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Multi-variable Calculus

Code: 104387
Credits: 6
2026/2027
Degree programme Type Course
Computational Mathematics and Data Analytics FB 1

Contact lecturer

Name :
Joaquin Martín Pedret
Email :
joaquin.martin@uab.cat

Teaching staff

Ángel Lorenzo Martínez

Group languages

You can consult this information at the end of the document.

Prerequisites

Calculus in one real variable. Linear Algebra.

Objectives

See the catalan document.

Learning outcomes

  • CM01 (Work intuitively, geometrically and formally with the notions of limit, derivative and integral.) Work intuitively, geometrically and formally with the notions of limit, derivative and integral.
  • CM03 (Contrast the use of calculus with the use of abstraction in algebra and analysis to solve a real problem.) Contrast the use of calculus with the use of abstraction in algebra and analysis to solve a real problem.
  • CM04 (Explain ideas and concepts of fundamental mathematics, communicating one's own reasoning to others.) Explain ideas and concepts of fundamental mathematics, communicating one's own reasoning to others.
  • KM01 (Identify the essential ideas of the proofs of some basic algebra and calculus theorems.) Identify the essential ideas of the proofs of some basic algebra and calculus theorems.
  • SM01 (Write small mathematical texts (exercises, solving theoretical questions, etc.) in an orderly and precise manner.) Write small mathematical texts (exercises, solving theoretical questions, etc.) in an orderly and precise manner.
  • SM02 (Handle inequalities, number sequences and derivatives and integrals of functions in one and several variables.) Handle inequalities, number sequences and derivatives and integrals of functions in one and several variables.

Contents

FIRST PART. DIFERENTIAL CALCULUS



  • Basic geometric and topological notions in the Euclidean space. Limits

  • Functions defined in R ^ n. Limits and continuity. Graphs and level sets.

  • The concept of differentiability. Partial derivatives and directional derivatives.

  • Local maximum and minimum of functions.

  • Derivatives of a higher order. Taylor's formula

  • Inverse function theorem. Implicit function theorem.

  • Optimization subjected to constraints.. The Lagrange Multipliers Theorem


SECOND PART. INTEGRAL CALCULUS



  • Riemann Integral of functions bounded in rectangles. Basic properties.

  • Fubini's Theorem.

  • Integration oon bounded sets.

  • Chance of variable theorem. Meaning of the Jacobian.

  • Elements of length and area, computation in noneuclidean coordinates. Integration on curves and surfaces.

  • The classical theorems of Vector Analysis.


 

Learning activities and methodology

Title Hours ECTS Learning outcomes
Exams 6 0.24
Supervised problems 10 0.4
Problems sessions 10 0.4
Homework 45 1.8
Deliberations on the concepts treated in the classroom 35 1.4
practice Sessions 12 0.48
Theoretical sessions 27 1.08
Supervision 5 0.2 
Thirty sessions of theory, 11 of problems and 12 of practices with adequate software will be carried out.
Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Midterm exam 40 0 0 CM04, KM01, SM01, SM02
Practice skills 15 0 0 CM03, CM04, SM02
Homework 5 0 0 CM01, CM03, SM01, SM02
Midterm exam 40 0 0 CM04, KM01, SM01, SM02

Midterm exams, assessment of practical sessions, and submission of problem sets.

Studnets can also ask for a unique evaluation.

The specific details must be consulted in the Catalan version of the teaching guide.



Without prejudice to other disciplinary measures deemed appropriate and in accordance with current academic regulations, any irregularities committed by a student that may lead to a change in their grade will be graded with a zero (0). For example, plagiarism, copying, allowing others to copy, or having communication devices (such as mobile phones, smart watches, etc.) during an assessment activity will result in the suspension of this assessment activity with a zero (0). Assessment activities graded in this way and by this procedure will not be recoverable. If it is necessary to pass any of these assessment activities in order to pass the course, this course will be failed directly, with no opportunity to retake it in the same academic year. The numerical grade on the transcript will be the lower of 3.0 and the weighted average of the grades if the student has committed irregularities in an assessment activity (and therefore it will not be possible to pass by compensation).


Prohibited use of Artificial Intelligence (AI) technologies

In this course, the use of Artificial Intelligence (AI) technologies is not permitted in any assessable activity or in any of its stages. Any work that includes AI-generated fragments will be considered a breach of academic integrity and may result in a partial or total penalty in the grade of the activity, or more severe sanctions in serious cases.

Bibliography

  • Functions of several variables, Martin Moskowitz and Fotios Paliogiannis, World Scientific, 2011
  • Cálculo Vectorial. J.E. Marsden y A.J.Tromba, Addison Wesley Longman
  • Teacher notes.

Software

Sagemath

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan second semester morning-mixed
(PLAB) Practical laboratories 1 Catalan second semester morning-mixed
(SEM) Seminars 1 Catalan second semester morning-mixed