Math 2250: Calculus I for Science and Engineering (Spring 2022, CRN 35643)

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 Limit definition of the derivative B5: The Definition of the Derivative, Applications, Estimating the Derivative at a Point Homework Check-In: Up to B4.
3 Jan 24 The Derivative as a Function B6: Sketching the Derivative, Derivatives and Continuity, Higher Order Derivatives; Applications  
  Jan 25 Differentiation Rules C1: Differentiation Rules - Constant, Power for integer exponent, sum/difference, constant multiple, product, quotient, applications (no e^x here)  
  Jan 26 Derivatives as Rates of Change C2: The Derivative as a Rate of Change  
  Jan 28 Derivatives of Trigonometric Functions C3: Derivatives of Trig Functions  
4 Jan 31 The Chain Rule C4: The Chain Rule  
  Feb 1 Review   Homework Check-In: up to C4
  Feb 2 Review    
  Feb 4 Exam 1: Openstax 2.1-3.5, Workbook up to C4 Exam  
5 Feb 7 Implicit Differentiation C5: Implicit Differentiation  
  Feb 8 Implicit Differentiation C5: Implicit Differentiation  
  Feb 9 Derivatives of Inverse Functions C6: Derivatives of Inverse Functions; the power rule for rational exponents, derivatives of inverse trig functions  
  Feb 11 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  
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 - must be interior, Closed Interval Max/Min Problems; Absolute/Local Extrema on Graphs  
  Feb 23 Review    
  Feb 25 Exam 2: Openstax 3.6-4.2, Workbook up to C8 Exam  
8 Feb 28 The Mean Value Theorem D3: MVT, IVT, EVT  
  Mar 1 Derivatives and the Shape of a Graph D2: EVT, Local and global minima and maxima, critical points  
  Mar 2 Derivatives and the Shape of a Graph 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 Review  
  Mar 29 Flex day Flex day  
  Mar 30 Review Review  
  Apr 1 Exam 3: Openstax 4.3-4.10, Workbook D1 – D9 Exam  
13 Apr 4 Approximating Area E1: Antiderivatives; Indefinite Integrals, Initial Value Problems  
  Apr 5 Approximating Area E2: Approximating Areas; Sigma Notation, Area Estimates, Riemann Sum, Upper/Lower Sums  
  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      

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