MAT 175 - Calculus I
Spring 2020 Tuesday - Thursday, 9:00 am - 10:40 am / 11:00 am - 12:40 pm Room GI-205
Kåre Gjaldbæk kaare.gjaldbaek@lehman.cuny.edu Office hours: Tuesday 1:00 pm - 2:00 pm, Room GI-303, by appointment
Problem Sets
Problem Sheet 1 Problem Sheet 2 Problem Sheet 3
| Date | Reading | Subjects | Hand-in Homework | Solutions |
|---|---|---|---|---|
| 01-28-19 | 1.1 - 1.3 |
Graphs of Equations,
Intercepts, Symmetries Straight Lines, Slope. Point-Slope Form, Slope-Intercept Form, General Form, Parallel/Perpendicular Lines Sets, Functions Read Chapters 1.1-1.3, (1.5), 1.6, C3 Exercises: 1.1/ 1-14, 19, 21, 53, 55, 63 1.2/ 19, 23-32, 35, 43, 49-55 odd, 77. 1.3/ 5-9 odd, 13, 17-21 odd, 57-63 odd 1.6/ 7-15 odd, 19, 25, 27, 49, 59, 91, 93 Trigonometry Appendix Edition 5: C3/ 11, 13, 15, 19, 31, 37, 51 |
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| 01-30-20 | (1.3) 2.2 | Sets, Functions Introduction to Limits Exercises: 2.2/ 1, 3, 5, 11, 13, 15, 17, 19, 21, 23 Review 1.5/ 1, 5, 53, 57, (ed 4: 89, 91, 93) (ed 5: 95, 97, 99) (math majors should also read Appendix A Thm 2.2-2.5 and do 2.1/31,33) | ||
| 02-04-20 | 2.3 | Formal Definition of Limits, Evaluating Limits Analytically, Limit Theorems Exercises: 2.3/ 9-21 odd, 37, 43, 45, 53, 57, 69, 79 (math majors should also read Appendix A Thm 2.8 and do 2.2/ 39, 2.3/ 118, 125 | ||
| 02-06-20 | 2.3 | Limit Theorems, The Squeeze Theorem, Three Special Limits Exercises: 2.3/ 9-21 odd, 37, 43, 45, 53, 57, 69, 79 (math majors should also read Appendix A Thm 2.8 and do 2.2/ 39, 2.3/ 118, 125 | ||
| 02-11-20 | 2.4 | Continuity, One-sided Limits Exercises: 2.4/ 1, 3, 5, 11, 31, 37, 39, 41, 43, 47 | ||
| 02-13-20 | 2.5 | Infinite Limits, Asymptotes Exercises: 2.4/ 49, 51, 55, 57, 59 2.5/ 1, 3, 7, 9-15 odd, 31, 33, 39, 45, 47 | ||
| 02-18-20 | 3.1 | Tangent Lines, Derivatives Exercises: 3.1/ 1, 5, 7, 11, 13, 21, 37, 39, 41, 61 Review 1.3/ Example 4, 59, 61, 63 | ||
| 02-20-20 | 3.2 | The Constant Rule, The Power Rule, The Constant Multiple Rule, The Sum/Difference Rule, Derivatives of Sine/Cosine Exercises: 3.2/ 3-23 odd | ||
| 02-25-20 | 3.2 | The Exponential Function, Rates of Change, Objects Moving along a Straight Line, Velocity Exercises: 3.2/ 43-61 odd; (Ed 5 3.2/101, 103) or (Ed 4. 3.2/93, 95) Review 1.5/ 1, 5, 7, 9, 11, 13 | From Problem Sheet 1, please hand in solutions to Prob. 1: (ii), (iii), (vi), (vii), (ix), (x) Prob. 2: (ii), (iii), (iv) Prob. 3: (i) Prob. 4: (i), (iv) Prob. 5: (ii), (iv) | Solutions |
| 02-27-20 | 3.3 | The Product Rule, The Quotient Rule Exercises: 3.3/ 1-7 odd, 17, 19, 25, 31, 41, 43, 45, 69; (Ed 5 3.2/ 105, 107, 111) or (Ed. 4 3.2/ 93, 99, 103) | ||
| 03-03-20 | 3.4 | The Chain Rule Exercises: 3.4/ 9-15 odd, 23, 25, 29, 49, 51, 55, 59, 63, 67, 79-83 odd, 115, 117 (math majors read Appendix A Thm 3.11) From Problem Sheet 2: Prob. 7: (i), (iv), (vii) | From Problem Sheet 2, feel free to hand in solutions to Prob. 1: (iii) Prob. 2: (iii), (v), (ix) Prob. 3: (i), (iii), (v) Prob. 4: (i) Prob. 5: (iii) Prob. 6: (ii), (v), (viii) | Solutions |
| 03-05-20 | Review chp. 2.2-3.4 Mock Exam 1 | |||
| 03-10-20 | Exam 1 | |||
| 03-12-20 | Classes Cancelled | |||
| 03-17-20 | Classes Cancelled | |||
| 03-19-20 | 3.5, 3.6 | Distance Learning Commences Topic: Implicit Differentiation Other Video Links: From PJMT: Implicit Differentiation, Basic Idea Extra Examples More Examples Second Derivative Example From Khan Academy: Implicit Differentiation Advanced Example | MyLab A11, A12 | |
| 03-24-20 | 3.7 | Topic: Related Rates Other Video Links: From PJMT: A Point on a Graph Involving Baseball Using Implicit Differentiation Involving Trigonometry Using Cones From Khan Academy: Introduction to Related Rates Solving Related Rates Problems | MyLab A13 | |
| 03-26-20 | 4.1 | Extrema, Global/Local, Extreme Value Theorem, Critical Points Other Video Links: From PJMT: Critical Numbers 1 Critical Numbers 2 Absolute Extrema on Closed Intervals From Khan Academy: Extreme Value Theorem Absolute (Global) Extrema | MyLab A14 | |
| 03-31-20 | Recalibration Period - No Lecture | |||
| 04-02-20 | 4.2, 4.3 | Monotony, First Derivative Test Other Video Links: From PJMT: Mean Value Theorem Local Max/min From Khan Academy: Mean Value Theorem Intervals on which a Function is Increasing or Decreasing Relative (Local) Extrema | MyLab A15 | |
| 04-07-20 | CUNY Wednesday | |||
| 04-09-20 | 4.4 | Spring Recess - No Live Meeting Concavity, Second Derivative Test Other Video Links: From PJMT: Concavity and the Second Derivative Local Maximums/Minimums - Second Derivative Test From Khan Academy: Concavity Introduction Analyzing Concavity Second Derivative Test Connecting f, f' and f'' | MyLab A16 | |
| 04-14-20 | 4.5 |
Limits at Infinity Other Video Links: From Khan Academy: Limits at Infinity |
MyLab A17 | |
| 04-16-20 | 4.6 |
Optimization Other Video Links: From PJMT: Optimization Problem 1 Optimization Problem 2 Optimization Problem 3 From Khan Academy: Solving Optimization Problems |
A18 | |
| 04-21-20 | 5.1 |
Antiderivatives,
Indeifinte Integration Other Video Links: From Khan Academy: Reverse Power Rule Indefinite Integrals of Common Functions |
A19 | |
| 04-23-20 |
Review chp. 3 and 4 |
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| 04-28-20 | Exam 2 | |||
| 04-30-20 | 5.2, 5.3 |
Area and Riemann Sums Other Video Links: From PJMT: Definite Integral – Understanding the Definition Approximating a Definite Integral Using Rectangles Riemann Sums: Calculating a Definite Integral – Part 1 Riemann Sums: Calculating a Definite Integral – Part 2 From Khan Academy: Summation Notation Riemann Approximation Introduction Riemann Sums in Summation Notation Defining Integrals with Riemann Sums |
A20 | |
| 05-05-20 | 5.4 |
The Fundamental Theorem of Calculus Other Video Links: From PJMT: Fundamental Theorem of Calculus Part 1 From Khan Academy: The Fundamental Theorem of Calculus and Accumulation Functions The Fundamental Theorem of Calculus and Definite Integrals |
A21 | |
| 05-07-20 | 5.5 |
Integration by Substitution Other Video Links: From PJMT: Integration by U-Substitution: Antiderivatives Integration by U-Substitution, Definite Integral Integration by U-Substitution - Indefinite Integral, Another 2 Examples Integration by U-substitution, More Complicated Examples From Khan Academy: Integrating with U-Substitution |
MyLab A22 | |
| 05-12-20 |
Review
Sample Final Type Problems
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| 05-14-20 |
Review for Final |
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| 05-19-20 | No Meeting | |||
| 05-21-20 | Finals |