Integral Calculus
Civil Engineering
Antiderivatives and Indefinite Integrals
Understanding antiderivatives, indefinite integral notation, basic integration formulas, and properties of linearity.
Definite Integrals
Understanding Riemann sums, the Fundamental Theorem of Calculus, properties of definite integrals, and improper integrals.
Techniques of Integration
A rigorous guide to substitution, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, Wallis' formula, hyperbolic integrals, and Gamma/Beta functions.
Applications of Integration
Engineering applications of definite integrals: area, volume, arc length, surface area, centroids, second moments of area, work, hydrostatics, Pappus, economics, and probability.
Multiple Integrals
Double integrals, iterated integration, planar regions, polar coordinates, and engineering applications to area, volume, mass, centroids, and surface area.
Triple Integrals and Change of Variables
Triple integrals over solids, cylindrical and spherical coordinates, mass properties, Jacobians, and the change-of-variables theorem in two and three dimensions.