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Math 201 – Calculus I

Course #: 20100
Career: Undergraduate
Category: Regular
Term Offered: Fall, Spring, Summer
Pre-requisites: C or better in Math 19500 or placement. Credit will be given for only one of Math 20100 or Math 20500.
Pre/Co-requisites: —
Hours/Credits: 4 HR/WK; 4 CR
Date Effective: Fall 2022
Course Supervisor: Cheikhna Mahawa Diagana

Catalog Description

Limits, continuity, derivatives, differentiation and its applications, differentials, definite and indefinite integrals.

Text: Stewart: Early Transcendentals (9th ed.), Clegg and Watson

Topics and Allotted Times

Periods Section Topics Suggested Problems
1 1.1 Functions and Their Graphs 1-4, 7, 9, 12, 15, 18, 24, 35, 40, 41, 43, 47-49, 66, 68, 8, 85, 86
1 1.2 A Catalog of Essential Functions 1-4, 5, 7, 9, 12
1 1.3 New Functions and Old Functions 1-3, 5, 6, 13, 17, 23, 33-35, 37, 43, 45, 55, 57, 59
1 1.4 Exponential Functions 1-3, 9, 13, 15, 17, 19, 29, 30
2 1.5 Inverse Functions and Logarithms 2-8, 10, 15, 17, 19, 20, 23, 26, 30, 35, 41, 44(b), 46, 57, 69
0.5 2.1 Tangent and Velocity Problems 2, 5, 7
2 2.2 Limit of a Function 1-9, 11, 15, 17, 19, 41, 29-31, 50*
1 2.3 Calculating Limits using Limit Laws 1, 2, 3, 7, 10, 14, 18, 19, 22, 25, 32, 34, 39-42, 44, 52, 53, 61, 62, 67
1 2.4 The Precise Definition of a Limit 1-4, 17, 18
1.5 2.5 Continuity 1, 3, 6, 7, 11, 13, 16-18, 21-24, 26, 28, 31, 37, 45, 47-50, 53, 55-58, 73
1.5 2.6 Limits Involving Infinity; Horizontal Asymptotes 1, 3, 5, 7, 10, 17, 21-23, 25, 26, 28, 29, 32, 35, 36, 38-41, 49, 57, 59, 67
2 2.7 Derivatives as Rate of Change 1, 5, 7, 8, 9(a)-(b), 12, 13, 15, 17, 22, 27, 43-48, 57, 58
2 2.8 The Derivative as a Function 1, 3, 21-32, 39, 41-44, 49, 65
1 3.1 Derivatives of Polynomial and Exponential Functions 3, 8, 11, 14, 17, 19, 25, 31, 33, 34, 37, 41, 53, 59-63, 75, 85, 86
2 3.2 Product Rules and Quotient Rules 1, 3-30, 31, 34, 35, 37, 45, 46, 49, 52, 53, 63*
1 3.3 Derivatives of Trigonometric Functions 1, 3, 6, 12, 13, 17, 22, 25, 29, 37, 41, 45, 48, 49, 52, 53, 57, 58, 61, 62
2 3.4 The Chain Rule 8, 10, 13, 14, 19, 23, 25, 27, 29, 33, 37, 41, 43, 53, 58, 68, 69, 71, 73, 84
1 3.5 Implicit Differentiation 1, 3, 5, 7, 9, 12, 16, 17, 21, 23, 25, 27, 29, 31, 33, 39, 43, 49, 50*, 63, 64
2.5 3.6 Derivatives of Inverse Functions and Logarithms 3, 5, 9, 11, 13, 17, 21, 27, 29, 35, 38, 39, 45, 47, 49, 56, 58*, 59, 63, 65, 75
— A46 Derivatives of Inverse Functions and Logarithms (Appendix F) p. 225: 83-86
1 3.7 Rate of Change in Natural and Social Sciences 1, 5, 6, 7, 8, 9, 11, 35*
1.5 3.9 Related Rates 1-7, 9, 12, 15, 17, 25
1 3.10 Linearization and Differentials 1-5, 11, 13, 17, 19, 21, 27, 29, 31-36, 41, 42, 51, 52
1 4.1 Maximum and Minimum Values 1, 2, 3, 5, 7, 11, 17, 19, 27, 31, 35, 42-44, 51, 53, 55, 59, 66*
1 4.2 The Mean Value Theorem 1, 5, 6, 9, 11, 15, 17, 23, 29, 30, 39
1 4.3 What Derivatives Tell Us About Graph’s Shape 1, 7-9, 11, 12, 17, 23, 26, 27, 30, 31, 35, 37, 39, 41, 43, 44, 46, 54, 60, 63, 84
2 4.4 Indeterminate Forms and L’Hôpital’s Rule 1-4, 5, 7, 9, 11, 13, 15, 18, 19, 21, 23, 25, 27, 33, 34, 37, 41, 47, 51, 53, 56, 75*
2 4.5 Summary of Curve Sketching 1-8, 11, 13, 15, 21, 23, 25, 27, 29, 31, 34, 37, 45, 51, 52, 55, 67, 71, 76*
1 4.7 Optimization Problems 1, 3, 4, 7, 8, 11, 14, 18-21, 25, 26, 41, 81
1.5 4.9 Antiderivatives 1, 3, 4, 7, 9, 11, 15, 19, 23, 27-29, 35, 40, 45, 51, 54-56, 61, 65, 67, 70, 83
1 5.1 Area and Distance Problems 1-3, 7-9, 13, 15-23, 25*
1 A36 Sigma Notation / Limit of Finite Sums (Appendix E) 1-10, 12, 14, 17, 19, 20, 22, 24, 27, 28, 34, 36, 41, 43, 45, 48-50
1 5.2 The Definite Integral* 1-8, 11, 14, 19, 21, 23, 25, 27-34, 36, 39, 41, 43, 46, 52, 57, 59, 61, 62, 67
1.5 5.3 The Fundamental Theorem of Calculus 3-6, 9, 13, 15, 20, 25, 31, 33, 35, 37, 421, 42, 49, 51, 53, 63, 67, 71, 73, 75, 77
1 5.4 Indefinite Integrals and the Net Change Theorem 1, 3, 7, 9, 17, 24, 31, 38, 44, 46, 53, 59, 61, 69
2.5 5.5 The Substitution Rule 1-8, 14, 16, 21-27, 29, 32, 35, 37, 39, 45, 51, 59, 65, 70, 75, 77, 84, 93, 98*
1 6.1 Areas Between Curves 1-7, 9, 11, 13, 17, 19, 21, 24, 30, 35, 37, 41, 42, 44, 61, 64, 65, 69*

Total Periods: 49

Course Learning Outcomes

After taking this course, the student should be able to:

  1. Evaluate limits, including the use of L’Hôpital’s Rule. (a, b, e1, e2)
  2. Differentiate algebraic and transcendental functions. (a, b, e1, e2)
  3. Solve maximum and minimum problems. (a, b, c, e1, e2)
  4. Apply methods of calculus to sketch curves. (a, b)
  5. Anti-differentiate algebraic and transcendental functions. (a, b, c, e1, e2)
  6. Approximate integrals by Riemann sums. (e1, e2, g)
  7. Evaluate elementary integrals using substitution. (a)

Course Assessment Tools

  1. Term Average: Based mostly on in-class examinations (60% of grade)
  2. Final Exam: Comprehensive written exam (40% of grade)

Departmental Learning Outcomes

The mathematics department, in its varied courses, aims to teach students to:

  • a. Perform numeric and symbolic computations
  • b. Construct and apply symbolic and graphical representations of functions
  • c. Model real-life problems mathematically
  • d. Use technology appropriately to analyze mathematical problems
  • e. State (e1) and apply (e2) mathematical definitions and theorems
  • f. Prove fundamental theorems
  • g. Construct and present (generally in writing, but occasionally orally) a rigorous mathematical argument