Calculus II ep01: Intro, derivatives & antiderivatives review (Sep 9, 2026)

Overview

Chris Staecker introduces Fairfield University’s math-intensive Calculus II course, including its 23-topic mastery checklist, weekly homework and quizzes, retake opportunities, and grading structure: 60% mastery, 25% homework, and 15% final exam. He reviews power-rule derivatives and antiderivatives, trigonometric formulas, the Fundamental Theorem of Calculus, and techniques for rewriting rational expressions as powers before integrating.

Key takeaways

The course’s mastery system tracks 23 topics at one, two, or three points; later quizzes, biweekly retakes, and catch-up exams let students improve without treating an early mistake as permanent.
The grade is divided into 60% topic mastery, 25% online homework, and 15% final exam, with at least two points required on every thick-boxed deal-breaker topic.
Homework is submitted through Gradescope as photographed handwritten pages or tablet work, is due Wednesday evening, and loses one-third credit per calendar day when late without an excuse.
Power-rule antiderivatives increase the exponent and divide by the new exponent, while every indefinite integral also needs +C; sums and constant multiples can be integrated term by term.
Definite integrals use the Fundamental Theorem of Calculus: evaluate an antiderivative at the upper endpoint and subtract its value at the lower endpoint.
Before integrating a quotient, rewrite it in a more manageable form, often using negative exponents; for example, 1/(8x⁴) is (1/8)x⁻⁴, not 8x⁻⁴.

Chapters

0:00 Fairfield Calculus II: Course Level and Class Format

Chris Staecker records class audio and screen content for students to review after absences or before tests.
The four-credit sequence is aimed at math-heavy majors and is broadly comparable to high-school BC Calculus.
Calculus II emphasizes integrals and sequences and series, while assuming students already know derivatives.
Students unsure whether the technical calculus sequence fits their major are encouraged to consult Staecker promptly.

2:50 Office Hours, Course Website, Textbook, and Final Exam

Students can contact Chris Staecker by email, visit his office in Bannow 17, or meet during office hours or on Zoom.
Homework and course materials are posted on the class website linked through Blackboard, not directly on Blackboard.
The course uses the Stewart Calculus textbook mainly for homework assignments.
Section 2’s final is scheduled for December 17 at 8:00 a.m.; students may ask about taking it with the other section.

7:13 Course Topics and Wednesday Gradescope Homework

The syllabus lists integration by substitution and parts, area and volume applications, inverse functions, L’Hôpital’s rule, improper integrals, and series topics.
Homework is due online Wednesday evening and covers material taught during the preceding week.
Students are encouraged to bring homework questions to Wednesday class before submitting.
Late homework without an excuse loses one-third credit per calendar day.

8:27 The 23-Topic Mastery Checklist and Weekly Quizzes

Most of the course grade comes from mastery of 23 listed topics, assessed with scores of one, two, or three points.
Weekly Thursday quizzes generally test topics covered in the previous week’s homework.
An incorrect quiz answer does not permanently damage the grade; students can demonstrate mastery on later assessments.
Quiz questions are labeled by checklist topic, and calculators and other electronic devices are not allowed.

13:35 Catch-Up Exams, Deal Breakers, and Final-Exam Scope

Students can arrange to retry one old mastery question every two weeks by appointment with Staecker.
Catch-up exams on October 15 and the last day of class let students earn credit on topics not yet mastered.
Thick-boxed deal-breaker topics require at least two points each; otherwise, the student fails the course.
The grading breakdown is 60% mastery, 25% homework, and 15% final; the final covers starred topics and deal breakers.

22:25 Gradescope Setup for Handwritten Homework

Students submit handwritten work to Gradescope by photographing pages with a phone or using a tablet such as an iPad.
Staecker creates a dummy assignment asking students to write something interesting about themselves and upload it.
The practice submission checks that everyone can access Gradescope before the first real assignment.
The first actual homework is due Wednesday, and students are asked to report any technical problems in advance.

29:44 Power-Rule Derivatives and Antiderivatives

For powers of x, the derivative rule brings the exponent down and reduces it by one: xⁿ differentiates to n·xⁿ⁻¹.
The corresponding antiderivative raises the exponent by one and divides by the new exponent, then adds the constant C.
Examples include d/dx(x⁴) = 4x³ and ∫x⁴ dx = x⁵/5 + C.
Staecker rewrites √x as x^(1/2) before differentiating and handles sums and constant multiples term by term.

36:18 Sine and Cosine Rules—and Why Integrals Need Special Tricks

The derivatives are d/dx(sin x) = cos x and d/dx(cos x) = −sin x; their antiderivatives are −cos x and sin x, respectively.
Students are expected to know the product, quotient, and chain rules for derivatives.
There is no general product, quotient, or chain rule for integrals; expressions such as sin x·cos x require a separate integration technique.
Indefinite integrals produce antiderivative functions with +C, while definite integrals produce numbers.

39:18 Definite Integrals, the Fundamental Theorem, and Radian Values

For a definite integral, Staecker finds an antiderivative and evaluates it at the upper endpoint minus the lower endpoint.
He identifies this evaluation process as the Fundamental Theorem of Calculus and interprets the result as signed area under a curve.
For ∫₀^(π/2) sin x dx, the antiderivative −cos x gives −cos(π/2) − [−cos(0)] = 1.
Students should review unit-circle values such as those at π/6, π/4, and π/3; the standard sine and cosine derivative formulas assume radians.

44:50 Rewriting Rational Expressions as Powers Before Integration

Staecker rewrites (x² − 7)/x² as 1 − 7x⁻², integrates term by term, and evaluates the antiderivative at 3 and 7.
He rewrites 1/(8x⁴) as (1/8)x⁻⁴, emphasizing that the coefficient is 1/8, not 8.
Applying the power rule to the second expression gives an antiderivative of −(1/24)x⁻³ before endpoint evaluation.
These examples complete checklist topic one: simple derivatives and antiderivatives.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Prof Staecker.