# General Info

## Meeting Times

• Course meetings: MWF 8:00 AM – 8:50 AM. Boyd 323.

• Discussion section: Tuesday 8:00 AM – 9:15 AM. Boyd 303.

The course begins Monday, January 10th. Our first meetings will be in-person.

## Syllabus and Scheduling

Week Number Month Day In-class Topic Preclass Work Notes
1 Jan 10 Review/Preview Course Intro (Icebreaker/Syllabus/Review)
Jan 11 Motivations for Calculus, Review of Functions A0: Precalc review, tangents and secants, position and (average) velocity
Jan 12 Domains, Inverse Functions, Line Tests B1: The Concept of Limit; Graphical Limits, One- and Two-Sided Limits, Vertical Asymptotes
Jan 14 More functions, abstract definition of the limit B2: The Limit Laws; forms 0/0 and $K/0$ ($K$ nonzero), The Squeeze Theorem
2 Jan 17 No class: MLK No class: MLK
Jan 18 Continuity, computing limits B4: The Limit Laws
Jan 19 Asymptotes, discontinuity B3: Continuity; Intermediate Value Theorem
Jan 21 More continuity B5: The Definition of the Derivative, Applications, Estimating the Derivative at a Point Homework Check-In: Up to B4.
3 Jan 24 Limit laws, showing functions are continuous, discontinuities B6: Sketching the Derivative, Derivatives and Continuity, Higher Order Derivatives; Applications
Jan 25 Limit definition of the derivative C1: Differentiation Rules - Constant, Power for integer exponent, sum/difference, constant multiple, product, quotient, applications (no e^x here)
Jan 26 Derivatve as an operator, examples using the limit definition, differentiable implies continuous C2: The Derivative as a Rate of Change
Jan 28 Order limit laws, squeeze theorem, gluing theorem, “highest power” trick C3: Derivatives of Trig Functions
4 Jan 31 Rates of change, finding asymptotes, derivative laws C4: The Chain Rule
Feb 1 Derivative laws, computing derivatives
Feb 2 Trig derivatives, the chain rule   Homework Check-In: up to C4 (Feb 3rd)
Feb 4 Instantaneous rates of change, linearization, tangent lines
5 Feb 7 Review Exam 1 practice on ELC
Feb 8 Exam 1: Openstax 2.1-3.5, Workbook up to C4
Feb 9 Implicit differentiation C5: Implicit Differentiation
Feb 11 Derivatives of inverse functions C6: Derivatives of Inverse Functions; the power rule for rational exponents, derivatives of inverse trig functions
6 Feb 14 Derivatives of Exponential and Logarithmic Functions C7: Derivatives of Exponential and Logarithmic functions - definition of e, derivatives of exponential functions, derivatives of logarithmic functions, logarithmic differentiation
Feb 15 Related Rates C8: Related Rates
Feb 16 Related Rates C8: Related Rates
Feb 18 Related Rates C8: Related Rates
7 Feb 21 Linear Approximations and Differentials D1: Linear Approximations and Differentials Homework Check-In: up to C8
Feb 22 Maxima and Minima D2: Extrema, Extreme Value Theorem, Critical Points, Local Extrema, Closed Interval Max/Min Problems; Absolute/Local Extrema on Graphs
Feb 23 Maximization
Feb 25 Review Exam review on ELC
8 Feb 28 Review D3: MVT, IVT, EVT
Mar 1 Exam 2: Openstax 3.6-4.2, Workbook up to C8 D2: EVT, Local and global minima and maxima, critical points
Mar 2 The Mean Value Theorem D1: Linear Approximation and Differentials
Mar 4 Derivatives and the Shape of a Graph D4: Derivative tests
9, SB Mar 7 SB SB
SB Mar 8 SB SB
SB Mar 9 SB SB
SB Mar 11 SB SB
10 Mar 14 Limits at Infinity and Asymptotes D4/D5: Derivative tests, concavity
Mar 15 Limits at Infinity and Asymptotes D5: Concavity, curve sketching, limits at infinity
Mar 16 Applied Optimization D6/D7/D8: Concavity, limits at infincity, optimization
Mar 18 Applied Optimization D7/D8: Optimization
11 Mar 21 Applied Optimization D8: Optimization
Mar 22 Flex day Flex day
Mar 23 L’Hopital’s Rule D9: L’Hopital’s Rule; Indeterminate Forms
Mar 25 L’Hopital’s Rule D9: L’Hopital’s Rule; Indeterminate Forms Homework Check-In: up to D9
12 Mar 28 Antiderivatives E1: Antiderivatives; Indefinite Integrals, Initial Value Problems
Mar 29 Approximating Area E1: Antiderivatives; Indefinite Integrals, Initial Value Problems
13 Mar 30 Antiderivatives E2: Approximating Areas; Sigma Notation, Area Estimates, Riemann Sum, Upper/Lower Sums
Apr 1 Review Review
Mar 4 Review Review
Apr 5 Exam 3: Openstax 4.3-4.10, Workbook D1 – D9 Exam
Apr 6 The Definite Integral E3/E4: The Definite Integral; Limit Definition of the Definite Integral, Notation, Net Signed Area, Total Area, Properties, Average Value
Apr 8 The Definite Integral E3/E4: The Definite Integral; Limit Definition of the Definite Integral, Notation, Net Signed Area, Total Area, Properties, Average Value
14 Apr 11 The Fundamental Theorem of Calculus E5: The Fundamental Theorem of Calculus; Mean Value Theorem for Integrals
Apr 12 The Fundamental Theorem of Calculus E5: The Fundamental Theorem of Calculus
Apr 13 Integration Formulas and the Net Change Theorem E5: Integration Formulas and the Net Change Theorem
Apr 15 Substitution E6/E7: Substitution; Indefinite and Definite Integrals with Substitution (Power, Trig); Integrals Involving Exponential and Logarithmic Functions; Integrals Involving Exponential and Logarithmic Functions; Integrals Resulting in Inverse Trig Functions (only do a=1; no inverse secant)
15 Apr 18 Substitution E6/E7: Substitution; Indefinite and Definite Integrals with Substitution (Power, Trig); Integrals Involving Exponential and Logarithmic Functions; Integrals Involving Exponential and Logarithmic Functions; Integrals Resulting in Inverse Trig Functions (only do a=1; no inverse secant)
Apr 19 Substitution E6/E7: Substitution; Indefinite and Definite Integrals with Substitution (Power, Trig); Integrals Involving Exponential and Logarithmic Functions; Integrals Involving Exponential and Logarithmic Functions; Integrals Resulting in Inverse Trig Functions (only do a=1; no inverse secant)
Apr 20 Areas Between Curves E8: Areas Between Curves
Apr 22 Areas Between Curves E8: Areas Between Curves Homework Check-In: up to E8
16 Apr 25 Review
Apr 26 Review
Apr 27 Review
Apr 29 Review
17 May 2 Exam 4: Openstax 5.1-6.1 Exam
May 3 Course Review

May TBA