Civil Engineering
Master the foundational concepts of calculus: basic function properties, domain and range, limits, limit laws, the Squeeze Theorem, and continuity.
Master the foundational concepts of calculus: domain and range, limits, limit laws, continuity, the Squeeze Theorem, and the Intermediate Value Theorem.
A comprehensive, highly structured overview of Differential Calculus, focusing on limits, derivatives, and their engineering applications.
Master the core of differential calculus: the historical context, one-sided derivatives, differentiability, differentiation rules, and implicit differentiation.
Master the core of differential calculus: derivatives, differentiation rules, chain rule, and implicit differentiation.
Expand your differentiation skills to trigonometric, exponential, logarithmic, and hyperbolic functions, including inverse hyperbolic derivatives.
Expand your differentiation skills to trigonometric, exponential, logarithmic, and hyperbolic functions with engineering applications.
Understand the foundational theorems that bridge the gap between continuous functions and derivatives: the Extreme Value Theorem, Rolle's Theorem, the Mean Value Theorem, and Cauchy's MVT.
Apply differentiation to solve problems in motion, optimization, geometric analysis, and marginal cost.
Apply differentiation to solve problems in motion, optimization, marginal cost, related rates, and geometric analysis.
Learn how to use differentials to approximate function values and calculate errors, and discover Newton's Method and Taylor/Maclaurin Polynomials.
Expand calculus to multivariable functions, partial derivatives, the gradient vector, the second partials test, and Lagrange Multipliers.
Expand calculus to functions of several variables, including the gradient vector, the second partials test, and Lagrange Multipliers.
Understand the curvature of a function, the radius of curvature, parametric/polar forms, and the osculating circle, essential concepts for highway engineering and structural analysis.
Understand the curvature of a function, the radius of curvature, and the osculating circle, essential concepts for highway engineering and structural analysis.
Learn how to find derivatives, slopes, and tangency angles for curves defined parametrically and in polar coordinates.
Learn how to find derivatives, slopes, and tangency angles for curves defined parametrically and in polar coordinates, with engineering applications.