## Course introduction

#### Calculus I

PABLO CATALÁN FERNÁNDEZ

JOSÉ A. CUESTA RUIZ

Department of Mathematics, Universidad Carlos III de Madrid

Area: Mathematics

Bachelor in Telecommunication Technologies Engineering,
Bachelor in Data Science and Engineering Bachelor in Mechanical Engineering,
Bachelor in Industrial Electronics and Automation Engineering.

September, 2022 Share:

Approximately 15 hours of lecture videos, 30 hours of solved exercises videos and 105 hours of student's work to understand the concepts, do the exercises and practice with the self-assessment tests.

Total time for the student: 150 hours.

HOW TO STUDY CALCULUS

#### PRERREQUISITES AND RECOMMENDED PREVIOUS KNOWLEDGE

High-school level mathematics.

#### GENERAL DESCRIPTION OF THE COURSE

The course is divided in four blocks.

• Part One: Real Numbers and Functions, where we will explore the properties of the real line as well as introducing functions of one real variable, with an overview of elementary functions.
• Part Two: Sequences and Series introduces and explores these two mathematical objects that will be fundamental for the remainder of the course.
• Part Three: Differential Calculus introduces limits of functions, properties of continuous functions, the derivative and, finally, Taylor expansions, with some applications to the study of functions.
• Part Four: Integral Calculus introduces primitives and integrals, and then explores the relationship between derivatives and integrals in the fundamental theorem of calculus. Finally, we discuss some geometric applications of integrals.

#### OBJECTIVES: KNOWLEDGE AND SKILLS

By the end of this content area, students will be able to have:

1. Knowledge and understanding of the mathematical principles underlying their branch of engineering.

2. The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems using established methods.

3. The ability to select and use appropriate tools and methods to solve mathematical problems.

4. The ability to combine theory and practice to solve mathematical problems.

5. The ability to understanding of mathematical methods and procedures, their area of application and their limitations.

#### TEACHING MATERIAL

• Lecture notes
• Lecture Videos
• Problem sheets, with solutions
• Problem resolution videos

PRACTICAL ASSIGMENTS AND ASSESSMENT ACTIVITIES

Exams.

Last modified: Monday, 5 September 2022, 1:17 PM