Description

Theory
1

Theory/Practice
2

Instructors

Helena Brás

Contents

CP1. Differential calculus in R and R^n ? 3 weeks
1. Trigonometric functions and their inverses.
2. Partial derivatives.
3. Differential and approximate calculation.
4. Derivatives of composite functions and given in implicit form.
 

CP2. Primitive of a one real value function ? 2 weeks
1. Definition; properties.
2. Techniques of integration: quasi-immediate, by algebraic manipulation, substitution and by parts integration.
 

CP3. Definite integral ? 2 weeks
1. Riemann sum. Properties. Calculus.
2. Integration methods.
3. Calculus of areas in cartesian coordinates.
 

CP4. Ordinary 1st order differential equations
1. Definition.
2. Separable, lin and exact differential equations.
 

CP5. Series ? 3 weeks
1. Definition of numerical series.
2. Necessary condition for convergence.
3. Series of non-negative terms. Convergence criteria.
4. Alternating series. Absolute x simple convergence. Leibniz criterion.
5. Definition of series of functions.
6. Power series: Taylor and MacLaurin.

Learning Outcomes

Learning objectives: knowledge, skills, and competences to be developed by students.
CO1: Develop reasoning and abstraction skills.
CO2: Apply critical thinking and mathematical thinking.
CO3: Apply mathematical techniques to new situations.
CO4: Identify and analyze trigonometric functions: domains, codomains, derivatives and inverses.
CO5: Apply the concept of differential.
CO6: Apply derivation to functions of several variables, composite and implicit.
CO7: Apply different techniques to obtain the primitive of a real function of a real variable.
CO8: Apply integration to the calculation of flat areas.
CO9: Determine the general and particular solution of first-order differential equations.
CO10: Analyze the convergence of a numerical series, using the appropriate criteria. CO11: Evaluate the convergence of a power series.
CO12: Explain the concept of series and apply it to the development of functions in MacLaren and Taylor series.
CO13: Evaluate the application of MacLaren and Taylor polynomials to the calculation of approximated values.