Objectifs

This course aims at refreshing mathematical notions and techniques and developing complements which will be useful for applications in the fields of actuarial science and finance. The goal is to provide a common base of general techniques of differential and integral calculus and of linear algebra used in the other courses. Many examples drawn for actuarial science will illustrate the necessity for future actuaries to master these skills.

Contenus

Differential and Integral Calculus

• Sets of Numbers, Sequences, Infinite Series
• Functions, Continuity, Differentiation
• Integration
• Partial Derivatives, Repeated Integrals
• Complex Numbers, Laplace/Fourier Transforms

Linear algebra

• Linear Equation Systems
• Vector Spaces
• Eigenvalues and Eigenvectors
• Decompositions of Matrices

Références

Lay, David C., Steven R. Lay, Judi J. McDonald, "Linear Algebra and Its Applications" (5th ed), Pearson, 2016

Ross, K.A., "Elementary Analysis: The Theory of Calculus", Springer, 2nd edition, 2013.

Rudin, W., "Real and complex analysis", McGraw-Hill, 3rd edition, 1987.

Rudin, W., "Principles of mathematical analysis", McGraw-Hill, 3rd edition, 1976.

Riley, K.F., Hobson, M.P., Bence, S.J., "Mathematical methods for physics and engineering", Cambridge University Press, 3rd edition, 2006.

Evaluation

1ère tentative

Examen:

Ecrit 3h00 heures

Documentation:

Autorisée avec restrictions

Calculatrice:

Autorisée avec restrictions

Evaluation:

Midterm: 30%

Final: 70% == 50% (Linear Algebra) + 20% (Calculus/Analysis)

Documentation: A single sheet (A4) hand-written (by the student) on both sides.

Calculator: Restriction on calculator (simple scientific calculator, non-programmable).

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Rattrapage

Examen:

Ecrit 3h00 heures

Documentation:

Autorisée

Calculatrice:

Autorisée avec restrictions

Evaluation:

Retake: 100% == 50% (Linear Algebra) + 50% (Calculus/Analysis)

Documentation: A single sheet (A4) hand-written (by the student) on both sides.

Calculator: Restriction on calculator (simple scientific calculator, non-programmable).