Unit · year 1

MU-102 · Calculus I

Threads change27 lectures9 theorems

The derivative and the integral, and the theorem that binds them into one subject.

PREREQUISITES

Lectures

L01	Functions, Graphs, and the Idea of a Limit —
L02	Limits: The ε–δ Definition —
L03	Limit Laws and Continuity —
L04	One-Sided Limits, Infinite Limits, and Asymptotes —
L05	Continuity on Closed Intervals The extreme value theorem
L06	The Extreme Value Theorem The extreme value theorem
L07	The Derivative as a Limit —
L08	Differentiation Rules: Product and Quotient —
L09	The Chain Rule The chain rule
L10	Implicit Differentiation and Inverse Functions The chain rule
L11	Derivatives of Exponential, Logarithmic, and Trigonometric Functions —
L12	Rolle's Theorem Rolle's theorem
L13	The Mean Value Theorem The mean value theorem
L14	Consequences of the MVT: Monotonicity and Constancy The mean value theorem
L15	Curve Sketching: Extrema, Concavity, Inflection The extreme value theorem
L16	Optimisation Problems The extreme value theorem
L17	Indeterminate Forms and L'Hôpital's Rule L'Hôpital's rule
L18	Linear Approximation and Differentials —
L19	Taylor Polynomials Taylor's theorem with remainder
L20	Taylor's Theorem with Remainder Taylor's theorem with remainder
L21	The Riemann Integral: Partitions and Sums —
L22	Properties of the Definite Integral —
L23	The Fundamental Theorem of Calculus, Part I The fundamental theorem of calculus
L24	The Fundamental Theorem of Calculus, Part II The fundamental theorem of calculus
L25	Techniques of Integration: Substitution and Parts The chain rule
L26	Improper Integrals and Convergence —
L27	Synthesis: Differentiation and Integration as Inverse Operations The fundamental theorem of calculus