# Course:MATH101

## Course objectives

In this course students will learn the basic ideas, tools and techniques of integral calculus and will use them to solve problems from real-life applications. In particular, students will learn

- to perform integration and other operations for certain types of functions and carry out the computation fluently;
- approximation techniques for integration;
- to determine whether a sequence or a series is convergent or divergent and evaluate the limit of a convergent sequence or the sum of a convergent series;
- to recognize when and explain why such operations are possible and/or required;
- to interpret results and determine if the solutions are reasonable.

In addition, students will apply the above skills and knowledge to translate a practical problem involving some real-life applications into mathematical problem and solve it by mean of Calculus. The applications include science and engineering problems involving areas, volumes, average values, kinematics, work, hydrostatic forces, centroid, and separable differential equations. Students will also learn simple concepts involving sequences, series and power series. In general, when solving a problem students will be able to:

- after reading a problem, correctly state in their own words what the problem is asking in mathematical terms and what information is given that is needed in order to solve the problem;
- after restating the problem, identify which mathematical techniques and concepts are needed to find the solution;
- apply those techniques and concepts and correctly perform the necessary algebraic steps to obtain a solution;
- interpret results within the problem context and determine if they are reasonable.