This course introduces the basic theory of functions of a single variable. Topics include function, limit and continuity; differential calculus of one variable functions; integral calculus of one variable functions and differential equations with constant coefficients.

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

·  use the notation of functions and find limits of functions;

· analyse the continuity of a function, classify discontinuous points and describe the general properties of a continuous function in closed interval;

·  apply the fundamental formula of a derivative, use operational rules of derivatives and find the derivative of an implicit function;

· calculate the first derivative, higher-order derivatives and apply derivatives to solve some extreme value problems;

· explain the concept of a differential, derive differential formulas of basic elementary functions, apply operational rules of differentiation;

· derive a linear approximation of a function;

·  evaluate limits using l’Hôpital’s rule;

· describe the concepts of primitive function and indefinite integral, apply basic integration methods;

· describe the concept of definite integral, use the substitution rule and integration by parts;

· describe the geometrical and physical applications of definite integrals;

· describe the basic concepts of differential equations and solve separable differential equations;

· solve first-order and second-order linear differential equations and some nonhomogeneous linear differential equations;

               · apply linear differential equations with constant coefficients to solve related problems in engineering.

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