Library Calculus MATH-1013
Year 1 Core Updated: ...

MATH-1013: Calculus I

Introduction to limits, continuity, and differentiation of algebraic and transcendental functions. Topics include the Mean Value Theorem, applications to optimization and curve sketching, related rates, and an introduction to integration including the Fundamental Theorem of Calculus.

Lecture Notes

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Lecture 01 - Functions Review.pdf

Domain, range, composition • 1.1 MB

Lecture 02 - Intro to Limits.pdf

Concept of limit, notation • 0.9 MB

Lecture 03 - Calculating Limits.pdf

Limit laws, direct substitution • 1.3 MB

Lecture 04 - Continuity.pdf

Types of discontinuity, IVT • 1.0 MB

Lecture 05 - Limits at Infinity.pdf

Horizontal asymptotes • 1.1 MB

Lecture 06 - Derivatives Introduction.pdf

Definition, tangent lines • 1.2 MB

Lecture 07 - Differentiation Rules.pdf

Power, product, quotient rules • 1.4 MB

Lecture 08 - Trigonometric Derivatives.pdf

Sin, cos, tan and special limits • 1.1 MB

Lecture 09 - The Chain Rule.pdf

Composite functions • 1.5 MB

Lecture 10 - Implicit Differentiation.pdf

Derivatives of implicitly defined curves • 1.2 MB

Lecture 11 - Higher Derivatives.pdf

Second and third derivatives • 0.9 MB

Lecture 12 - Related Rates.pdf

Real world rate problems • 1.6 MB

Lecture 13 - Linear Approximation.pdf

Differentials and linearization • 1.0 MB

Lecture 14 - Maxima and Minima.pdf

Critical numbers, extreme values • 1.3 MB

Lecture 15 - Mean Value Theorem.pdf

Rolle's theorem and MVT proofs • 1.1 MB

Lecture 16 - Derivatives & Curve Shapes.pdf

Concavity, inflection points • 1.4 MB

Lecture 17 - Optimization Problems.pdf

Applied max/min problems • 1.7 MB

Lecture 18 - Antiderivatives.pdf

Reverse power rule, basic forms • 1.0 MB

Lecture 19 - Indefinite Integrals.pdf

Notation and basic properties • 1.1 MB

Lecture 20 - Definite Integrals.pdf

Area under the curve, Fundamental Theorem • 1.5 MB

Reference Materials

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Calculus I Comprehensive Cheat Sheet.pdf

Limits, Derivatives & Integrals Summary • 0.8 MB