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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.
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