Differential Calculus
Civil Engineering
Functions, Limits, and Continuity
Master the foundational concepts of calculus: basic function properties, domain and range, limits, limit laws, the Squeeze Theorem, and continuity.
The Derivative
Master the core of differential calculus: the historical context, one-sided derivatives, differentiability, differentiation rules, and implicit differentiation.
Derivatives of Transcendental Functions
Expand your differentiation skills to trigonometric, exponential, logarithmic, and hyperbolic functions, including inverse hyperbolic derivatives.
Theorems of Calculus
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.
Applications of the Derivative
Apply differentiation to solve problems in motion, optimization, geometric analysis, and marginal cost.
Differentials and Approximations
Learn how to use differentials to approximate function values and calculate errors, and discover Newton's Method and Taylor/Maclaurin Polynomials.
Partial Differentiation
Expand calculus to multivariable functions, partial derivatives, the gradient vector, the second partials test, and Lagrange Multipliers.
Radius of Curvature
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.
Derivatives of Parametric and Polar Curves
Learn how to find derivatives, slopes, and tangency angles for curves defined parametrically and in polar coordinates.