Substitution, integration by parts, partial fractions, and trigonometric substitution methods for evaluating complex integrals. Connects foundational calculus concepts to advanced applications in area, volume, and physics.
A comprehensive graduate-level exploration of series solutions for differential equations with variable coefficients, focusing on power series, the Method of Frobenius, and the properties of Bessel and Legendre functions within the framework of Sturm-Liouville theory.
This sequence introduces undergraduate students to first-order differential equations through geometric visualization, analytical solving techniques (separation, integrating factors), and real-world modeling of thermal, biological, and electrical systems.
This sequence introduces advanced volume techniques in calculus, including the Shell Method and solids with known cross-sections. Students move from theoretical derivation to a project-based application where they model and calculate the volume of real-world objects.
A comprehensive 11th-grade calculus unit focused on strategic method selection for complex integration. Students transition from basic procedural fluency to high-level diagnostic thinking and real-world applications in physics and engineering.
A comprehensive 11th-grade calculus unit focusing on Partial Fraction Decomposition for integration. The sequence moves from pure algebraic skill-building to complex integration techniques and real-world logistic growth modeling.
A comprehensive unit on trigonometric substitution in calculus, moving from geometric visualization of radicals to complex integration techniques and algebraic back-substitution. Students learn to map radical expressions onto right triangles and use trigonometric identities to simplify and solve integrals.
Une leçon complète sur le calcul intégral appliqué à l'économie, couvrant l'intégration par parties, l'indice de Gini et les surplus du consommateur et du producteur.
A high-school calculus preparation lesson focused on solving non-standard algebraic equations using substitution techniques, with a focus on domain restrictions and preparation for integration by substitution.
