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
...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
...Calculus I Comprehensive Cheat Sheet.pdf
Limits, Derivatives & Integrals Summary • 0.8 MB