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MATH 161: Single Variable Calculus I

Summer 2023 Syllabus

May 29 – June 23, 2023

Course Catalog Description

This course will provide an introduction to the topics and techniques of single-variable calculus. Differential calculus topics will include limits and derivatives of algebraic and transcendental functions as well as applications of the derivative. Integral calculus topics will include antiderivatives, area and the Fundamental Theorem of Calculus. (CMAR)

Textbook

Calculus – Early Transcendentals (With WebAssign), 8th edition, by James Stewart. Students must purchase access to WebAssign, but a hard copy of the text is optional. Access to WebAssign includes access to an electronic version of the textbook.

Topic Calendar

No. Sections Covered                                                              Week

1     Chapter 1 Functions and Models Review                                 Week 1

2     2.1 The Tangent and Velocity Problems                                   Week 1

3     2.2 The Limit of a Function                                                    Week 1

4     2.3 Calculating Limits Using the Limit Laws                              Week 1

5     2.4 The Precise Definition of a Limit                                       Week 1

6     2.5 Continuity                                                                      Week 1

7     2.6 Limits at Infinity, Horizontal Asymptotes                             Week 1

8     2.7 Derivatives and Rates of Change                                        Week 1

9     2.8 The Derivative as a Function                                             Week 1

10     3.1 Derivatives of Polynomials and Exponential Functions         Week 2

11     3.2 The Product and Quotient Rules                                      Week 2

12     3.3 Derivatives of Trigonometric Functions                              Week 2

13     3.4 The Chain Rule                                                               Week 2

14     3.5 Implicit Differentiation                                                     Week 2

15     3.6 Derivatives of Logarithmic Functions                                  Week 2

16     3.7 Rates of Change in the Natural and Social Sciences              Week 2

17     3.8 Exponential Growth and Decay                                          Week 2

18     3.9 Related Rates                                                                  Week 2

19     3.10 Linear Approximation and Differentials                             Week 2

20     4.1 Maximum and Minimum Values                                         Week 3

21     4.2 The Mean Value Theorem                                                  Week 3

22     4.3 How Derivatives Affect the Shape of a Graph                       Week 3

23     4.4 Indeterminate Forms and L’Hopital’s Rule                            Week 3

24     4.5 Summary of Curve Sketching                                             Week 3

25     4.6 Optimization Problems                                                      Week 3

26     4.8 The Newton Method                                                         Week 3

27     4.9 Antiderivatives                                                                Week 3

28     5.1 Areas and Distances                                                        Week 4

29     5.2 The Definite Integral                                                       Week 4

30     5.3 The Fundamental Theorem of Calculus                             Week 4

31     5,4 Indefinite Integrals and the Net Change Theorem               Week 4

32     5.5 The Substitution Rule                                                      Week 4

Course Outcomes

By the end of this course, you will be expected to:

• Calculate limits, derivatives, and indefinite integrals of a single variable

• Apply the definition of the derivative to differentiate functions of a single variable

• Understand derivatives of power, exponential, logarithmic, trigonometric functions

• Utilize the chain rule to find derivatives of composite functions

• Find maxima and minima, critical points and inflection points of functions

• Be able to sketch graphs, find asymptotes, and find tangents

• Understand the Fundamental Theorem of Calculus and the techniques of integration

Homework

Homework problems are online, we will use the online resource WebAssign for weekly homework assignments and tutorial videos. Make sure to access WebAssign from the BlackBoard. Please refer to WebAssign Instruction on the blackboard for more details. Written homework may also be collected. NO LATE HOMEWORK WILL BE ACCEPTED.

Blackboard

Grades and additional course content will be uploaded to Blackboard. Make sure to check it regularly for updates.

Attendance

Attendance for the course will be the Watch It/Lecture videos with questions on WebAssign. For each section, videos with questions are available on WebAssign. Please complete the Watch It/Lecture to receive the full attendance credits.

Midterm and Final Exams

You will take 1 midterm exam given online, time will be limited to class time. Each will involve a mix of mechanical skills and conceptual reasoning. The best possible preparation for them is regular attendance and completion of assigned homework. Make-up exams are only given in case of documented emergencies.

Grading

Your final course grade will be determined by

Homework: 30%

Attendance: 10%

Midterms: 30%

Final Exam: 30%

Grading Scale:

Letter grades will be assigned as follows:

A 93-100           C 73-76

A- 90-92           C- 70-72

B+ 87-89          D+ 67-69

B 83-86            D 63-66

B- 80-82           D- 60-62

C+ 77-79          F below 60