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Integral Calculus
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/25 - 6/4/25
Integral Calculus
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18257
Transcript Source: Partner Institution
Course Details: Level 100
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Fundamentals of Algebra, Linear Algebra, Differential Calculus
DESCRIPTION
1. Antiderivatives and the indefinite integral
Linearity property. Basic integrals. Initial value problem.
Techniques of integrations: Substitution method and integration by parts, the method of partial fractions. Trigonometric integrals and irrational expressions.
Strategies for integration.
2. The Riemann-Stieltjes integral
Definition and existence of the integral.
Properties of the integral. Change of variable.
Fundamental theorem of Calculus. Remainder term of Taylor polynomial.
Applications: Area, volume, density, average value, center of mass, work and energy.
Uniform convergence and integration.
Numerical integration: The trapezoid rule and Simpson's rule.
3. Integration of vector value functions.
Area between two curves. Arc length and area of surface of revolution.
Improper integrals. Applications: Probability and integration.
Integrals depending on parameters. Differentiation of integrals. Some special functions.
4. Integration in several variables.
Fubini's theorem. Integration over non-rectangular regions.
Mean value theorem. Application of multiple integrals.
Improper integrals. Integrals depending on parameters.
Linearity property. Basic integrals. Initial value problem.
Techniques of integrations: Substitution method and integration by parts, the method of partial fractions. Trigonometric integrals and irrational expressions.
Strategies for integration.
2. The Riemann-Stieltjes integral
Definition and existence of the integral.
Properties of the integral. Change of variable.
Fundamental theorem of Calculus. Remainder term of Taylor polynomial.
Applications: Area, volume, density, average value, center of mass, work and energy.
Uniform convergence and integration.
Numerical integration: The trapezoid rule and Simpson's rule.
3. Integration of vector value functions.
Area between two curves. Arc length and area of surface of revolution.
Improper integrals. Applications: Probability and integration.
Integrals depending on parameters. Differentiation of integrals. Some special functions.
4. Integration in several variables.
Fubini's theorem. Integration over non-rectangular regions.
Mean value theorem. Application of multiple integrals.
Improper integrals. Integrals depending on parameters.