Calculus I

Recommended Prerequisites

 Differential calculus, analytic geometry and algebra taught in Mathematics A (Secondary School).

Teaching Methods

Lectures: theoretical exposition of the material (blackboard, slides and algebraic and graphical computer programs) with examples. At the end related exercises are proposed. All contents are articulated, fostering in students the recognition that only a good understanding of the theory will allow them to tackle with applications P classes: designed to be discussion classes of exercises that students tried to solve previously. Teacher and students focus on exercises viewed as harder Tutorial attendance: to keep a regular pace of study and to fill gaps in learning and individual work.

Learning Outcomes

Overall obj. The student shall understand, master and apply the mathematical methods presented. Specific The student shall: apply techniques of differential calculus (DC) of real valued functions (rvf) of one or n real variables in mathematical exercises and in economic problems; exercise and apply logical-deductive reasoning (ldr). Generic competencies The student shall: use mathematics as a tool to read and act on real world situations; use analysis/synthesis to solve mathematical problems and the ability to work autonomously; communicate (orally and written) the procedures required to solve problems or exercises. Specific The student shall: reveal analysis/synthesis skills to solve DC problems; define the main mathematical concepts inherent to the DC; describe and apply the DC in mathematical exercises; describe and apply DC mathematical techniques  in economic-financial problems; apply ldr in exercises and applications involving DC techniques.

Work Placement(s)

No

Syllabus

Chapter 1. Differential calculus on : complementary aspects and applications.

1.1First definitions

1.2Graphs of some elementary functions

1.2.1Polynomial functions

1.2.2Rational functions

1.2.3Trigonometric functions

1.2.4Inverse trigonometric functions

1.2.5Exponentials and logarithmic functions

1.2.6Exponential-power functions

1.3Limits and continuity

1.3.1Limit: numerical, graphical and analytical approaches

1.3.2Infinite limits and limits at the infinity: asymptotes

1.3.3More properties on limits

1.3.4Continuous functions

1.4Derivatives and differentials

1.4.1Definition and first interpretations

1.4.2Calculation of derivatives

1.4.3Implicit derivation

1.4.4Differentials and linear approximations

1.4.5Aplications of derivatives

Chapter 2. Differential calculus on .

2.1Domain and graphic representations

2.2Limits and continuity

2.3Parcial derivatives

2.4Differentials

2.5Chain rules

2.6Tangent plane, gradient and directional derivatives

2.7Optimisation

2.8Constrained optimisation

  

Head Lecturer(s)

Paulo Manuel David Mota Saraiva

Assessment Methods

Assessment
Periodic or by final exam as given in the course information: 100.0%

Bibliography

AZENHA, Acilina ; JERÓNIMO, Maria Amélia - Cálculo diferencial e integral em IR e IRn. Lisboa : Editora McGraw-Hill de Portugal, 1995. [BP 517 AZE]
BINMORE, Ken ; DAVIES, Joan – Calculus : [concepts and methods]. Cambridge : Cambridge University Press, 2007. [BP 517 BIN]
LARSON, Ron ;  HOSTETLER, Robert P. ; EDWARDS, Bruce H. – Cálculo. 8ª ed.. São Paulo : McGraw-Hill Interamericana do Brasil, 2006. 2 vol.. [BP 517 LAR]
SARAIVA, Maria dos Anjos Fonseca ; SILVA, Maria Aldina Carvalho - Cálculo diferencial em Rn : resumo da teoria, exercícios resolvidos, exercícios para resolver. 2ª ed., reimp.. Coimbra : Livraria Almedina, 2000. [BP 517 SAR]
SARAIVA, Paulo Manuel David Mota - Cálculo I : apontamentos teóricos e folhas práticas. Coimbra : FEUC, 2015. [Ed. de 2014: BP 517 SAR]