Ohio University MATH 2301
Professor Mark Barsamian · Ohio University · 16 lectures with notes
Students in this class: ask your lecturer for the class code, and these lectures will already be in your library when you sign up.
Wed Aug 26, 2026 Lecture (L02) Stewart Section 1.4 (Calculating Limits)
A 0/0 result is indeterminate, not a limit value: simplify algebraically, cancel only for nearby unequal inputs, then substitute.
Mon Aug 24, 2026 Lecture (L01) Stewart Section 1.3 (Limits)
A limit describes the value a function approaches, even when the function is undefined or different at that input.
Fri Aug 28, 2026 Lecture (L03) Stewart Sections 1.4 (Calculating Limits) and 1.5 (Continuity).
A practical method for checking theorem hypotheses connects squeeze limits, continuity, and the Intermediate Value Theorem.
Mon Aug 31, 2026 Lecture (L04) Stewart Sect. 1.6 Limits Involving Infinity Part 1: Infinite Limits
Infinite limits describe unbounded function behavior near finite inputs; infinity is not a number, and one-sided limits determine whether a two-sided limit exists.
Wed Sep 2, 2026 Lecture (L05) Stewart Section. 1.6 Part 2: Limits at Infinity
For rational functions, comparing polynomial degrees reveals end behavior and the horizontal asymptote as x approaches positive or negative infinity.
Fri Sep 4, 2026 Lecture (L06) Stewart Sect. 2.1 Derivatives and Rates of Change
A ball-height example connects secant slopes, instantaneous velocity, and the tangent line y = 4t + 4.
Wed Sep 9, 2026 Lecture (L07) Stewart Sect. 2.2 The Derivative as a Function
The derivative function assigns each input x the slope of the tangent to f at x, found from a limit.
Fri Sep 11, 2026 Lecture (L08) Stewart Sect. 2.2 The Derivative as a Function, Part 2
The limit definition yields the derivative of 1/√t, while continuity, cusps, and vertical tangents explain when derivatives fail to exist.
Mon Sep 14, 2026 Lecture (L09) Stewart Sect. 2.3 Basic Differentiation Formulas, Part 1
The power rule and basic derivative properties turn many limit-definition problems into direct calculations.
Wed Sep 16, 2026 Lecture (L10) Stewart Sect. 2.3 Basic Differentiation Formulas, Part 2
Rewrite quotients as sums of power functions, then use derivative rules to analyze motion and evaluate limits.
Mon Sep 21, 2026 Lecture (L11) Stewart Sect. 2.4 Product Rule; Quotient Rule
Learn the product and quotient rules, avoid common differentiation and notation errors, and apply them to trigonometric and tangent-line problems.
Wed Sep 23, 2026 Lecture (L12) Stewart Sect. 2.5 The Chain Rule
Identify each nested function’s layers, differentiate from the outside inward, and multiply by each layer’s derivative.
Fri Sep 25, 2026 Lecture (L13) Stewart Sections 2.6 Implicit Differentiation and 2.7 Related Rates
Implicit differentiation finds slopes on curves defined by equations, while related rates connects changing quantities through time-differentiated equations.
Mon Sep 28, 2026 Lecture (L14) Stewart Section 2.7 Related Rates, Part 2
Use implicit differentiation and carefully signed rates to solve right-triangle related-rates problems.
Mon Oct 5, 2026 Lecture (L16) Stewart Sections 3.1 Exponential Functions, 3.2 Inverse Functions
The limit defining e and the inverse-function derivative formula connect exponential behavior to core calculus concepts.
Fri Oct 9, 2026 Lecture (L18) Stewart Sections 3.5 derivatives of Inverse Trig Functions
Principal-value ranges govern inverse-trig cancellation, while the inverse-function rule yields the derivatives of arcsin, arccos, and arctan.