MA1200 Calculus I
Concept Maps:
Chapter 2 Limits Chapter 3 Derivatives Chapter 4 Application of Derivatives Chapter 5 Integrals
Handouts:
Lecture Videos YouTube Playlist
Week 1
Algebra formula sheet, Trig formula sheet, Trig graph, Calculus formula sheet, Review of functions, 2.1 - 2.2 Definition of limits
1.1 Part A Part B Notes with answers
Week 2
2.3 techniques of differentiation, 2.4 vertical asymptotes, 2.5 infinite limits
2.4 Part A Part B Notes with
Week 3
2.6 Part A Part B Notes with answers
Week 4
3.1 Introduction to derivatives, 3.2 Derivative rule,
Week 5
3.3 Product rule and Quotient rule, 3.4 Trig derivatives
Week 6
3.5 Derivatives as Rate of change
3.4 Part A Part B Notes with answers
Week 7
3.6 chain rule, 3.7 implicit, differentiation, 1.3 inverse function
Week 8
3.8 derivatives of natural log and exponential function, 3.9 derivatives of inverse trig, 3.10 related rates
3.8 Part A Part B Notes with answers
3.10 Part A Part B Notes with answers
Week 9
Week 10
4.2 What derivative tells us, 4.4 optimization problems
4.2 Part A Part B Part C Notes with answers
4.4 Part A Part B Notes with answers
Week 11
4.5 Linear Approximation, 4.6 Mean Value Theorem
Week 12
4.7 L'Hospital's rule , Continuous and differential piecewise function
4.7 Part A Part B Notes with answers
Ch4 review Blank notes Notes with answers
Week 13
4.8 Anti-derivatives, 5.1, 5.2 Riemann Sum,
Week 14
5.3 Fundamental Theorem of Calculus, 5.4 working with integrals,
5.3 Part A Part B Notes with answers
Week 15
5.5 Part A Part B Notes with answers
Link to all blank notes as Word document files
Extra Credit Projects:
1. Using GeoGebra to verify derivative as slope of tangent line. Due on 3/12 pdf instructions
Please make sure you have watched the YouTube video in the instructions before you start the project. Send me the link of your project after you are done. :-) Cheers!
Example: Project 1, Project 2, Project 3, Project 4, Project 5,
Students' projects: Project by Abraham, Project by Kala, Project by Adriana, Project by Elin, Project by Zach, Project by Naiyea, Project by Charlotte, Project by Michael, Project by Luke, Project by Kieyin,
2. Using GeoGebra to approximate integral. Due on 5/1 pdf instructions
Example: Project 1, Project 2, Project 3
Students' projects: Project by Adriana, Project by Abraham, Project by Elin, Project by Zach, Project by Kala, Project by Naiyea, Project by Charlotte, Project by Michael, Project by Luke, Project by Kieyin,
Practice exams and solutions:
Derivative formula sheet blank
4. Practice final exam Solution Anti-derivative formula sheet blank Answer
More exercises on Related rate and Optimization problems. Do not need to turn in. You can review your notes and homework problems first, then try:
Application Related Rates Solution
Application Optimization Solution
True of False exercises: Some students find T or F problems very challenging, because these problems require a deeper understanding of the concepts compared with computational problems. Here are some exercises from (Briggs & Cochran, Calculus: Early Transcendentals, Pearson, 2011, ISBN: 9780321570567)
Chapter 3 Derivatives T or F Answer
Chapter 4 Application of derivatives T or F Answer
Chapter 5 Integrals T or F Answer
Extra Exercises:
Please be aware that our section numbers differ from those in Opentax. This variation is due to the switch in our textbook to Openstax. To locate the corresponding section exercises in Openstax for practice, please refer to the following mapping.
Section number in Worksheets/videos Section number in OpenStax Suggested exercises
Review of Functions 1.1Review of Functions 15, 17, 19, 21, 29, 33, 39, 41, 53, 55
1.2Basic Classes of Functions 61, 67, 71, 81, 95, 97
1.3Trigonometric Functions 113, 115, 119, 123, 127, 129, 131, 139, 143,
145, 155, 159, 163, 169, 173, 181
1.4Inverse Functions 185, 189, 193, 197, 201, 205, 207, 211, 213, 217, 223
1.5Exponential and Logarithmic Functions 243, 251, 261, 265, 273, 279, 289, 301, 307
2.1-2.2 Definition of limits 2.1A Preview of Calculus 7, 13
2.2The Limit of a Function 30, 31, 35, 41, 43, 46-64, 77, 79
2.3 Techniques of Computing Limits 2.3The Limit Laws 84, 85, 90, 95, 97, 99, 101, 102, 105, 109, 111, 115, 117, 119, 121,
123, 125
2.4 Infinite Limits
2.5 Limits at infinity 4.6Limits at Infinity and Asymptotes 253, 259, 265, 267, 270, 277, 281, 282, 283,
2.6 Continuity 2.4Continuity 125, 137, 138, 139, 141, 143, 144, 147, 148, `49, 153, 154, 157,
3.1 Introducing the derivative 3.1Defining the Derivative 3, 5, 8, 9, 15, 19, 23, 26, 41, 43, 48, 51,
3.2The Derivative as a Function 59, 61, 63, 65, 67, 69, 73, 74, 77, 78, 79, 80,
3.2 Rules of differentiations 3.3Differentiation Rules 109, 111, 113, 115, 117, 119-121, 126-129, 131-132, 139, 141, 147
3.3 The product & quotient rule
3.4 Derivatives of Trigonometric function 3.5Derivatives of Trigonometric Functions 175, 177, 181, 183, 187, 189, 191, 192, 195, 198, 203, 213
3.5 Derivatives as rates of change 3.4Derivatives as Rates of Change 151, 155, 160, 163, 165,
3.6 The Chain Rule 3.6The Chain Rule 223, 224, 227, 231, 233, 235, 236, 237, 239, 241, 245-251, 255,
256, 257,
3.7 Implicit differentiation 3.8Implicit Differentiation 303, 305, 307, 313, 317, 321, 323,
1.3 Inverse, Exp & Log functions 1.4Inverse Functions 185, 189, 193, 197, 201, 205, 207, 211, 213, 217, 223
3.8 Derivatives of Log and Exp functions 3.7Derivatives of Inverse Functions 261, 265, 268, 271, 273, 275, 277, 281, 283, 287
3.9Derivatives of Exponential and Logarithmic Functions 333, 337, 341, 343, 344, 345, 347, 349, 353, 355,
3.9 Derivatives of Inverse Trig functions
3.10 Related rates 4.1Related Rates 3, 6, 9, 10, 14, 19, 22, 25, 29, 30, 31, 37, 39
4.1 Maxima & Minima 4.3Maxima and Minima 101-103, 109, 111, 113, 114, 115, 117, 119, 121, 123, 126, 127, 131, 133, 135, 139
4.2 What derivatives tell us 4.5Derivatives and the Shape of a Graph 202, 207, 210, 215, 221, 223, 227, 233, 237, 239,
4.4 Optimization Problems 4.7Applied Optimization Problems 316, 319, 322, 326, 343, 353,
4.5 Linear Approximation and Differentials 4.2Linear Approximations and Differentials 51, 55, 59, 61, 63, 69-71, 75, 83, 85,
4.6 Mean Value Theorem 4.4The Mean Value Theorem 155, 159, 163, 167, 173, 175, 177, 186, 189,
4.7 L’hopital’s rule 4.8L’Hôpital’s Rule 163, 371, 375, 378, 381, 390, 394, 395, 399, 401, 403, 405,
4.8 Antiderivatives 4.10Antiderivatives 473, 479, 485, 487, 495, 497, 501, 505, 508, 517,
5.1 Approximating Areas under curves 5.1Approximating Areas 13, 15, 23, 25, 41, 43,
5.2 Definite integrals 5.2The Definite Integral 67, 70, 71, 75, 79, 81, 111, 115,
5.3 Fundamental Theorem of Calculus 5.3The Fundamental Theorem of Calculus 151, 155, 157, 167, 173, 185, 193, 195, 203
5.4 Working with integrals 5.4Integration Formulas and the Net Change Theorem 207, 208, 221, 227, 231, 249
5.6Integrals Involving Exponential and Logarithmic Functions 321, 323, 325, 331, 333, 335, 339, 341, 357, 365
5.7Integrals Resulting in Inverse Trigonometric Functions 395, 397, 400, 402, 407, 409, 411, 413, 419, 421, 427, 429
5.5 Substitution Rule 5.5Substitution 257, 267, 275, 279, 283, 285, 291, 295, 299, 302, 311
2020 Spring Class Recordings about some extra exercises:
Chapter 3 3/20 office hour recording Notes
3/27 office hour recording Notes
4/3 office hours recording Notes
Chapter 4 4/10 office hours recording Notes
4/17 office hours recording Notes
Chapter 5 4/24 office hours recording Notes
5/1 office hours recording Notes
Acknowledgement: The examples in the worksheets are taken from the book (Briggs & Cochran, Calculus: Early Transcendentals, Pearson, 2011, ISBN: 9780321570567) and Kiryl Tsishchanka's notes. The formula sheets are taken from Paul Dawkins' online math notes. If you find some useful online resources which may be beneficial to the whole class, please let me know. Thank you!!! :-)