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.
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.
Synthesizes previous topics through the lens of Sturm-Liouville theory, focusing on the orthogonality of eigenfunctions and generalized Fourier series.
Examines Legendre's equation and the derivation of Legendre polynomials via Rodrigues' formula, emphasizing their role in spherical potential problems.
Explores Bessel's equation and the resulting Bessel functions of the first and second kind, particularly their applications in systems with cylindrical symmetry.
Covers the classification of singular points and the application of the Method of Frobenius to find solutions near regular singularities by solving the indicial equation.
Focuses on solving second-order linear differential equations near ordinary points using power series, deriving recurrence relations, and determining the radius of convergence.
Applies ODE techniques to complex mixing problems and RC electrical circuits, focusing on transient and steady-state behavior.
Contrasts exponential and logistic growth models, analyzing carrying capacity and equilibrium in biological systems.
Introduces the method of integrating factors to solve non-homogeneous first-order linear differential equations.
Focuses on the technique of separation of variables and its application to Newton's Law of Cooling and radioactive decay.
Students explore direction fields and existence/uniqueness theorems to qualitatively analyze ODEs before seeking analytical solutions.
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.
This sequence introduces Integration by Parts as the inverse of the Product Rule, equipping students to handle products of unrelated functions. Through inquiry, students derive the formula, apply the LIATE heuristic, master the Tabular Method for repeated integration, and solve cyclic integrals.
A comprehensive 5-lesson unit for 11th Grade Calculus students focusing on the u-substitution method for integration, emphasizing pattern recognition, definite integral boundary changes, and advanced algebraic manipulation.
A 12th-grade calculus unit focusing on advanced integration techniques, including improper integrals, partial fractions, and trigonometric substitution, applied to real-world modeling scenarios like population growth and physics.
This sequence explores trigonometric integration techniques, from power reduction and identity manipulation to the geometric power of trigonometric substitution. Students learn to bridge the gap between algebraic radicals and right-triangle geometry.
This calculus sequence focuses on mastering complex integration techniques beyond basic antiderivatives. Students learn to navigate Advanced Substitution, Integration by Parts, the Tabular Method, and Partial Fraction Decomposition through a strategy-first lens, culminating in a mastery-based mixed practice challenge.
A comprehensive series of lessons for undergraduate Calculus II students, focusing on mastering advanced integration techniques including substitution, integration by parts, trigonometric methods, and partial fraction decomposition, culminating in a strategic synthesis workshop.
Guide de correction détaillé pour les exercices d'intégrales appliquées à l'économie (IPP, Gini, Surplus).
Feuille d'exercices sur les intégrales appliquées à l'économie pour L1 Éco-Gestion (IPP, Gini, Surplus).
Présentation visuelle pour le cours de calcul intégral appliqué à l'économie (IPP, Surplus, Gini).
A comprehensive teacher facilitation guide including learning objectives, a detailed pacing guide, a video analysis key, and the full answer key for the Equation Relay activity.
A concise exit ticket featuring a rational-exponent substitution problem and a reflection prompt on the conceptual utility of variable change in advanced mathematics.
A set of four discussion prompts designed to facilitate deep conceptual understanding of variable substitution, domain restrictions, and the connection to future calculus topics.
A tiered 'relay' worksheet where students solve a series of equations in quadratic form. Each station's answer is used to unlock the coefficients of the next problem, covering polynomial, radical, binomial, and rational substitution.
A comprehensive slide deck for teaching non-standard equation solving via substitution, featuring a warm-up drill, video analysis, strategic thinking slides, and a connection to future calculus topics.
A final exit ticket assessing conceptual understanding of weight functions, orthogonality, and the significance of completeness in Sturm-Liouville theory.
A rigorous proof workshop for graduate students to derive the Sturm-Liouville form of Bessel's equation and prove the general orthogonality theorem.
Final lecture slides on Sturm-Liouville theory, defining self-adjoint operators, weight functions, and the orthogonality of eigenfunctions.
A facilitation guide for instructors, connecting Legendre polynomials to physical potential theory and providing discussion strategies for graduate seminars.
