1 Limits of Functions Defining limits of functions via ε-δ and proving limit laws and the squeeze theorem 2 Continuous Functions Definition of continuity and properties of continuous functions: extreme and intermediate value theorems 3 Limits of Sequences Convergence, limit laws, standard limits, e, and monotone convergence 4 Infinite Series Partial sums and convergence, geometric and p-series, convergence tests, absolute and conditional convergence 5 Power Series Power series, radius of convergence, elementary function expansions, and analytic functions 6 Differentiation and Derivatives Definition of derivative, differentiability and continuity, derivatives and higher-order derivatives 7 Differentiation Termwise differentiation of power series, derivatives of elementary functions, product, quotient, and chain... 8 Mean Value Theorem Mean value theorem and its applications: monotonicity, extrema, convexity, L’Hospital’s rule, optimization 9 Taylor’s Theorem Taylor polynomials, Lagrange remainder, Maclaurin series, approximation and limits 10 Integration Antiderivatives, Riemann sums, definite integrals, properties, and the mean value theorem 11 The Fundamental Theorem of Calculus Fundamental theorem, existence of primitives, Leibniz rule, termwise integration of power series 12 Improper Integrals Infinite and singular integrals, comparison test, absolute convergence 13 Curves and Vector-Valued Functions Vector-valued functions, parametric curves, velocity and tangent, arc length, curvature and acceleration de... 14 Functions of Several Variables and Partial Derivatives Partial derivatives, gradient, differentiability, multivariable chain rule, extrema 15 Multiple Integrals Multiple integrals, Fubini’s theorem, change of variables and the Jacobian determinant 16 Vector Fields Vector fields, gradient and conservative fields, divergence and curl, differential identities 17 Line Integrals Scalar and vector line integrals, work, fundamental theorem, and conservative fields 18 Green’s Theorem Green’s theorem, area formulas, circulation and flux forms, simply connected domains and conservative fields 19 Surface Integrals and Flux Parametric surfaces, normal vectors, surface area, scalar surface integrals, flux 20 The Divergence Theorem and Stokes’ Theorem Divergence theorem, Stokes’ theorem, irrotational and conservative fields, unification of integral theorems