#### Differential Calculus

ELENA ROMERA COLMENAREJO

Area: Mathematical Analysis

Bachelor's Degree in Applied Mathematics and Computing

July, 2023 (first edition)Share:

#### ESTIMATED LEARNING TIME

The estimated learning time to study this subject is 30 hours for theory and 30 hours for problems.
The total estimated learning time for the student is 150 hours.

#### PREREQUISITES AND RECOMMENDED PREVIOUS KNOWLEDGE

The Mathematics of the Baccalaureate in Spain or the International Baccalaureate.

#### GENERAL DESCRIPTION OF THE COURSE

This is a first-year course on Mathematical Analysis dedicated to Differential Calculus. It is prepared for the Degree in Applied Mathematics and Computation. The beauty of the proofs and the development of the theory make it accessible to study and deep in content.

#### OBJECTIVES: KNOWLEDGE AND SKILLS

The student will learn to deal with one variable functions, their limits, continuity, derivatives, graphs, and approximations. The student will manage sequences and series of numbers and real functions. Besides, the student will be able to make proofs and to argue the resolution of the problems. Also, to model situations arising in other sciences or the daylife.

#### TEACHING MATERIAL

The materials in this course include:

1. Summaries of each chapter.
2. List of problems for each chapter.
3. Solutions to the problems for each chapter.

PRACTICAL ASSIGNMENTS AND ASSESSMENT ACTIVITIES

For the assessment of the subject, there are three different kinds of proofs:

1. Self-evaluation tests. This is homework in the form of a test that helps the student to prepare the partial proofs. There are two, one for chapters 1, 2 and 3 and the other for chapters 4, 5 and 6. The solutions are also given.
2. Partial exams. The first, Control 1, covers chapters 1, 2 and 3, and Control 2 covers chapters 4, 5 and 6. The solutions are given.
3. Final and Extraordinary exams. They cover the whole subject. The solutions are given.