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Multi-variable Calculus

Code: 104387 ECTS Credits: 6
2025/2026
Degree Type Year
Computational Mathematics and Data Analytics FB 1

Contact

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

Teachers

Alberto Debernardi Pinos

Teaching groups languages

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


Prerequisites

Calculus in one real variable. Linear Algebra.


Objectives and Contextualisation

See the catalan document.


Learning Outcomes

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

Content

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.

 


Activities and Methodology

Title Hours ECTS Learning Outcomes
Type: Directed      
Exams 6 0.24
practice Sessions 12 0.48
Problems sessions 10 0.4
Theoretical sessions 27 1.08
Type: Supervised      
Supervised problems 10 0.4
Supervision 5 0.2
Type: Autonomous      
Deliberations on the concepts treated in the classroom 35 1.4
Homework 45 1.8 

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

Continous Assessment Activities

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

Partial exams, evaluation of practices and delivery of problems.

Studnets can also ask for a unique evaluation.

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).


Bibliography

  • Cálculo Vectorial. J.E. Marsden y A.J.Tromba, Addison Wesley Longman
  • Teacher notes.

Software

Sagemath


Groups and Languages

Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.

Name Group Language Semester Turn
(PLAB) Practical laboratories 1 Catalan second semester morning-mixed
(SEM) Seminars 1 Catalan second semester morning-mixed
(TE) Theory 1 Catalan second semester morning-mixed