maurice D Weir

Joel R Hass

Published by Pearson (September 2nd 2009) - Copyright © 2010

https://www.pearson.com/store/p/thomas-calculus/P100001389913/9780321587992